The marginal cost function of a product, in dollars per unit, is
C′(q)=q2−40q+700. If fixed costs are $500, find the total cost to
produce 40 items.

Round your answer to the nearest integer.

The

Answers

Answer 1

By integrating the marginal cost function and adding the fixed costs, we can find the total cost to produce 40 items.

The total cost to produce 40 items can be determined by integrating the marginal cost function and adding the fixed costs. By evaluating the integral and adding the fixed costs, we can find the total cost to produce 40 items, rounding the answer to the nearest integer.

The marginal cost function is given by C′(q) = q² - 40q + 700, where q represents the quantity of items produced. To find the total cost, we need to integrate the marginal cost function to obtain the cost function, and then evaluate it at the quantity of interest, which is 40.

Integrating the marginal cost function C′(q) with respect to q, we obtain the cost function C(q) = (1/3)q³ - 20q² + 700q + C, where C is the constant of integration.

To determine the constant of integration, we use the given information that fixed costs are $500. Since fixed costs do not depend on the quantity of items produced, we have C(0) = 500, which gives us the value of C.

Now, substituting q = 40 into the cost function C(q), we can calculate the total cost to produce 40 items. Rounding the answer to the nearest integer gives us the final result.

Therefore, by integrating the marginal cost function and adding the fixed costs, we can find the total cost to produce 40 items.

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Related Questions

blems 2 - 10, we consider a simple electrical circuit with voltage V (measured in volts), resistance R (measured in ohms), and current I (measured in amps). These three positive variables are related to one another by "Ohms Law": V=IR. We may consider this law as written, or treat I as a function of R and V, and write : 1 = (R,V) = 2. Evaluate I(3,12), and fully describe what this means. 3. Show that the limit Jim [] does not exist by evaluating limits along the positive R-axis and along the line R = V in the RV-plane. (RV)-(0,0)'

Answers

Ohm's Law, which states that "V = IR," may be used to assess "I(3, 12)" and find "I" for "R = 3" and "V = 12" respectively:

(I(3, 12) = fracVR = frac12(3, 3) = frac12(3, 4))

This indicates that the circuit's current (I) is 4 amperes when the resistance (R) is 3 ohms and the voltage (V) is 12 volts.

We assess limits along the positive (R)-axis and the line (R = V) in the (RV)-plane to demonstrate that the limit of (I) is not real.

1. Along the '(R)'-axis that is positive: Ohm's Law (I = fracVR) states that the current would tend to infinity when (R) approaches zero. Therefore, along the positive "(R)"-axis, the limit of "(I)" does not exist.

2. Along the line "R = V": If you replace "R" with "V" in Ohm's Law,

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A population has a mean of mu = 80 with sigma = 20.
a. If a single score is randomly selected from this population, how much distance, on average, should you find between the score and the population mean?
b. If a sample of n = 6 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean?
c. If a sample of n = 100 scores is randomly selected from this population, how much distance, on average, should you find between the sample mean and the population mean?

Answers

The average distance between the sample mean and the population mean, when a sample of n = 100 scores is selected, is 2.

a. The distance between a single score and the population mean can be measured using the population standard deviation, which is given as σ = 20. Since the mean and the score are on the same scale, the average distance between the score and the population mean is equal to the population standard deviation. Therefore, the average distance is 20.

b. When a sample of n = 6 scores is randomly selected from the population, the average distance between the sample mean and the population mean is given by the standard error of the mean, which is calculated as the population standard deviation divided by the square root of the sample size:

Standard Error of the Mean (SE) = σ / sqrt(n)

Here, the population standard deviation is σ = 20, and the sample size is n = 6. Plugging these values into the formula, we have:

SE = 20 / sqrt(6)

Calculating the standard error,

SE ≈ 8.165

Therefore, the average distance between the sample mean and the population mean, when a sample of n = 6 scores is selected, is approximately 8.165.

c. Similarly, when a sample of n = 100 scores is randomly selected from the population, the average distance between the sample mean and the population mean is given by the standard error of the mean:

SE = σ / sqrt(n)

Using the same population standard deviation σ = 20 and the sample size n = 100, we can calculate the standard error:

SE = 20 / sqrt(100)

SE = 20 / 10

SE = 2

Therefore, the average distance between the sample mean and the population mean, when a sample of n = 100 scores is selected, is 2.

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A survey asked families with 1, 2, 3, or 4 children how much they planned to spend on vacation this summer. The data collected by the survey are shown in the table.

What is the probability that a family with 3 children is budgeting to spend more than $3,000 on vacation? Round your answer to the nearest hundredth, like this: 0.42 (Its not B)

A. 0.30
B. 0.19 (not this one)
C. 0.06
D. 0.26

Answers

The probability that a family with 3 children is budgeting to spend more than $3,000 on vacation is 0.30.

Looking at the table, we see that for families with 3 children:

The number of families planning to spend more than $3,000 on vacation is 11.

The total number of families with 3 children is 37

Now, we can calculate the probability:

= (Number of families with 3 children planning to spend more than $3,000) / (Total number of families with 3 children)

= 11 / 37

≈ 0.297

= 0.30.

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how would a taxpayer calculate the california itemized deduction limitation

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Taxpayers in California may need to calculate the itemized deduction limitation when filing their state income taxes. This limitation sets a cap on the amount of itemized deductions that can be claimed, based on the taxpayer's federal adjusted gross income (AGI) and other factors.

