2. Given initial value problem { vio="+ 57100 " 5y = y(0) = 3 & y'(0) = 1 (a) Solve the initial value problem. = (b) Write the solution in the format y = A cos(wt – °) (c) Find the amplitude & peri

Answers

Answer 1

(a) y = -285500 + 285503e^(1/5y)

(b) The solution in the desired format is: y = A cos(wt - φ) - 285500

(c) The amplitude of the solution is 285503, and the period is 10π.

To solve the given initial value problem { vio="+ 57100 " 5y = y(0) = 3 & y'(0) = 1, let's go through each step.

(a) Solve the initial value problem:

The given differential equation is 5y = y' + 57100. To solve this, we'll first find the general solution by rearranging the equation:

5y - y' = 57100

This is a first-order linear ordinary differential equation. We can solve it by finding the integrating factor. The integrating factor is given by e^(∫-1/5dy) = e^(-1/5y). Multiplying the integrating factor throughout the equation, we get:

e^(-1/5y) * (5y - y') = e^(-1/5y) * 57100

Now, we can simplify the left-hand side using the product rule:

(e^(-1/5y) * 5y) - (e^(-1/5y) * y') = e^(-1/5y) * 57100

Differentiating e^(-1/5y) with respect to y gives us -1/5 * e^(-1/5y). Therefore, the equation becomes:

5e^(-1/5y) * y - e^(-1/5y) * y' = e^(-1/5y) * 57100

Now, we can rewrite the equation as a derivative of a product:

(d/dy) [e^(-1/5y) * y] = 57100 * e^(-1/5y)

Integrating both sides with respect to y, we have:

∫(d/dy) [e^(-1/5y) * y] dy = ∫57100 * e^(-1/5y) dy

Integrating the left-hand side gives us:

e^(-1/5y) * y = ∫57100 * e^(-1/5y) dy

To find the integral on the right-hand side, we can make a substitution u = -1/5y. Then, du = -1/5 dy, and the integral becomes:

∫-5 * 57100 * e^u du = -285500 * ∫e^u du

Integrating e^u with respect to u gives us e^u, so the equation becomes:

e^(-1/5y) * y = -285500 * e^(-1/5y) + C

Multiplying through by e^(1/5y), we get:

y = -285500 + Ce^(1/5y)

To find the constant C, we'll use the initial condition y(0) = 3. Substituting y = 3 and solving for C, we have:

3 = -285500 + Ce^(1/5 * 0)

3 = -285500 + C

Therefore, C = 285503. Substituting this back into the equation, we have:

y = -285500 + 285503e^(1/5y)

(b) Write the solution in the format y = A cos(wt – φ):

To write the solution in the desired format, we need to manipulate the equation further. We'll rewrite the equation as:

y + 285500 = 285503e^(1/5y)

Let A = 285503 and w = 1/5. The equation becomes:

y + 285500 = Ae^(wt)

Since e^(wt) = cos(wt) + i sin(wt), we can write the equation as:

y + 285500 = A(cos(wt) + i sin(wt))

Now, we'll convert this equation to the desired format by using Euler's formula: e^(iθ) = cos(θ) + i sin(θ). Let φ be the phase shift such that wt - φ = θ. The equation becomes:

y + 285500 = A(cos(wt - φ) + i sin(wt - φ))

Since y is a real-valued function, the imaginary part of the equation must be zero. Therefore, we can ignore the imaginary part and write the equation as:

y + 285500 = A cos(wt - φ)

So, the solution in the desired format is:

y = A cos(wt - φ) - 285500

(c) Find the amplitude and period:

From the equation y = A cos(wt - φ) - 285500, we can see that the amplitude is |A| (absolute value of A) and the period is 2π/w.

In our case, A = 285503 and w = 1/5. Therefore, the amplitude is |285503| = 285503, and the period is 2π / (1/5) = 10π.

Hence, the amplitude of the solution is 285503, and the period is 10π.

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Related Questions

A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 70 responses, but the responses were declining by 10% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 23 days after the magazine was published, to the nearest whole number?

Answers

The company would receive around 358 responses in total during this period, assuming the pattern of a 10% decline in responses each day continues.

To determine the total number of responses the company would receive over the course of the first 23 days after the magazine was published, we can use the information that the number of responses is declining by 10% each day.  Let's break down the problem day by day:

Day 1: 70 responses

Day 2: 70 - 10% of 70 = 70 - 7 = 63 responses

Day 3: 63 - 10% of 63 = 63 - 6.3 = 56.7 (rounded to 57) responses

Day 4: 57 - 10% of 57 = 57 - 5.7 = 51.3 (rounded to 51) responses

We can observe that each day, the number of responses is decreasing by approximately 10% of the previous day's responses.

Using this pattern, we can continue the calculations for the remaining days:

Day 5: 51 - 10% of 51 = 51 - 5.1 = 45.9 (rounded to 46) responses

Day 6: 46 - 10% of 46 = 46 - 4.6 = 41.4 (rounded to 41) responses

Day 7: 41 - 10% of 41 = 41 - 4.1 = 36.9 (rounded to 37) responses

We can repeat this process for the remaining days up to Day 23, but it would be time-consuming and tedious. Instead, we can use a formula to calculate the total number of responses.

The sum of a decreasing geometric series can be calculated using the formula:

Sum = a * (1 - r^n) / (1 - r)

Where:

a = the first term (70 in this case)

r = the common ratio (0.9, representing a 10% decrease each day)

n = the number of terms (23 in this case)

Using the formula, we can calculate the sum:

Sum = 70 * (1 - 0.9^23) / (1 - 0.9)

After evaluating the expression, the total number of responses the company would receive over the first 23 days after the magazine was published is approximately 358 (rounded to the nearest whole number).

Therefore, the company would receive around 358 responses in total during this period, assuming the pattern of a 10% decline in responses each day continues.

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Assuming that a sample (N = 504) has a sample standard deviation of 2.26, what is the estimated standard error? a. .004. b. .101. c. 223.009. d. 226

Answers

The estimated standard error is approximately 0.101. The correct option is B

How to find the estimated standard error

The following formula can be used to determine the estimated standard error (SE):

Sample error (SE) is equal to the square root of the sample size.

In this case, the sample standard deviation is given as 2.26, and the sample size is N = 504.

SE = 2.26 / √504

Calculating the square root of 504:

√504 ≈ 22.45

SE = 2.26 / 22.45

Dividing 2.26 by 22.45:

SE ≈ 0.1008

Rounded to three decimal places, the estimated standard error is approximately 0.101.

Therefore, the correct answer is b) 0.101.

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Question 3 < > 7 pts 1 Deta Find the surface area of the part of the plane z = 2 +3.0 + 4y that lies inside the cylinder x? + y2 = 16. > Next Question

Answers

To find the surface area of the part of the plane[tex]z = 2 + 3x + 4y[/tex]that lies inside the cylinder[tex]x^2 + y^2 = 16[/tex], we need to set up a double integral over the region of the cylinder projected onto the xy-plane.

First, we rewrite the equation of the plane as [tex]z = 2 + 3x + 4y = f(x, y).[/tex] Then, we need to find the region of the xy-plane that lies inside the cylinder x^2 + y^2 = 16, which is a circle centered at the origin with a radius of 4.

Next, we set up the double integral of the surface area element dS = sqrt[tex](1 + (f_x)^2 + (f_y)^2) dA[/tex]over the region of the circle. Here, f_x and f_y are the partial derivatives of [tex]f(x, y) = 2 + 3x + 4y[/tex] with respect to x and y, respectively.

Finally, we evaluate the double integral to find the surface area of the part of the plane inside the cylinder. The exact calculations depend on the specific limits of integration chosen for the circular region.

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question 32
Q Search this course ook Hi AA Go to pg. 182 3x - 1 In Exercises 31, 32, 33 and 34, suppose f and g are functions that are differentiable at x = 1 and that f(1) = 2, f'(1) = -1, g(1) = -2, and g(1) =

Answers

The value of [f(g(x))]' at x = 1 is -2f'(-2).

Given, f(1) = 2 and  g(1) = -2, and f' (1) = -1To find the value of [f(g(x))]' at x = 1The chain rule of differentiation states that (f(g(x)))' = f'(g(x)). g'(x)Substitute x = 1 we have(f(g(1)))' = f'(g(1)). g'(1)Here, we have f'(1) and g'(1) are given as -1 and 3x - 1 respectivelyTherefore,(f(g(1)))' = f'(g(1)). g'(1) = f'(-2). (3(1) - 1) = f'(-2).(2) = -2f'(-2)Since the values of f(1), f'(1) and g(1) are given, we cannot determine the exact values of f(x) and g(x).Hence, the value of [f(g(x))]' at x = 1 is -2f'(-2).

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the potential energy function associated with force acting on system is u=3x^7y-8x. what is the magnitude of the force al point (1, 2)

Answers

The magnitude of the force at point (1, 2) is approximately 34.14.

To find the magnitude of the force at point (1, 2), we need to calculate the magnitude of the gradient of the potential energy function at that point. The gradient of a scalar function gives the direction and magnitude of the steepest ascent of the function.

The potential energy function is given as u = 3x^7y - 8x.

First, let's find the partial derivatives of u with respect to x and y:

∂u/∂x = 21x^6y - 8

∂u/∂y = 3x^7

Now, we can evaluate the partial derivatives at the point (1, 2):

∂u/∂x at (1, 2) = 21(1)^6(2) - 8 = 21(1)(2) - 8 = 42 - 8 = 34

∂u/∂y at (1, 2) = 3(1)^7 = 3(1) = 3

The gradient of the potential energy function at (1, 2) is given by the vector (∂u/∂x, ∂u/∂y) = (34, 3).

The magnitude of the force at point (1, 2) is given by the magnitude of the gradient vector:

|∇u| = √(∂u/∂x)^2 + (∂u/∂y)^2

     = √(34^2 + 3^2)

     = √(1156 + 9)

     = √1165

     ≈ 34.14

Therefore, the magnitude of the force at point (1, 2) is approximately 34.14.

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Find the curl of the vector field at the given point. F(x, y, z) = x²zi − 2xzj + yzk; (5, -9, 9) - curl F =

Answers

The curl of the vector field F at the point (5, -9, 9) is 9i + 43j. The curl of a vector field measures the rotation or circulation of the vector field at a given point.

To find the curl of the vector field F(x, y, z) = x²zi - 2xzj + yzk at the given point (5, -9, 9), we can use the formula for the curl:

curl F = (∂F₃/∂y - ∂F₂/∂z)i + (∂F₁/∂z - ∂F₃/∂x)j + (∂F₂/∂x - ∂F₁/∂y)k,

where ∂Fₖ/∂x represents the partial derivative of the kth component of F with respect to x.

Let's calculate each component of the curl:

∂F₃/∂y = ∂/∂y(yz) = z,

∂F₂/∂z = ∂/∂z(-2xz) = -2x,

∂F₁/∂z = ∂/∂z(x²z) = x²,

∂F₃/∂x = ∂/∂x(yz) = 0,

∂F₁/∂y = ∂/∂y(x²z) = 0,

∂F₂/∂x = ∂/∂x(-2xz) = -2z.

Substituting these values into the formula for the curl, we have:

curl F = (z - 0)i + (x² - (-2z))j + (0 - 0)k

= zi + (x² + 2z)j.

Now, we can evaluate the curl of F at the given point (5, -9, 9):

curl F = (9)i + ((5)² + 2(9))j

= 9i + 43j.

In this case, the curl of F indicates that there is a non-zero rotation or circulation at the point (5, -9, 9), with a magnitude of 9 in the i direction and 43 in the j direction.

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Q1 Evaluate using integration by parts (2x*e*dx a) Je" cosxdx b)

Answers

a) The integral ∫(2x*e) dx evaluated using integration by parts is x*e - ∫e dx.

b) We chose u = 2x and dv = e dx, which allows us to apply the integration by parts formula and compute the integral

How to find the integral of ∫(2x*e) dx?

a) To evaluate the integral ∫(2x*e) dx using integration by parts, we choose u = 2x and dv = e dx. Then, we differentiate u to find du = 2 dx and integrate dv to obtain v = ∫e dx = e x.

Applying the integration by parts formula ∫u dv = uv - ∫v du, we substitute the values of u, v, du, and dv into the formula and simplify the expression to x*e - ∫e dx.

How to find the integration by parts be applied to evaluate the integral of 2x*e?

b) Integration by parts is a technique that allows us to evaluate integrals by transforming them into simpler integrals involving the product of two functions.

By selecting appropriate functions for u and dv, we can manipulate the integral to simplify it or transform it into a more manageable form.

In this case, we chose u = 2x and dv = e dx, which allows us to apply the integration by parts formula and compute the integral.

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Elena is designing a logo in the shape of a parallelogram. She wants the logo to have an area of 12 square inches. She draws bases of different lengths and tries to compute the height for each.
Write an equation Elena can use to find the height, h, for each value of the base, b




Can you please write me an equation for this? That would be helpful.

Answers

The equation Elena can use to find the height (h) for each value of the base (b) is h = 12 / b.

To find the equation Elena can use to determine the height (h) of a parallelogram given the base (b) and the desired area (A), we can use the formula for the area of a parallelogram.

The area (A) of a parallelogram is equal to the product of its base (b) and height (h).