Calculating the California itemized deduction limitation involves several steps and considerations to ensure compliance with the state tax regulations. To calculate the California itemized deduction limitation, taxpayers should first determine their federal AGI. This can be found on their federal tax return. Next, they need to identify any federal deductions that are not allowed for California state tax purposes, as these will be excluded from the calculation. Once the applicable deductions are determined, taxpayers must compare their federal AGI to the threshold specified by the California Franchise Tax Board (FTB). The limitation is typically a percentage of the federal AGI, and the percentage may vary depending on the taxpayer's filing status. If the federal AGI exceeds the threshold, the itemized deductions will be limited to the specified percentage. Taxpayers should consult the official guidelines and instructions provided by the California FTB or seek professional tax advice to ensure accurate calculation and compliance with the state tax regulations. Calculating the California itemized deduction limitation is an important step in accurately reporting and calculating state income taxes. It helps determine the maximum amount of itemized deductions that can be claimed, ensuring that taxpayers adhere to the tax laws and regulations of the state.

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Let a be the distance between the points (1,1,3) and (3,0,1) plus the norm of the vector (3, 0, -4).

Answers

Therefore, the value of a is the sum of the distance d₁ and the norm of the vector (3, 0, -4):

a = d₁ + ‖(3, 0, -4)‖ = 3 + 5 = 8.

To find the distance between two points in three-dimensional space, we use the distance formula, which is derived from the Pythagorean theorem. The distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is given by:

d = √((x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²).

In this case, the distance between the points (1, 1, 3) and (3, 0, 1) is:

d₁ = √((3 - 1)² + (0 - 1)² + (1 - 3)²) = √(2² + (-1)² + (-2)²) = √(4 + 1 + 4) = √9 = 3.

The norm (magnitude) of a vector (a, b, c) is given by:

‖(a, b, c)‖ = √(a² + b² + c²).

In this case, the norm of the vector (3, 0, -4) is:

‖(3, 0, -4)‖ = √(3² + 0² + (-4)²) = √(9 + 0 + 16) = √25 = 5.

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Solve the separable differential equation dor 7 dt 2 and find the particular solution satisfying the initial condition z(0) = 4. = z(t) = Question Help: Video Post to forum Add Work Submit Question Question 6 B0/1 pt 32 Details Solve dy dt = 5(y - 10), y(0) = 7 y(t)=

Answers

By solving the separable differential equation dy/dt = 5(y - 10), we can separate the variables and integrate both sides, the particular solution satisfying the initial condition y(0) = 7 is: y(t) = e^(5t + ln(-3)) + 10.

First, let's separate the variables: dy/(y - 10) = 5 dt

Next, we integrate both sides: ∫ dy/(y - 10) = ∫ 5 dt

Integrating the left side gives us: ln|y - 10| = 5t + C

where C is the constant of integration.

Now, let's solve for y by taking the exponential of both sides:

|y - 10| = e^(5t + C)

Since e^(5t + C) is always positive, we can remove the absolute value sign: y - 10 = e^(5t + C)

To find the particular solution satisfying the initial condition y(0) = 7, we substitute t = 0 and y = 7 into the equation:

7 - 10 = e^(5(0) + C)

-3 = e^C

Solving for C: C = ln(-3)

Substituting C back into the equation, we have: y - 10 = e^(5t + ln(-3))

Finally, we can simplify the expression to obtain the particular solution:

y = e^(5t + ln(-3)) + 10

Therefore, the particular solution satisfying the initial condition y(0) = 7 is:

y(t) = e^(5t + ln(-3)) + 10.

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Express (loga 9 + 2log 5) - log2 3 as a single Rewrite, expand or condense the following. 1 12. What is the exponential form of log, 81 logarithm 15. Expand log 25x yz 14. Condense loge 15+ [loge 25 - loge 3) 17. Condense 4 log x + 6 logy 16. Condense log x - logy - 3 log 2

Answers

The logarithmic expressions when condensed or expanded are

(log₂ 9 + 2log₂5) - log₂3 = log₂(75)1/81 = 9⁻²log₈15 + (1/2log₈25 - log₈3) = log₈(25)4 log x + 6 log y= log(x⁴y⁶)log x - log y - 3 log z = log(x/[yz³])

How to solve the logarithmic expressions

Expressing (log₂ 9 + 2log₂5) - log₂3 as a single logarithm

Given that

(log₂ 9 + 2log₂5) - log₂3

Apply the power rule

So, we have

(log₂ 9 + 2log₂5) - log₂3 = (log₂ 9 + log₂5²) - log₂3

Evaluate the exponent

(log₂ 9 + 2log₂5) - log₂3 = (log₂ 9 + log₂25) - log₂3

Apply the product and the quotient rules

(log₂ 9 + 2log₂5) - log₂3 = log₂(9 * 25/3)

So, we have

(log₂ 9 + 2log₂5) - log₂3 = log₂(75)

The exponential form of log₉ 1/81 = -2

Here, we have

log₉ 1/81 = -2

Apply the change of base rule

So, we have

1/81 = 9⁻²

Condensing log₈15 + (1/2log₈25 - log₈3)

Given that

log₈15 + (1/2log₈25 - log₈3)

Express 1/2 as exponent

log₈15 + (1/2log₈25 - log₈3) = log₈15 + (log₈√25 - log₈3)

When evaluated, we have

log₈15 + (1/2log₈25 - log₈3) = log₈(15 * 5/3)

So, we have

log₈15 + (1/2log₈25 - log₈3) = log₈(25)

Condensing 4 log x + 6 log y

Given that

4 log x + 6 log y

Apply the power rule

4 log x + 6 log y = log x⁴ + log y⁶

So, we have

4 log x + 6 log y= log(x⁴y⁶)

Condensing log x - log y - 3 log z

Here, we have

log x - log y - 3 log z

Apply the power rule

log x - log y - 3 log z = log x - log y - log z³

So, we have

log x - log y - 3 log z = log(x/[yz³])

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Which of the following sentences is correct?
a. Main effects should still be investigated and interpreted even when there is a significant interaction involving that main effect.
b. You don’t need to interpret main effects if an interaction effect involving that variable is significant.
c. Main effects are effects of higher order than interaction effects.
d. Non-parallel lines on an interaction graph always reflect significant interaction effects.

Answers

Of the given sentences, sentence A is correct: "Main effects should still be investigated and interpreted even when there is a significant interaction involving that main effect."

This sentence accurately states that main effects should be examined and interpreted even in the presence of a significant interaction involving that main effect. This is because main effects represent the individual effects of each independent variable on the dependent variable, regardless of whether there is an interaction.

Sentence B is incorrect: "You don’t need to interpret main effects if an interaction effect involving that variable is significant." This sentence suggests that main effects can be disregarded if there is a significant interaction effect. However, main effects are still important to interpret, as they provide information about the individual impact of each independent variable on the dependent variable.

Sentence C is incorrect: "Main effects are effects of higher order than interaction effects." Main effects and interaction effects are not categorized into different orders. Main effects represent the direct influence of an independent variable on the dependent variable, while interaction effects represent the combined effect of multiple independent variables.

Sentence D is incorrect: "Non-parallel lines on an interaction graph always reflect significant interaction effects." Non-parallel lines on an interaction graph may indicate a significant interaction effect, but they do not always reflect one. Other factors, such as the magnitude of the effect or the sample size, need to be considered when determining the significance of an interaction effect.

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Use the ratio test to determine whether n(-7)n! n=16 converges or diverges. (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n > 16,
n^2 an+1 lim n->00 = lim n->00 an (n+1)^2 (b) Evaluate the limit in the previous part. Enter o as infinity and - as -infinity. If the limit does not exist, enter DNE. an+1 lim 0 an n-> (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Converges

Answers

a. We can cancel out common terms an+1 / an = -(n+1)(n+1)! / n(n)! = -(n+1) / n

b. The limit as n approaches infinity is -∞.

c. The series n(-7)n! converges according to the ratio test.

What is ratio test?

When n is large, an is nonzero, and the ratio test is a test (or "criterion") for the convergence of a series where each term is a real or complex integer. The test, often known as d'Alembert's ratio test or the Cauchy ratio test, was first published by Jean le Rond d'Alembert.

To determine whether the series n(-7)n! converges or diverges using the ratio test, let's find the ratio of successive terms. The ratio test states that if the limit of the ratio of consecutive terms is less than 1, the series converges. Otherwise, if the limit is greater than 1 or the limit is equal to 1, the series diverges or the test is inconclusive, respectively.

(a) Find the ratio of successive terms:

an+1 / an = (n+1)(-7)(n+1)! / (n)(-7)(n)! = -(n+1)(n+1)! / n(n)!

To simplify this expression, we can cancel out common terms:

an+1 / an = -(n+1)(n+1)! / n(n)! = -(n+1) / n

(b) Evaluate the limit of the ratio as n approaches infinity:

lim(n->∞) -(n+1) / n = -∞

The limit as n approaches infinity is -∞.

(c) By the ratio test, if the limit of the ratio of consecutive terms is less than 1, the series converges. In this case, the limit is -∞, which is less than 1. Therefore, the series n(-7)n! converges according to the ratio test.

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determine the open intervals on which the function is increasing, decreasing, or constant. (enter your answers using interval notation. if an answer does not exist, enter dne.)
f(x) = x2 − 6x

Answers

The function f(x) = x² - 6x is increasing on the interval (-∞, 3) and decreasing on the interval (3, +∞).

To determine the intervals on which the function is increasing, decreasing, or constant, we need to analyze the behavior of its derivative. The derivative of f(x) = x² - 6x can be found by applying the power rule: f'(x) = 2x - 6.

For the function to be increasing, its derivative must be greater than zero. Thus, we solve the inequality 2x - 6 > 0:

2x > 6

x > 3

This means that the function is increasing for x values greater than 3. Therefore, the interval of increase is (3, +∞).

For the function to be decreasing, its derivative must be less than zero. Thus, we solve the inequality 2x - 6 < 0:

2x < 6

x < 3

This indicates that the function is decreasing for x values less than 3. Therefore, the interval of decrease is (-∞, 3).

Since there are no additional intervals mentioned in the question, we can conclude that the function is neither increasing nor decreasing outside the intervals mentioned above.

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Consider the following functions: x - 8 • f(x) X - 8 3 g(x) = x² - 13x + 40 h(x) = 5 - 2x Use interval notation to describe the domain of each function: • Type "inf" and "-inf" for [infinity] an

Answers

The domain of f(x), g(x), and h(x) can be represented in interval notation as (-∞, ∞) for all three functions since they are defined for all real numbers.

The domain of the function f(x) is all real numbers since there are no restrictions or limitations stated. Therefore, the domain can be represented as (-∞, ∞).

For the function g(x) = x² - 13x + 40, we need to find the values of x for which the function is defined. Since it is a quadratic function, it is defined for all real numbers. Thus, the domain of g(x) is also (-∞, ∞).

Considering the function h(x) = 5 - 2x, we have a linear function. It is defined for all real numbers, so the domain of h(x) is (-∞, ∞).

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1. Let a, b € R with a 0 for all t € (a, b) and that ||Y0|| is not constant. Then N(t) and y"(t) are not parallel.

Answers

If a and b are real numbers with a < b, and a function y(t) satisfies certain conditions, such as being continuously differentiable and having a non-constant initial norm ||Y0||, then the vectors N(t) and y"(t) are not parallel for all t in the interval (a, b).

Let's consider a function y(t) that satisfies the given conditions. The vector N(t) represents the unit normal vector to the curve defined by y(t), while y"(t) denotes the second derivative of y(t).

If N(t) and y"(t) were parallel for all t in the interval (a, b), it would imply that the curvature of the curve defined by y(t) is constant. However, if ||Y0|| is not constant, it indicates that the magnitude of the tangent vector to the curve is changing as t varies.

The non-constancy of ||Y0|| implies that the curve is not a straight line. Therefore, the curvature of the curve varies along the interval (a, b). Consequently, N(t) and y"(t) cannot be parallel for all t in the interval (a, b).