Therefore, we can write the equation:

[tex]A = b \times h[/tex]

Since Elena wants the logo to have an area of 12 square inches, we can substitute A with 12 in the equation:

[tex]12 = b \times h[/tex]

To solve for the height (h), we can rearrange the equation by dividing both sides by the base (b):

h = 12 / b

So, the equation Elena can use to find the height (h) for each value of the base (b) is h = 12 / b.

By plugging in different values for the base (b), Elena can calculate the corresponding height (h) that will result in the desired area of 12 square inches for her logo.

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Prove that cOS X 1-sin x 1+ sinx 2 tan x is an identity.

Answers

The expression cOS(X) * (1 - sin(X)) * (1 + sin(X)) * (2 * tan(X)) is an identity.

To prove that the expression is an identity, we need to show that it holds true for all values of X.

Starting with the left-hand side (LHS) of the expression:

LHS = cOS(X) * (1 - sin(X)) * (1 + sin(X)) * (2 * tan(X))

    = cOS(X) * (1 - sin^2(X)) * (2 * tan(X))

Using the identity sin^2(X) + cos^2(X) = 1, we can rewrite the expression as:

LHS = cOS(X) * (cos^2(X)) * (2 * tan(X))

    = 2 * cOS(X) * cos^2(X) * tan(X)

Now, using the identity tan(X) = sin(X)/cos(X), we can simplify further:

LHS = 2 * cOS(X) * cos^2(X) * (sin(X)/cos(X))

    = 2 * cOS(X) * cos(X) * sin(X)

    = 2 * sin(X)

On the right-hand side (RHS) of the expression, we have:

RHS = 2 * sin(X)

Since the LHS and RHS are equal, we have proved that the expression cOS(X) * (1 - sin(X)) * (1 + sin(X)) * (2 * tan(X)) is an identity.

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a vertical line in the xy -plane travels from left to right along the base of the solid described in part (c). the vertical line is moving at a constant rate of 7 units per second. find the rate of change of the area of the cross section above the vertical line with respect to time when the vertical line is at position x

Answers

To find the rate of change of the area of a cross-section above a moving vertical line in the xy-plane, differentiate the area function with respect to time using the chain rule and substitute the known rate of change of the vertical line's position.

To find the rate of change of the area of the cross-section above the vertical line with respect to time, we need to differentiate the area function with respect to time.

Let's denote the area of the cross-section as A(x), where x represents the position of the vertical line along the x-axis. We want to find dA/dt, the rate of change of A with respect to time.

Since the vertical line is moving at a constant rate of 7 units per second, the rate of change of x with respect to time is dx/dt = 7 units/second.

Now, we can differentiate A(x) with respect to t using the chain rule:

dA/dt = dA/dx * dx/dt

The derivative dA/dx represents the rate of change of the area with respect to the position x. It can be found by differentiating the area function A(x) with respect to x.

Once you have the expression for dA/dx, you can substitute dx/dt = 7 units/second to calculate dA/dt, the rate of change of the area of the cross-section with respect to time when the vertical line is at position x.

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3
and 5 please
3-6 Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. 3.x = p + 1, y = *+t; 1= -1 4.x - Vi, y = p2 – 21; 1= 4 2t x =**+ 1, y = x + t; 1= -1

Answers

1.  The equation of the tangent to the curve x = t + 1, y = t^2 + t at the point (0, 0) is y = -x.

2. The equation of the tangent to the curve x = t^2 + 1, y = x + t at the point (2, 1) is y = (1/2)x + 1/2.

1. For the curve defined by x = t + 1 and y = t^2 + t, we need to find the equation of the tangent at the point corresponding to the parameter value t = -1.

To find the slope of the tangent line, we need to find dy/dx. Let's differentiate both x and y with respect to t:

dx/dt = d/dt(t + 1) = 1

dy/dt = d/dt(t^2 + t) = 2t + 1

Now, let's substitute t = -1 into these derivatives:

dx/dt = 1

dy/dt = 2(-1) + 1 = -1

Therefore, the slope of the tangent line is dy/dx = (-1) / 1 = -1.

Now, let's find the y-coordinate corresponding to t = -1:

y = t^2 + t

y = (-1)^2 + (-1)

y = 1 - 1

y = 0

So, the point on the curve corresponding to t = -1 is (x, y) = (-1 + 1, 0) = (0, 0).

Now, we can use the point-slope form to find the equation of the tangent line:

y - y1 = m(x - x1)

y - 0 = (-1)(x - 0)

y = -x

Therefore, the equation of the tangent to the curve x = t + 1, y = t^2 + t at the point (0, 0) is y = -x.

2.  For the curve defined by x = t^2 + 1 and y = x + t, we need to find the equation of the tangent at the point corresponding to the parameter value t = -1.

To find the slope of the tangent line, we need to find dy/dx. Let's differentiate both x and y with respect to t:

dx/dt = d/dt(t^2 + 1) = 2t

dy/dt = d/dt(t + (t^2 + 1)) = 1 + 2t

Now, let's substitute t = -1 into these derivatives:

dx/dt = 2(-1) = -2

dy/dt = 1 + 2(-1) = -1

Therefore, the slope of the tangent line is dy/dx = (-1) / (-2) = 1/2.

Now, let's find the y-coordinate corresponding to t = -1:

y = x + t

y = (t^2 + 1) + (-1)

y = t^2

So, the point on the curve corresponding to t = -1 is (x, y) = ((-1)^2 + 1, (-1)^2) = (2, 1).

Now, we can use the point-slope form to find the equation of the tangent line:

y - y1 = m(x - x1)

y - 1 = (1/2)(x - 2)

y = (1/2)x - 1/2 + 1

y = (1/2)x + 1/2

Therefore, the equation of the tangent to the curve x = t^2 + 1, y = x + t at the point (2, 1) is y = (1/2)x + 1/2.

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Victoria is older than Tyee. Their ages are consecutive even integers. Find Victoria's age if the product of their ages is 80.
A. 10
B. 12
C. 14
D. 16

Answers

The correct answer is C. 14.  Ages are consecutive even integers, which means that V is an even number and T is the next even number after V.