In conclusion, if a function y(t) satisfies the given conditions, including a non-constant initial norm ||Y0||, the vectors N(t) and y"(t) cannot be parallel for all t in the interval (a, b), indicating that the curvature of the curve varies.

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Determine whether the series converges absolutely or conditionally, or diverges. Ž (-1)^ √n+8 n=0 converges conditionally O converges absolutely Odiverges Show My Work (Required)?

Answers

The given series; ∑((-1)^(√n+8)) diverges.

To determine whether the series ∑((-1)^(√n+8)) converges absolutely, conditionally, or diverges, we can analyze the behavior of the individual terms and apply the alternating series test.

Let's break down the steps:

1. Alternating Series Test: For an alternating series ∑((-1)^n * a_n), where a_n > 0, the series converges if:

  a) a_(n+1) ≤ a_n for all n, and

  b) lim(n→∞) a_n = 0.

2. Analyzing the terms: In our series ∑((-1)^(√n+8)), the term (-1)^(√n+8) alternates between positive and negative values as n increases. However, we need to check if the absolute values of the terms (√n+8) satisfy the conditions of the alternating series test.

3. Condition a: We need to check if (√(n+1)+8) ≤ (√n+8) for all n.

  Let's examine (√(n+1)+8) - (√n+8):

  (√(n+1)+8) - (√n+8) = (√(n+1) - √n)

  Applying the difference of squares formula: (√(n+1) - √n) = (√(n+1) - √n) * (√(n+1) + √n) / (√(n+1) + √n) = (1 / (√(n+1) + √n))

  As n increases, the denominator (√(n+1) + √n) also increases. Therefore, (1 / (√(n+1) + √n)) decreases, satisfying condition a of the alternating series test.

4. Condition b: We need to check if lim(n→∞) (√n+8) = 0.

  As n approaches infinity, (√n+8) also approaches infinity. Therefore, lim(n→∞) (√n+8) ≠ 0, which does not satisfy condition b of the alternating series test.

Since condition b of the alternating series test is not met, we can conclude that the series ∑((-1)^(√n+8)) diverges.

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( Part 1: Evaluate c where C is represented by r(t) C:r(1) =cos (1) i+sen (1)j. Osis"/2 al b) F(x,y,2) =xyi + x2j + yzkC:r(1) ==i+14+2k, osisi Part 2: Evaluate the integral using the Fundamental t

Answers

Part 1: From the given information, we have the parameterization of curve C as r(t) = cos(t)i + sin(t)j, where t ranges from 0 to π/2.

To evaluate c, we need additional information or a specific equation or context related to c. Without further information, it is not possible to determine the value of c. Part 2: Based on the given information, we have a vector field F(x, y, z) = xyi + x^2j + yzk. To evaluate the integral using the Fundamental Theorem of Line Integrals, we need the specific curve C and its limits of integration. It seems that the information about the curve C and the limits of integration is missing in your question.

Please provide the complete question or provide additional details about the curve C and the limits of integration so that I can assist you further with evaluating the integral using the Fundamental Theorem of Line Integrals.

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(q4) Find the area of the region bounded by the graphs of
and x = y - 4.

Answers

The area of the region bounded by the graphs of x=±√(y-2) and x=y-4 is 31.14 square units.

The given equations are x=±√(y-2) and x=y-4.

Here, x=±√(y-2) ------(i) and x=y-4 ------(ii)

y-4 = ±√(y-2)

Squaring on both side, we get

(y-4)²= y-2

y²-8y+16=y-2

y²-8y+16-y+2=0

y²-9y+18=0

y²-6y-3y+18=0

y(y-6)-3(y-6)=0

(y-6)(y-3)=0

y-6=0 and y-3=0

y=6 and y=3

x=±√(6-2) = 2 and x=3-4=-1

Here, (2, 6) and (-1, 3)

∫√(y-2) dy -∫(y-4) dy

= [tex]\frac{(y-2)^\frac{3}{2} }{\frac{3}{2} }[/tex] - (y-4)²/2

= [tex]\frac{(6-2-2)^\frac{3}{2} }{\frac{3}{2} }[/tex] - (-3-1-4)²/2

= 1.3×2/3 - 32

= 0.86-32

= 31.14 square units

Therefore, the area of the region bounded by the graphs of x=±√(y-2) and x=y-4 is 31.14 square units.

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Perdaris Enterprises had an expenditure rate of
E' (x) = e'. * dollars per day and an income rate of I'(x) = 98.8 - °Is dollars per day on a particular job, where r was the number of days from the start of the job. The company's profit on that job will equal total income less total expendi- tures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet. Find the
following.
(a) The optimum number of days for the job to last
(b) The total income for the optimum number of days
(c) The total expenditures for the optimum number of days
(d) The maximum profit for the job

Answers

Profit = I(x) - E(x).Evaluating this expression using the optimal value of x will give us the maximum profit for the job.

To find the optimum number of days for the job, we need to determine when the income rate, I'(x), equals the expenditure rate, E'(x). Setting them equal to each other, we have:

98.8 - 0.5x = e'

Solving for x, we find that x = (98.8 - e') / 0.5. This gives us the optimum number of days for the job.

To calculate the total income for the optimum number of days, we substitute this value of x into the income function, I(x). So the total income, I(x), will be:

I(x) = ∫(98.8 - 0.5r) dr from 0 to x

Integrating and evaluating the integral, we obtain the total income.

To find the total expenditures for the optimum number of days, we substitute the same value of x into the expenditure function, E(x). So the total expenditures, E(x), will be:

E(x) = ∫(e') dr from 0 to x

Again, integrating and evaluating the integral will give us the total expenditures.