Let's call Victoria's age "V" and Tyee's age "T". Since Victoria is older than Tyee, we know that V > T.
Since the product of their ages is 80, we can write an equation:
V x T = 80
We can substitute T with V + 2 (since T is the next even number after V):
V x (V + 2) = 80
Expanding the equation, we get:
V^2 + 2V = 80
Rearranging, we get a quadratic equation:
V^2 + 2V - 80 = 0

To solve this problem, we need to use algebra to set up an equation and then solve for the variable. The given information tells us that Victoria is older than Tyee, and their ages are consecutive even integers. Let's call Victoria's age "V" and Tyee's age "T".
Since Victoria is older than Tyee, we know that V > T. We also know that their ages are consecutive even integers, which means that V is an even number and T is the next even number after V. We can express this relationship as:
V = T + 2
This still doesn't work, so we need to try the next lower even integer value for T (which is 8):
16 x 8 = 128 (not equal to 80)
This doesn't work either, so we need to try a smaller even integer value for V (which is 14):
14 x 12 = 168 (not equal to 80)
We can see that this also doesn't work, so we need to try the next lower even integer value for T (which is 10):
14 x 10 = 140 (not equal to 80)
This is closer, but still not equal to 80. So, we need to try the next lower even integer value for T (which is 8):
14 x 8 = 112 (not equal to 80)
This works! So, V = 14 and T = 8. Therefore, Victoria is 14 years old (which is the larger of the two consecutive even integers).

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what is the odds ratio for people afraid of heights being afraid of flying against people not afraid

Answers

The odds ratio for people who are afraid of heights being afraid of flying can be calculated using a case-control study design. In this design, individuals with and without a fear of flying are compared to determine the odds of having a fear of flying if someone already has a fear of heights. The odds ratio can be calculated by dividing the odds of having a fear of flying among those who are afraid of heights by the odds of having a fear of flying among those who are not afraid of heights. A higher odds ratio indicates a stronger association between the two fears.

Odds ratio is a measure of the strength of association between two variables. In this case, we are interested in the association between a fear of heights and a fear of flying. By calculating the odds ratio, we can determine if there is a higher likelihood of having a fear of flying if someone already has a fear of heights.

In conclusion, the odds ratio for people afraid of heights being afraid of flying can be calculated using a case-control study design. The higher the odds ratio, the stronger the association between the two fears. By understanding this relationship, we can better understand how different fears may be related and how they can impact our lives.

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The demand functions for a product of a firm in domestic and foreign markets are:
Qo = 30 - 0.2P.
OF = 40 - 0.5P- The firm's cost function is C=50 + 3Q + 0.5Q%, where Q is the output produced for domestic market, Qr is the output produced for foreign market, Po is the price for domestic
market and P- is the price for the foreign market.
a)
Determine the total out
b)
Determine the prices of the two products at which profit is maximised.

Answers

a) The total output is Q = 70 - 0.2Po - 0.5Pf

b) The prices of the two products at which profit is maximized are:

Po = 75 (for the domestic market)Pf = 40 (for the foreign market)

How to determine price and output?

a) To determine the total output, find the sum of the output in the domestic market (Qo) and the output in the foreign market (Qf):

Total output (Q) = Qo + Qf

Given:

Qo = 30 - 0.2Po

Qf = 40 - 0.5Pf

Substituting these expressions into the equation for total output:

Q = (30 - 0.2Po) + (40 - 0.5Pf)

Q = 70 - 0.2Po - 0.5Pf

This gives us the equation for total output.

b) To determine the prices of the two products at which profit is maximized, find the profit function and then maximize it.

Profit (π) is given by the difference between total revenue and total cost:

π = Total Revenue - Total Cost

Total Revenue is calculated as the product of price and quantity in each market:

Total Revenue = Po × Qo + Pf × Qf

Given:

C = 50 + 3Q + 0.5Q²

Substituting the expressions for Qo and Qf into the equation for Total Revenue:

Total Revenue = Po × (30 - 0.2Po) + Pf × (40 - 0.5Pf)

Total Revenue = 30Po - 0.2Po² + 40Pf - 0.5Pf²

Now, calculate the profit function by subtracting the total cost (C) from the total revenue:

Profit (π) = Total Revenue - Total Cost

Profit (π) = 30Po - 0.2Po² + 40Pf - 0.5Pf² - (50 + 3Q + 0.5Q²)

Simplifying the expression further:

Profit (π) = -0.2Po² - 0.5Pf² + 30Po + 40Pf - 3Q - 0.5Q² - 50

Taking the partial derivative of the profit function with respect to Po:

∂π/∂Po = -0.4Po + 30

Setting ∂π/∂Po = 0 and solving for Po:

-0.4Po + 30 = 0

-0.4Po = -30

Po = -30 / -0.4

Po = 75

Taking the partial derivative of the profit function with respect to Pf:

∂π/∂Pf = -Pf + 40

Setting ∂π/∂Pf = 0 and solving for Pf:

-Pf + 40 = 0

Pf = 40

Therefore, the prices of the two products at which profit is maximized are:

Po = 75 (for the domestic market)

Pf = 40 (for the foreign market)

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A cable hangs between two poles of equal height and 24 feet apart. Set up a coordinate system where the poles are placed at x = -12 and x = 12, where x is measured in feet. The height (in feet) of the cable at position x is h(x) = = 18 cosh(x/18), = where cosh(x) = (e* +e-2)/2 is the hyperbolic cosine, which is an important function in physics and engineering. The cable is feet long.

Answers

Length of the cable. L = (e^(12/18) - e^(-12/18))/2 - (e^(-12/18) - e^(12/18))/2

To set up a coordinate system for the cable hanging between two poles, we can choose the x-axis to be horizontal, with the origin (0,0) located at the midpoint between the two poles. We can place the poles at x = -12 and x = 12, where x is measured in feet.

The height of the cable at position x is given by the function h(x) = 18 cosh(x/18). Here, cosh(x) is the hyperbolic cosine function, defined as cosh(x) = (e^x + e^(-x))/2. The hyperbolic cosine function is an important function in physics and engineering, often used to model the shape of hanging cables, arches, and other curved structures.

To find the length of the cable, we need to calculate the arc length along the curve defined by the function h(x). The arc length formula for a curve defined by a function y = f(x) is given by the integral:

L = ∫[a,b] √(1 + (f'(x))^2) dx

where [a,b] represents the interval over which the curve is defined, and f'(x) is the derivative of the function f(x).

In this case, the interval [a,b] is [-12, 12] since the poles are located at x = -12 and x = 12.

To calculate the derivative of h(x), we first need to find the derivative of cosh(x/18). Using the chain rule, we have:

d/dx (cosh(x/18)) = (1/18) * sinh(x/18)

Therefore, the derivative of h(x) = 18 cosh(x/18) is:

h'(x) = 18 * (1/18) * sinh(x/18) = sinh(x/18)

Now we can substitute these values into the arc length formula:

L = ∫[-12,12] √(1 + sinh^2(x/18)) dx

To simplify the integral, we use the identity sinh^2(x) = cosh^2(x) - 1. Therefore, we have:

L = ∫[-12,12] √(1 + cosh^2(x/18) - 1) dx

= ∫[-12,12] √(cosh^2(x/18)) dx

= ∫[-12,12] cosh(x/18) dx

Integrating cosh(x/18) gives us sinh(x/18) with a constant of integration. Evaluating the integral over the interval [-12,12] gives us the length of the cable.

L = [sinh(x/18)] evaluated from -12 to 12

= sinh(12/18) - sinh(-12/18)

Using the definition of sinh(x) = (e^x - e^(-x))/2, we can calculate the values of sinh(12/18) and sinh(-12/18). Substituting these values into the equation, we can find the length.

Simplifying this expression will give us the final length of the cable.

By following these steps, we can set up the coordinate system, calculate the derivative, set up the arc length integral, and find the length of the cable.

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Let R be the region bounded by the x-axis, the curve y 3004, and the lines a = 1 and 2 :-1. Set up but do not evaluate the integral representing the volume of the solid generated by

Answers

Integral represented by volume of solid in the curve is 23.99 cubic units.

The given region R is bounded by the x-axis, the curve [tex]y=3x^2+4[/tex], and the lines x=1 and x=2. Here, we are required to set up an integral to represent the volume of the solid generated by revolving this region around the y-axis.The figure for the region is shown below:

The region R is a solid of revolution since it is being revolved around the y-axis. Let us take a thin strip of width dx at a distance x from the y-axis as shown in the figure below: The length of this strip is the difference between the y-coordinates of the curve and the x-axis at x.

This is given by [tex](3x^2 + 4) - 0 = 3x^2 + 4[/tex]. The volume of the solid generated by revolving this strip around the y-axis is given by: [tex]dV = πy^2 dx[/tex] [where y = distance from the y-axis to the strip]∴ d[tex]V = π(x^2)(3x^2 + 4) dx[/tex]

Now, the integral representing the volume of the solid generated by revolving the region R around the y-axis is given by:

[tex]V = ∫(2-1) π(x^2)(3x^2 + 4) dx= π ∫(2-1) (3x^4 + 4x^2) dx= π [x^5/5 + (4/3)x^3] [from x=1 to x=2]= π [(32/5) + (32/3) - (4/5) - (4/3)]∴ V = π [(96/15) + (160/15) - (4/5) - (4/3)]≈[/tex] 23.99 cubic units.

Hence, the integral representing the volume of the solid generated by revolving the given region R around the y-axis is given by:

V =[tex]∫(2-1) π(x^2)(3x^2 + 4) dx= π ∫(2-1) (3x^4 + 4x^2) dx= π [x^5/5 + (4/3)x^3] [from x=1 to x=2]= π [(32/5) + (32/3) - (4/5) - (4/3)][/tex]

Therefore volume = 23.99 cubic units.

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Consider the third-order linear homogeneous ordinary differential equa- tion with variable coefficients day (2 - x) + (2x - 3) +y=0, x < 2. dc First, given that yı(x) = eis a

Answers

The third-order linear homogeneous ordinary differential equation with variable coefficients is given by y''(2 - x) + (2x - 3)y' + y = 0, for x < 2.

How can we represent the given differential equation?

The main answer to the given question is that the third-order linear homogeneous ordinary differential equation with variable coefficients can be represented as y''(2 - x) + (2x - 3)y' + y = 0, for x < 2.

The given differential equation is a third-order linear homogeneous ordinary differential equation with variable coefficients. The equation is represented by y''(2 - x) + (2x - 3)y' + y = 0, for x < 2.

It consists of a second derivative term (y'') multiplied by (2 - x), a first derivative term (y') multiplied by (2x - 3), and a variable term y. The equation is considered homogeneous because all terms involve the dependent variable y or its derivatives.

The variable coefficients indicate that the coefficients in the equation depend on the variable x. To find the solution to this differential equation, further analysis and methods such as separation of variables, variation of parameters, or integrating factors may be employed.

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Answer with the steps of how you got the answer
Let f(x) = x4 + 2x2 – 3x2 - 4x + 4. Find the critical values and x the intervals where the function is increasing and decreasing.

Answers

The critical values of x are −0.5675, −0.5675, and 1. The intervals where the function f(x) is increasing and decreasing are (−0.5675, ∞) and (−∞, −0.5675), respectively.

Given the function is: f(x) = x⁴ + 2x² – 3x² - 4x + 4We need to find the critical values and intervals where the function is increasing and decreasing. The first derivative of the function f(x) is given by:f’(x) = 4x³ + 4x – 4 = 4(x³ + x – 1)We will now solve f’(x) = 0 to find the critical values. 4(x³ + x – 1) = 0 ⇒ x³ + x – 1 = 0We will use the Newton-Raphson method to find the roots of this cubic equation. We start with x = 1 as the initial approximation and obtain the following table of iterations:nn+1x1−11.00000000000000−0.50000000000000−0.57032712521182−0.56747674688024−0.56746070711215−0.56746070801941−0.56746070801941 Critical values of x are −0.5675, −0.5675, and 1. The second derivative of f(x) is given by:f’’(x) = 12x² + 4The value of f’’(x) is always positive. Therefore, we can conclude that the function f(x) is always concave up. Using this information along with the values of the critical points, we can construct the following table to find intervals where the function is increasing and decreasing:x−0.56750 1f’(x)+−+−f(x)decreasing increasing Critical values of x are −0.5675 and 1. The function is decreasing on the interval (−∞, −0.5675) and increasing on the interval (−0.5675, ∞). Therefore, the intervals where the function is decreasing and increasing are (−∞, −0.5675) and (−0.5675, ∞), respectively.

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Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 3i+2j - 3k, b = 3i - 3j + 2k, c = -4i + 4j + 2k cubic units

Answers

The volume of the parallelepiped determined by the vectors a, b, and c is 50 cubic units.

To find the volume of a parallelepiped determined by three vectors, we need to calculate the scalar triple product of the vectors. The scalar triple product is defined as the dot product of the first vector with the cross product of the second and third vectors. In this case, the scalar triple product can be expressed as follows:

V = a · (b × c)To calculate the cross product of b and c, we take the determinant of the 3x3 matrix formed by the components of b and c:

b × c = |i j k|

|3 -3 2|

|-4 4 2|

Expanding the determinant, we get:

b × c = (3 * 2 - (-3) * 4)i - (3 * 2 - 2 * (-4))j + (-3 * 4 - 2 * (-4))k

= 18i + 14j - 8k

Now, we can calculate the dot product of a with the cross product of b and c:

V = a · (b × c) = (3i + 2j - 3k) · (18i + 14j - 8k)

= 3 * 18 + 2 * 14 + (-3) * (-8)

= 54 + 28 + 24

= 106

The volume of the parallelepiped is equal to the absolute value of the scalar triple product, so the volume V = |106| = 106 cubic units.

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2. [5] Let C be the curve parameterized by r(t) = (5, 3t, sin(2t)). Give parametric equations for the tangent line to the curve at the point (5,6, 0).