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Differentiate the following function and factor fully. f(x) = (x + 4) (x – 3) 36 = O a) 3(x+5)(x+4)2(x-3)5 (5 b) 6(x+5)(x+4)3(x-3)4 C) 3(3x+5)(x+4)2(x-3)5 d) (9x+15)(x+4)(x-3)

Answers

the fully factored form of the derivative of f(x) = (x + 4)(x - 3)^36 is f'(x) = (x - 3)^35(37x + 141).

None of the options provided match the fully factored form.

To differentiate the function f(x) = (x + 4)(x - 3)^36, we can apply the product rule and chain rule.

Using the product rule:

f'(x) = (x - 3)^36 * (d/dx)(x + 4) + (x + 4) * (d/dx)((x - 3)^36)

Applying the chain rule, we have:

f'(x) = (x - 3)^36 * (1) + (x + 4) * 36(x - 3)^35 * (d/dx)(x - 3)

Simplifying:

f'(x) = (x - 3)^36 + 36(x + 4)(x - 3)^35

To factor the derivative fully, we can factor out (x - 3)^35 as a common factor:

f'(x) = (x - 3)^35[(x - 3) + 36(x + 4)]

Simplifying further:

f'(x) = (x - 3)^35(x - 3 + 36x + 144)

f'(x) = (x - 3)^35(37x + 141)

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14. (4 points each) Evaluate the following indefinite integrals: (a) ) /(2* + 23 (25 + 2x4) dx = + da 2 (b) / dr = = (e) [e? e2 da

Answers

The indefinite integral of (eˣ / e⁽²ˣ⁾) dx is -e⁽⁻ˣ⁾ + c.

(a) ∫(1/(2x + 23))(25 + 2x⁴)dx

to evaluate this integral, we can use u-substitution.

let u = 2x + 23, then du = 2dx.

rearranging, we have dx = du/2.

substituting these values into the integral:

∫(1/(2x + 23))(25 + 2x⁴)dx = ∫(1/u)(25 + (u - 23)⁴)(du/2)

simplifying the expression inside the integral:

= (1/2)∫(25/u + (u - 23)⁴/u)du

= (1/2)∫(25/u)du + (1/2)∫((u - 23)⁴/u)du

= (1/2)(25ln|u| + ∫((u - 23)⁴/u)du)

to evaluate the second integral, we can use another u-substitution.

let v = u - 23, then du = dv.

substituting these values into the integral:

= (1/2)(25ln|u| + ∫(v⁴/(v + 23))dv)

= (1/2)(25ln|u| + ∫(v⁴/(v + 23))dv)

this integral does not have a simple closed-form solution. however, it can be evaluated using numerical methods or approximations.

(b) ∫(eʳ / (1 + eʳ))² dr

to evaluate this integral, we can use substitution.

let u = eʳ, then du = eʳ dr.

rearranging, we have dr = du/u.

substituting these values into the integral:

∫(eʳ / (1 + eʳ))² dr = ∫(u / (1 + u))² (du/u)

simplifying the expression inside the integral:

= ∫(u² / (1 + u)²) du

to evaluate this integral, we can expand the expression and then integrate each term separately.

= ∫(u² / (1 + 2u + u²)) du

= ∫(u² / (u² + 2u + 1)) du

now, we can perform partial fraction decomposition to simplify the integral further. however, i need clarification on the limits of integration for this integral in order to provide a complete solution.

(c) ∫(eˣ / e⁽²ˣ⁾) dx

to evaluate this integral, we can simplify the expression by combining the terms with the same base.

= ∫(eˣ / e²x) dx

using the properties of exponents, we can rewrite this as:

= ∫e⁽ˣ ⁻ ²ˣ⁾ dx

= ∫e⁽⁻ˣ⁾ dx

integrating e⁽⁻ˣ⁾ gives:

= -e⁽⁻ˣ⁾ + c please let me know if you have any further questions or if there was any mistake in the provided integrals.

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Solve
216. The function C = T(F) = (5/9) (F32) converts degrees Fahrenheit to degrees Celsius. a. Find the inverse function F = T¹(C) b. What is the inverse function used for?
218. A function that convert

Answers

a) To find the inverse function of T(F) = (5/9)(F - 32), we can interchange the roles of F and C and solve for F.

Let's start with the given equation:

C = (5/9)(F - 32)

To find the inverse function F = T^(-1)(C), we need to solve this equation for F.

First, let's multiply both sides of the equation by 9/5 to cancel out the (5/9) factor:

(9/5)C = F - 32

Next, let's isolate F by adding 32 to both sides of the equation:

F = (9/5)C + 32

Therefore, the inverse function of T(F) = (5/9)(F - 32) is F = (9/5)C + 32.

b) The inverse function F = T^(-1)(C), which is F = (9/5)C + 32 in this case, is used to convert degrees Celsius to degrees Fahrenheit.

While the original function T(F) converts degrees Fahrenheit to degrees Celsius, the inverse function T^(-1)(C) allows us to convert degrees Celsius back to degrees Fahrenheit.

This inverse function is particularly useful when we have temperature values in degrees Celsius and need to convert them to degrees Fahrenheit for various purposes, such as comparing temperature measurements, determining temperature thresholds, or using Fahrenheit as a unit of temperature in specific contexts.

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Explain why S is not a basis for R2 S = {(2,8), (1, 0), (0, 1)) A. Sis linearly dependent
B. S does not span R
C. Osis linearly dependent and does not span R.

Answers

The correct explanation for why S is not a basis for R2 is option C: S is linearly dependent and does not span R2.

In order for a set of vectors to form a basis for a vector space, two conditions must be satisfied. First, the vectors in the set must be linearly independent, meaning that no vector in the set can be written as a linear combination of the other vectors.

Second, the vectors must span the entire vector space, meaning that any vector in the space can be expressed as a linear combination of the vectors in the set.

In this case, S = {(2,8), (1, 0), (0, 1)} is not a basis for R2 because it is linearly dependent. The vector (2,8) can be expressed as a linear combination of the other two vectors: (2,8) = 2(1,0) + 8(0,1). Therefore, S fails the linear independence condition.