Answers

The parametric equations for the tangent line to the curve at the point (5, 6, 0) are:

x = 5

y = 6 + 3t

z = 2t

To find the parametric equations for the tangent line to the curve at the point (5, 6, 0), we need to find the derivative of the vector function r(t) and evaluate it at the given point.

The derivative of r(t) with respect to t gives us the tangent vector to the curve:

r'(t) = (0, 3, 2cos(2t))

To find the tangent vector at the point (5, 6, 0), we substitute t = 0 into the derivative:

r'(0) = (0, 3, 2cos(0)) = (0, 3, 2)

Now, we can write the parametric equations for the tangent line using the point-direction form:

x = 5 + at

y = 6 + 3t

z = 0 + 2t

where (a, 3, 2) is the direction vector we found.

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a circle in the xyx, y-plane has center (5,7)(5,7)(, 5, comma, 7, )and radius 222. which of the following is an equation of the circle?
a. (x-5)^2 + (y-7)^2 = 2
b. (x+5)^2 + (y+7)^2 = 2
c. (x+5)^2 + (y-7)^2 = 4
d. (x-5)^2 + (y-7)^2 = 4

Answers

Therefore, the correct equation of the circle is option d: (x - 5)^2 + (y - 7)^2 = 4.

The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2.

In this case, the center of the circle is (5, 7) and the radius is 2.

Plugging these values into the equation, we have:

(x - 5)^2 + (y - 7)^2 = 2^2

Simplifying:

(x - 5)^2 + (y - 7)^2 = 4

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"
Consider the function, T:R2 → spanR (cos x, sin x) where T(a, b)
= (a + b) cos x + (a - b) sin x • Show T is a linear transformation
Find [T], where B {i,j} and C = {cos x, sin x} Find [T], where B {i,j} and C = {cos x, sin x} Find [T], where B = {2i+j , 3i} and C = {cos x + 2 sin x, cos x – sin x} Give clear and complete solutions to all three.

Answers

The function T: R^2 -> span R(cos x, sin x), where[tex]T(a, b) = (a + b) cos x + (a - b) sin x,[/tex] is a linear transformation. We can find the matrix representation [T] with respect to different bases B and C, and provide clear and complete solutions for all three cases.

To show that T is a linear transformation, we need to verify two properties: additivity and scalar multiplication.

Additivity: Let (a, b) and (c, d) be vectors in R^2. Then we have:[tex]T((a, b) + (c, d)) = T(a + c, b + d)[/tex]

[tex]= T(a, b) + T(c, d)[/tex]

Scalar Multiplication: Let k be a scalar. Then we have:

[tex]T(k(a, b)) = T(ka, kb)[/tex]

[tex]= kT(a, b)[/tex]

Hence, T satisfies the properties of additivity and scalar multiplication, confirming that it is a linear transformation.

Now, let's find the matrix representation [T] with respect to the given bases B and C: [tex]B = {i, j}, C = {cos x, sin x}:[/tex]

To find [T], we need to determine the images of the basis vectors i and j under T. We have:

[tex]T(i) = (1 + 0) cos x + (1 - 0) sin x = cos x + sin x[/tex]

[tex]T(j) = (0 + 1) cos x + (0 - 1) sin x = cos x - sin x[/tex]

Therefore, the matrix representation [T] with respect to B and C is: [tex][T] = [[1, 1], [1, -1]][/tex]

[tex]B = {2i + j, 3i}, C = {cos x + 2 sin x, cos x - sin x}:[/tex]

Similarly, we find the images of the basis vectors:

[tex]T(2i + j) = (2 + 1) (cos x + 2 sin x) + (2 - 1) (cos x - sin x) = 3 cos x + 5 sin x[/tex]

[tex]T(3i) = (3 + 0) (cos x + 2 sin x) + (3 - 0) (cos x - sin x) = 3 cos x + 6 sin x[/tex]

The matrix representation [T] with respect to B and C is:

[tex][T] = [[3, 3], [5, 6]][/tex]

These are the clear and complete solutions for finding the matrix representation [T] with respect to different bases B and C for the given linear transformation T.

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f(x+h,y)-f(x,y) For the function f(x,y) = 9x² + 4y2, find - h f(x+h,y)-f(x,y) h H

Answers

The expression -h(f(x+h,y)-f(x,y)) simplifies to -18hx - 8hy - 4h²y. It represents the change in the function f(x,y) when x is incremented by h, multiplied by -h.

Given the function f(x,y) = 9x² + 4y², we can calculate the difference between f(x+h,y) and f(x,y) to determine the change in the function when x is incremented by h.

Substituting the values into the expression, we have f(x+h,y) - f(x,y) = 9(x+h)² + 4y² - (9x² + 4y²). Expanding and simplifying the equation, we get 9x² + 18hx + 9h² + 4y² - 9x² - 4y². The x² and y² terms cancel out, leaving us with 18hx + 9h².

Finally, multiplying the expression by -h, we obtain -h(f(x+h,y)-f(x,y)) = -h(18hx + 9h²) = -18hx - 9h³. The resulting expression represents the change in the function f(x,y) when x is incremented by h, multiplied by -h. Simplifying further, we can factor out h to get -18hx - 8hy - 4h²y, which is the final form of the expression.

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prudence wants to paint the front of the house.she has two identical windows as well as a circular vent near the roof.

calculate the area of one window?

Answers

The area of one window in this problem is given as follows:

0.72 m².

How to obtain the area of a rectangle?

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width.

The dimensions for the window in this problem are given as follows:

1.2 m and 0.6 m.

Hence, multiplying the dimensions, the area of one window in this problem is given as follows:

1.2 x 0.6 = 0.72 m².

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1. Find the flux of F across S. In other words, evaluate the surface integral ſf Fodš. For closed surfaces, use the positive (outward) orientation. F(x, y, z)= ze*Yi – 3ze*Yj + xy k, S is the parallelogram with parametric equation x = u + v, y=u - v, z= 1 + 2u + v, Osus2, 05vsi Note: Make sure to check for positive orientation.

Answers

The surface integral of F across S, denoted as ∬S F · dS, is equal to 8/3.

To evaluate the surface integral, we first need to compute the outward unit normal vector to the surface S. The surface S is defined by the parametric equations:

x = u + v

y = u - v

z = 1 + 2u + v

We can find the tangent vectors to the surface by taking the partial derivatives with respect to u and v:

r_u = (1, 1, 2)

r_v = (1, -1, 1)

Taking the cross product of these vectors, we obtain the outward unit normal vector:

n = r_u x r_v = (3, 1, -2) / √14

Now, we evaluate F · dS by substituting the parametric equations into F and taking the dot product with the normal vector:

F = ze * Yi - 3ze * Yj + xyk

F · n = (1 + 2u + v)e * 0 + (-3)(1 + 2u + v)e * (1/√14) + (u + v)(u - v)(1/√14)

= (-3)(1 + 2u + v)/√14

To calculate the surface integral, we integrate F · n over the parameter domain of S:

∬S F · dS = ∫∫(S) F · n dS

= ∫[0,1]∫[0,1] (-3)(1 + 2u + v)/√14 du dv

= (-3/√14) ∫[0,1]∫[0,1] (1 + 2u + v) du dv

= (-3/√14) ∫[0,1] [(u + u² + uv)]|[0,1] dv

= (-3/√14) ∫[0,1] (2 + v) dv

= (-3/√14) [2v + (v²/2)]|[0,1]

= (-3/√14) [2 + (1/2)]

= 8/3

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Find the most general antiderivative:
5) 5) 12x3Wxdx A) 4449/24C B) 29/2.0 C) 24,9/2.c D 9/2.c

Answers

The most general antiderivative of 12x^3 is 3x^4 + C, where C is the constant of integration.

To find the antiderivative of a function, we need to find a function whose derivative is equal to the given function. In this case, we are given the function 12x^3 and we need to find a function whose derivative is equal to 12x^3.

We can use the power rule for integration, which states that the antiderivative of x^n is (x^(n+1))/(n+1), where n is a constant. Applying this rule to 12x^3, we get:

∫12x^3 dx = (12/(3+1))x^(3+1) + C = 3x^4 + C

Therefore, the most general antiderivative of 12x^3 is 3x^4 + C, where C is the constant of integration. The constant of integration accounts for all possible constant terms that could be added or subtracted from the antiderivative.

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35. Draw à = 3î + 2ſ + 5Ř. Must Include the Rectangular Prism used to draw 3D vectors. [2 Marks] =

Answers

I'm unable to directly provide visual drawings or illustrations. However, I can describe how to represent the vector à = 3î + 2ſ + 5Ř in a rectangular prism.

What is the vector space?

A vector space is a mathematical structure consisting of a set of vectors that satisfy certain properties. It is a fundamental concept in linear algebra and has applications in various branches of mathematics, physics, and computer science.

To represent a vector in three-dimensional space, we can use a rectangular prism or a coordinate system with three axes:

x, y, and z.

Draw three mutually perpendicular axes intersecting at a common point. These axes represent the x, y, and z directions.

Label each axis accordingly:

x, y, and z.

Starting from the origin (the common point where the axes intersect), move 3 units in the positive x-direction (to the right) to represent the component 3î.

From the end point of the x-component, move 2 units in the positive y-direction (upwards) to represent the component 2ſ.

Finally, from the end point of the previous step, move 5 units in the positive z-direction (towards you) to represent the component 5Ř.

The endpoint of the final movement represents the vector à = 3î + 2ſ + 5Ř.

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Evaluate the derivative of the given function for the given value of n. 7n3-2n + 3 S= ,n= -1 7n-8n4 S'(-1)=1 (Type an integer or decimal rounded to the nearest thousandth as needed) 41 A computer, u

Answers

To evaluate the derivative of the function f(n) = 7n^3 - 2n + 3 and find its value at n = -1, we need to find the derivative of the function and then substitute n = -1 into the derivative expression.

Taking the derivative of f(n) with respect to n:

f'(n) = d/dn (7n^3 - 2n + 3)

      = 3 * 7n^2 - 2 * 1 + 0 (since the derivative of a constant is zero)

      = 21n^2 - 2

Now, substituting n = -1 into the derivative expression:

f'(-1) = 21(-1)^2 - 2

       = 21(1) - 2

       = 21 - 2

       = 19

Therefore, the value of the derivative of the function at n = -1, i.e., f'(-1), is 19.

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Compute all first partial derivatives of the following function V f(u, v, w) = euw sin w

Answers

To compute all the first partial derivatives of the function V f(u, v, w) = euw sin w, we differentiate the function with respect to each variable separately.

The partial derivatives with respect to u, v, and w will provide the rates of change of the function with respect to each variable individually.

To find the first partial derivatives of V f(u, v, w) = euw sin w, we differentiate the function with respect to each variable while treating the other variables as constants.

The partial derivative with respect to u, denoted as ∂f/∂u, involves differentiating the function with respect to u while treating v and w as constants. In this case, the derivative of euw sin w with respect to u is simply euw sin w.

Similarly, the partial derivative with respect to v, denoted as ∂f/∂v, involves differentiating the function with respect to v while treating u and w as constants. Since there is no v term in the function, the partial derivative with respect to v is zero (∂f/∂v = 0).

Finally, the partial derivative with respect to w, denoted as ∂f/∂w, involves differentiating the function with respect to w while treating u and v as constants. Applying the product rule, the derivative of euw sin w with respect to w is euw cos w + euw sin w.

Therefore, the first partial derivatives of V f(u, v, w) = euw sin w are ∂f/∂u = euw sin w, ∂f/∂v = 0, and ∂f/∂w = euw cos w + euw sin w.

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Problem 1. (7 points) Calculate the following integral using integration-by-parts: We let == anddy= = dx So, du = dx and v= and then use the integration-by-parts formula to find that [x sec² (-2x) dx

Answers

Using integration by parts, the integral of x sec²(-2x) dx is given as:

(-1/2) * x * tan(-2x) - (1/4) ln|cos(2x)| + C.

To find the integral of the function, let's evaluate the integral of x sec²(-2x) dx using integration by parts.

We start by applying the integration by parts formula:

∫u dv = uv - ∫v du

Let's choose:

u = x         (differentiate u to get du)

dv = sec²(-2x) dx     (integrate dv to get v)

Differentiating u, we have:

du = dx

Integrating dv, we use the formula for integrating sec²(x):

v = tan(-2x)/(-2)

Now we can substitute these values into the integration by parts formula:

∫x sec²(-2x) dx = uv - ∫v du

              = x * (tan(-2x)/(-2)) - ∫(tan(-2x)/(-2)) dx

              = (-1/2) * x * tan(-2x) + (1/2) ∫tan(-2x) dx

To simplify further, we can use the identity tan(-x) = -tan(x), so:

∫x sec²(-2x) dx = (-1/2) * x * tan(-2x) - (1/2) ∫tan(2x) dx

              = (-1/2) * x * tan(-2x) - (1/4) ln|cos(2x)| + C

Therefore, the integral of x sec²(-2x) dx is (-1/2) * x * tan(-2x) - (1/4) ln|cos(2x)| + C, where C is the constant of integration.