Additionally, S does not span R2 because it does not contain enough vectors to span the entire space. R2 is a two-dimensional vector space, and a basis for R2 must consist of two linearly independent vectors.

Therefore, since S is linearly dependent and does not span R2, it cannot be considered a basis for R2.

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benjamin is trying to break a combination lock. this particular type of lock has 5 digits from 0 to 9, and benjamin just happens to know that there can be no repeated digits in the code for this type of lock. how many valid codes are there?

Answers

For a combination lock with 5 digits ranging from 0 to 9 and no repeated digits allowed, there are 5 options for the first digit, 9 options for the second digit  8 options for the third digit, 7 options for the fourth digit, and 6 options for the fifth digit. Therefore, there are a total of 5 x 9 x 8 x 7 x 6 = 15,120 valid codes.

For a combination lock with 5 digits ranging from 0 to 9 and no repeated digits allowed, there are 5 options for the first digit, 9 options for the second digit  8 options for the third digit.

Since the lock does not allow repeated digits, each digit in the code must be unique.

For the first digit, there are 5 options (0 to 9, excluding the previously used digits).

For the second digit, there are 9 options (0 to 9, excluding the already used digit for the first digit).

For the third digit, there are 8 options (0 to 9, excluding the already used digits for the first and second digits).

For the fourth digit, there are 7 options (0 to 9, excluding the already used digits for the first, second, and third digits).

For the fifth digit, there are 6 options (0 to 9, excluding the already used digits for the first, second, third, and fourth digits).

To find the total number of valid codes, we multiply the number of options for each digit: 5 x 9 x 8 x 7 x 6 = 15,120.

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A set of 5 vectors in R4 is given. Are they linearly dependent? Do they span R4? Do they form a basis? Explain clearly.

Answers

The given set of 5 vectors in R4 is linearly dependent, does not span R4, and therefore does not form a basis.

For a set of vectors to be linearly dependent, there must exist a nontrivial solution to the equation c1v1 + c2v2 + c3v3 + c4v4 + c5v5 = 0, where c1, c2, c3, c4, and c5 are scalars and v1, v2, v3, v4, and v5 are the given vectors. If this equation has a nontrivial solution, it means that at least one of the vectors can be expressed as a linear combination of the others. In this case, since there are more vectors (5) than the dimension of the vector space (4), the vectors are guaranteed to be linearly dependent.

Since the given set of vectors is linearly dependent, it cannot span R4, which is the entire 4-dimensional vector space. A set of vectors spans a vector space if every vector in that space can be expressed as a linear combination of the given vectors. However, because the vectors are linearly dependent, they cannot represent all possible vectors in R4. Therefore, the given set of vectors does not form a basis for R4.

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when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be group of answer choices reliable. standardized. valid. normally distributed.

Answers

When a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be standardized.

Standardization refers to the process of establishing norms or standards for a test by administering it to a representative and pretested sample of individuals. This allows for a comparison of an individual's test performance to that of the larger group. When a test is standardized, it means that it has undergone rigorous development and validation procedures to ensure that it is fair, consistent, and reliable.

Standardized tests provide a benchmark for evaluating an individual's performance by comparing their scores to those of the norm group. The norm group consists of individuals who have already taken the test and represents the population for which the test is intended. By comparing an individual's scores to the norm group, it is possible to determine how their performance ranks relative to others.

Therefore, when a person's test performance can be compared with that of a representative and pretested sample of people, it indicates that the test is standardized. Standardization is an essential characteristic of reliable and valid tests, as it ensures consistency and allows for meaningful comparisons among test-takers.

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A find the solutions of the equation using a graphing calculator approximate your answer to the nearest thousandth Markedsolutions must be included a) 2 cos(x) = 2 sin(x) + 1 b) 7 tantx) • Cos(2x) =

Answers

The solutions to the equation 2 cos(x) = 2 sin(x) + 1 are approximately x = 0.7854 and x = 2.3562.

To solve the equation 2 cos(x) = 2 sin(x) + 1, we can first subtract 2 sin(x) from both sides to get 2 cos(x) - 2 sin(x) = 1. We can then use the identity cos(x) = sin(x + π/2) to rewrite the left-hand side as 2 sin(x + π/2) = 1. Dividing both sides by 2, we get sin(x + π/2) = 1/2.

The solutions to this equation are the angles whose sine is 1/2. These angles are π/6 and 5π/6. However, we need to keep in mind that the original equation was in terms of x, which is measured in radians. So, we need to convert these angles to radians.

π/6 is equal to 0.5236 radians, and 5π/6 is equal to 2.6179 radians. So, the solutions to the equation 2 cos(x) = 2 sin(x) + 1 are approximately x = 0.7854 and x = 2.3562.

graph of 2 cos(x) = 2 sin(x) + 1 and y = x, with red dots marking the solutions Opens in a new window

As you can see, the solutions are approximately x = 0.7854 and x = 2.3562.

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                                      "Complete question"

Use the desmos graphing calculator to find all solutions of the given equation. Approximate the answer to the nearest thousandth. Graph with marked solutions must be

included for full credit.

a) 2 cos(x) = 2 sin(x) + 1

b) 7 tan(x) · cos(2x) = 1

The set {(1, 4, 6),(1, 5, 8) (2,−1,1)(0,1,0)} is a linearly independent subset of r3.

Answers

we obtain a row of zeros in subset, indicating that the set {(1, 4, 6), (1, 5, 8), (2, -1, 1), (0, 1, 0)} is not linearly independent.

To determine if a set of vectors is linearly independent, we need to check if the only solution to the equation a(1, 4, 6) + b(1, 5, 8) + c(2, -1, 1) + d(0, 1, 0) = (0, 0, 0) is when a = b = c = d = 0.

By setting up the corresponding system of equations and solving it, we can find the values of a, b, c, and d that satisfy the equation. However, a more efficient method is to create an augmented matrix with the vectors as columns and row-reduce it.