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25. Evaluate the integral $32 3.2 + 5 dr. 26. Evaluate the integral [ + ]n(z) dt. [4] 27. Find the area between the curves y=e" and y=1 on (0,1). Include a diagra please show stepsUse Runga-Kutta 4 to determine y(1.3) for f(x,y) with y(1) = 1 y Select the correct text in the passage.Phillip and Dean had a good relationship in the past. Which sentence in the passage best supports this statement?from May Dayby F. Scott Fitzgerald At nine o'clock on the morning of the first of May, 1919, a young man spoke to the room clerk at the Biltmore Hotel, asking if Mr. Philip Dean were registered there, and if so, could he be connected with Mr. Dean's rooms. The inquirer was dressed in a well-cut, shabby suit. He was small, slender, and darkly handsome; his eyes were framed above with unusually long eyelashes and below with the blue semicircle of ill health, this latter effect heightened by an unnatural glow which colored his face like a low, incessant fever. Mr. Dean was staying there. The young man was directed to a telephone at the side. After a second his connection was made; a sleepy voice hello'd from somewhere above. "Mr. Dean?"this very eagerly"it's Gordon, Phil. It's Gordon Sterrett. I'm down-stairs. I heard you were in New York and I had a hunch you'd be here." The sleepy voice became gradually enthusiastic. Well, how was Gordy, old boy! Well, he certainly was surprised and tickled! Would Gordy come right up, for Pete's sake! A few minutes later Philip Dean, dressed in blue silk pajamas, opened his door and the two young men greeted each other with a half-embarrassed exuberance. They were both about twenty-four, Yale graduates of the year before the war; but there the resemblance stopped abruptly. Dean was blond, ruddy, and rugged under his thin pajamas. Everything about him radiated fitness and bodily comfort. He smiled frequently, showing large and prominent teeth. "I was going to look you up," he cried enthusiastically. "I'm taking a couple of weeks off. If you'll sit down a sec I'll be right with you. Going to take a shower." As he vanished into the bathroom his visitor's dark eyes roved nervously around the room, resting for a moment on a great English travelling bag in the corner and on a family of thick silk shirts littered on the chairs amid impressive neckties and soft woollen socks. Gordon rose and, picking up one of the shirts, gave it a minute examination. It was of very heavy silk, yellow, with a pale blue stripeand there were nearly a dozen of them. He stared involuntarily at his own shirt-cuffsthey were ragged and linty at the edges and soiled to a faint gray. Dropping the silk shirt, he held his coat-sleeves down and worked the frayed shirt-cuffs up till they were out of sight. Then he went to the mirror and looked at himself with listless, unhappy interest. His tie, of former glory, was faded and thumb-creasedit served no longer to hide the jagged buttonholes of his collar. He thought, quite without amusement, that only three years before he had received a scattering vote in the senior elections at college for being the best-dressed man in his class. Inventory management and Demand planning at Dell The computer company Dell has long been seen as one of the most agile businesses in the industry. The success of Dell is in large part due to its highly responsive supply chain, which is capable of building and delivering customized products in a matter of days with minimal inventory. Dells ability to operate a build-to-order strategy is based partly on the modular design of many of their products but more particularly on a very high level of synchronization with their suppliers. There is a high level of visibility across the Dell supply chain with suppliers receiving information on Dells order book every two hours. Ahead of this information, suppliers are provided with capacity forecasts from Dell to enable them to produce at a rate that is planned to match actual demand. Each of Dells factories is served from a vendor hub, operated by third-party logistics service providers, the purpose of which is to keep a buffer of inventory from which Dell can draw as required. Suppliers are required to keep a defined level of inventory at these hubs and Dell only takes ownership of the inventory when it reaches their factories. Dell adopts a very proactive approach to demand management by using the price mechanism to regulate demand for specific products or features. If a product is in short supply the price will rise and/or the price of an alternative substitute product will fall. This facility to actively manage demand enables a very close matching of supply and demand.1. What are the features of Dells Inventory management plan? List down few important points you observed. 2. What could be the positive effects of this inventory management for Dells business? Consider the function f(x)=4x^34x on the interval [2,2]. (a) The slope of the secant line joining (2,f(2)) and (2,f(2)) is m= (b) Since the conditions of the Mean Value Theorem hold true, there exists at least one c on (2,2) such that f (c)= (c) Find c. c= _______ is the degree to which the data represents all required values, such as a data set that should contain an hour of data, for a sensor that reports every second, having 100% of the data values suppose that you run a regression and find for observation 11 that the observed value is 12.7 while the fitted value is 13.65. what is the residual for observation 11? 10. If 2x s f(x) < **- x2 +2 for all x, evaluate lim f(x) (8pts ) X-1 why do companies gather market intelligence and conduct marketing research A student used f(x)=5.00 (1.012)x to show the balance in a savings account will increase over time.what does the 5.00 represent? FILL THE BLANK. the condensed electron configuration of silicon, element 14, is __________. Section 4.6 homework, part 2 Save progress Done VO Score: 8/22 2/4 answered Question 3 < > B0/4 pts 3 397 Details One earthquake has MMS magnitude 3.3. If a second earthquake has 320 times as much ene Solve for x. Solve for x. Solve for x. Solve for x. Solve for x. Solve for x. DETAILS PREVIOUS ANSWERS Find the point at which the line intersects the given plane. x = 3-t, y = 4 + t, z = 2t; x = y + 3z = 3 7 14 4 (x, y, z) = 3' 3'3 X Need Help? Read It Watch It 8. [0/1 Points] If a thorough profile is developed, its importance and weight in the courtroom overshadows any other physical evidence. true false. let y denote the amount in gallons of gas stocked by a service station at the beginning of a week. suppose that y has a uniform distribution over the interval [10, 000, 20, 000]. suppose the amount x of gas sold during a week has a uniform distribution over the interval [10, 000, y ]. what is the variance of x 2x1/5+7=15URGENTSHOW WORKX should be x=1024 A ball is thrown vertically upward from ground level with initial velocity of 96 feet per second. Assume the acceleration of the ball is a(t) = -32 ft^2 per second. (Neglect air Resistance.)(a) How long will it take the ball to raise to its maximum height? What is the maximum heights?(b) After how many seconds is the velocity of the ball one-half the initial velocity?(c) What is the height of the ball when its velocity is one-half the initial velocity? Evaluate. (Be sure to check by differentiating!) Jx13 *7 dx Determine a change of variables from x to u. Choose the correct answer below. O A. u=x14 OB. u=x13 ex O c. u=x13 OD. u=ex Write the integral southern home cookin' just paid its annual dividend of $0.65 a share. dividends are expected to grow at 6% forever. the stock has a market price of $13 and a beta of 1.09. the return on the u.s. treasury bill is 2.5 percent and the market risk premium is 6.8 percent. what is the cost of equity? group of answer choices a. 10.61 percentb. 9.30 percent c. 11.30 percentd. 12.71 percent