Performing row operations on the augmented matrix, we can transform it to its reduced row-echelon form. If the resulting matrix has a row of zeros, it would indicate that the vectors are linearly dependent. However, if the matrix does not have a row of zeros, it means that the vectors are linearly independent.

In this case, when we row-reduce the augmented matrix, we obtain a row of zeros, indicating that the set {(1, 4, 6), (1, 5, 8), (2, -1, 1), (0, 1, 0)} is not linearly independent.

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f(4+h)-f(4) Find lim h h-0 if f(x) = x² + 5. + f(4+h) – f(4) lim h h-0 (Simplify your answer.)

Answers

The limit of the expression (f(4+h) - f(4))/h as h approaches 0 can be simplified to the derivative of the function f(x) = x² + 5 evaluated at x = 4. The derivative of f(x) is 2x, so substituting x = 4 gives the answer of 8.

To find the limit as h approaches 0, we start by evaluating the expression (f(4+h) - f(4))/h. Substituting the given function f(x) = x² + 5, we have:

(f(4+h) - f(4))/h = [(4+h)² + 5 - (4² + 5)]/h

= [(16 + 8h + h² + 5) - (16 + 5)]/h

= (8h + h² + 5)/h

= (h(8 + h) + 5)/h.

Now, we can simplify this expression further by canceling out the h in the numerator and denominator:

(h(8 + h) + 5)/h = 8 + h + 5/h.

As h approaches 0, the term 5/h goes to 0, so we are left with:

lim(h->0) (8 + h + 5/h) = 8 + 0 + 0 = 8.

Therefore, the limit of (f(4+h) - f(4))/h as h approaches 0 is equal to 8.

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Evaluate the indefinite integral. (Use C for the constant of integration.) X5 sin(1 + x7/2) dx +

Answers

The simplified expression for the indefinite integral is :

-2/7*x^5*cos(1 + x^(7/2)) + 10/49 * ∫x^4*cos(1 + x^(7/2)) dx + C

To evaluate the indefinite integral of the function x^5 * sin(1 + x^(7/2)) dx, we can use integration by parts. Integration by parts formula is ∫udv = uv - ∫vdu, where u and dv are parts of the integrand.

Let's choose:
u = x^5, then du = 5x^4 dx
dv = sin(1 + x^(7/2)) dx, then v = -2/7*cos(1 + x^(7/2))

Now, apply the integration by parts formula:
∫x^5 * sin(1 + x^(7/2)) dx = -2/7*x^5*cos(1 + x^(7/2)) - ∫(-2/7*5x^4)*(-2/7*cos(1 + x^(7/2))) dx

Simplify the expression:
∫x^5 * sin(1 + x^(7/2)) dx = -2/7*x^5*cos(1 + x^(7/2)) + 10/49 * ∫x^4*cos(1 + x^(7/2)) dx + C

This is the simplified expression for the indefinite integral. The term +C represents the constant of integration.

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solve both parts in 30 mints.
Thann you . I will give up vote
13. (a) Use the Newton-Raphson method to find √5 correct to 3 decimal places. (b) Find the mean value of the function f(x)=x²-5 over the interval [0, 10].

Answers

To find √5 correct to 3 decimal places using the Newton-Raphson method, we need to solve the equation f(x) = x² - 5 = 0.

1. Choose an initial guess for the root, let's say x0 = 2.

2. Apply the Newton-Raphson iteration formula:

xₙ₊₁ = xₙ - f(xₙ) / f'(xₙ)

where f'(x) is the derivative of f(x).

3. Calculate f(x) and f'(x) for each iteration and update xₙ₊₁ until the desired accuracy is achieved.

Let's perform the iterations:

For the function f(x) = x² - 5:

f(x) = x² - 5

f'(x) = 2x

Iteration 1:

x₁ = x₀ - f(x₀) / f'(x₀)

  = 2 - (2² - 5) / (2*2)

  = 2 - (4 - 5) / 4

  = 2 - (-1) / 4

  = 2 + 1/4

  = 2.25

Iteration 2:

x₂ = x₁ - f(x₁) / f'(x₁)

  = 2.25 - (2.25² - 5) / (2*2.25)

  = 2.25 - (5.0625 - 5) / 4.5

  = 2.25 - (0.0625) / 4.5

  = 2.25 - 0.0139

  = 2.2361

Iteration 3:

x₃ = x₂ - f(x₂) / f'(x₂)

  = 2.2361 - (2.2361² - 5) / (2*2.2361)

  = 2.2361 - (4.9999 - 5) / 4.4721

  = 2.2361 - (0.0001) / 4.4721

  = 2.2361 - 0.0000

  = 2.2361

The Newton-Raphson method converges to the root √5 ≈ 2.2361 correct to 4 decimal places. To obtain the value correct to 3 decimal places, we round it to √5 ≈ 2.236.

(b) To find the mean value of the function f(x) = x² - 5 over the interval [0, 10], we use the formula:

mean value = (1 / (b - a)) * ∫[a, b] f(x) dx

Substituting the given values:

mean value = (1 / (10 - 0)) * ∫[0, 10] (x² - 5) dx

          = (1 / 10) * [∫(x² dx) - ∫(5 dx)] from 0 to 10

          = (1 / 10) * [(x³/3) - (5x)] from 0 to 10

          = (1 / 10) * [(10³/3) - (5 * 10) - (0³/3) + (5 * 0)]

          = (1 / 10) * [(1000/3) - 50]

          = (1 / 10) * [(1000 - 150) / 3]

          = (1 / 10) * (850 /

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Let U § C be a region containing D(0; 1) and let f be a meromorphic function on U, which
has no zeros and no poles on dD (0;1). If f has a zero at 0 and if Ref (z) > 0 for every
ZE AD (0;1), show that f has a pole in D(0; 1).

Answers

We can apply the maximum modulus principle, which states that if a non-constant analytic function has its maximum modulus on the boundary of a region, then it is constant.

to prove that f has a pole in the region d(0, 1), we can make use of the argument principle and the maximum modulus principle.

given that f is meromorphic on the region u, it has no zeros or poles on the boundary dd(0, 1), which is the unit circle centered at the origin.

since f has a zero at 0, it means that the function f(z) = zⁿ * g(z), where n is a positive integer and g(z) is a meromorphic function with no zeros or poles in d(0, 1).

now, let's consider the function h(z) = 1/f(z). since f has no poles on dd(0, 1), h(z) is analytic on and within the region d(0, 1). we need to show that h(z) has a zero at z = 0.

if we assume that h(z) has no zero at z = 0, then h(z) is non-zero and analytic in the region d(0, 1). in this case, the region is d(0, 1), and h(z) has no zero at 0, so its modulus |h(z)| achieves a maximum on the boundary dd(0, 1).

however, this contradicts the fact that ref(z) > 0 for all z in ad(0, 1). if ref(z) > 0, then the real part of h(z) is positive, which implies that |h(z)| is also positive.

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Differential Equation
y" + 4y = 0, t²-8t+16, t²-6t+4, t26 0≤t

Answers

The solution to the given differential equation y" + 4y = 0, is:

y(t) = (1/2)sin(2t) + 0(t^2 - 8t + 16) + 0*(t^2 - 6t + 4),

which simplifies to: y(t) = (1/2)*sin(2t).

The given differential equation is y" + 4y = 0. Let's solve this differential equation using the method of characteristic equations.

The characteristic equation corresponding to this differential equation is r^2 + 4 = 0.

Solving this quadratic equation, we get:

r^2 = -4

r = ±√(-4)

r = ±2i

The roots of the characteristic equation are complex conjugates, which means the general solution will have a combination of sine and cosine functions.

The general solution of the differential equation is given by:

y(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are arbitrary constants to be determined based on initial conditions.

Now, let's solve the initial value problem using the given conditions.

For t = 0, y = 0:

0 = c1cos(20) + c2sin(20)

0 = c1*1 + 0

c1 = 0

For t = 0, y' = 1:

1 = -2c1sin(20) + 2c2cos(20)

1 = 2c2

c2 = 1/2

Therefore, the particular solution satisfying the initial conditions is:

y(t) = (1/2)*sin(2t).

Now let's solve the given non-homogeneous differential equations:

For t^2 - 8t + 16:

Let's find the particular solution for this equation. Assume y(t) = A*(t^2 - 8t + 16), where A is a constant to be determined.

y'(t) = 2A*(t - 4)

y''(t) = 2A

Substituting these into the differential equation:

2A + 4A*(t^2 - 8t + 16) = 0

6A - 32A*t + 64A = 0

Comparing coefficients, we get:

6A = 0 => A = 0

So the particular solution for this equation is y(t) = 0.

For t^2 - 6t + 4:

Let's find the particular solution for this equation. Assume y(t) = B*(t^2 - 6t + 4), where B is a constant to be determined.

y'(t) = 2B*(t - 3)

y''(t) = 2B

Substituting these into the differential equation:

2B + 4B*(t^2 - 6t + 4) = 0

6B - 24B*t + 16B = 0

Comparing coefficients, we get:

6B = 0 => B = 0

So the particular solution for this equation is y(t) = 0.

In summary, the solution to the given differential equation y" + 4y = 0, along with the provided non-homogeneous equations, is:

y(t) = (1/2)sin(2t) + 0(t^2 - 8t + 16) + 0*(t^2 - 6t + 4),

which simplifies to:

y(t) = (1/2)*sin(2t).

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Suppose g(t) = x(t) cos t and the Fourier transform of the g(t) is G(jw) = 1, ll 20, otherwise(a) Determine x(t). (b) Specify the Fourier transform X1 (j) of a signal x,) such that g(t) = x1(t) cos (2/3t) Differential Equationy" + 4y = 0, t-8t+16, t-6t+4, t26 0t the key to the automated underwriting system is an ability to evaluate _____A. propertyB. liabilitiesC. creditD. layered risk ngo company purchased a truck for $54,000. sales tax amounted to $5,400; shipping costs amounted to $1,200; and one-year registration of the truck was $100. what is the total amount of costs that should be capitalized? A find the solutions of the equation using a graphing calculator approximate your answer to the nearest thousandth Markedsolutions must be included a) 2 cos(x) = 2 sin(x) + 1 b) 7 tantx) Cos(2x) = T or F?PCR reactions are carried out in machines called thermocyclers. Suppose that consumer and business confidence fall. What is the ultimate outcome for the economy if monetary policymakers respond to keep inflation on an unchanged target?a. If monetary policymakers respond, output would remain close to potential output.b. If monetary policymakers respond, output would fall below potential output.c. If monetary policymakers respond, output would rise above potential output.d. If monetary policymakers respond, output would remain close to potential output but inflation would still rise despite their actions. True/false: shotgun shells loaded with flechettes are legal in california Which of the following commands can be used to see files that are currently being used by a specific process ID (PID)? a. psfiles b. lsof c. pstatus d. pids. Determine whether the series converges absolutely or conditionally, or diverges. (-1)^ n+8 n=0 converges conditionally O converges absolutely Odiverges Show My Work (Required)? Which of the following forms of supporting materials are most effective when used in conjunction with a presentation aid? a. expert testimony b. statistics c. definitions d. examples e. narratives f. lay testimony T/F solid state drives consist of a microcontoller and flash memroy A single-business company's strategy involves all of the following exceptMultiple Choiceo planned, proactive moves to attract customers and outcompete rivals via improved product design and higher quality.o efforts to build on its strengths and avoid partnerships and alliances with other enterprises within its industry.o moves to respond to changing conditions in the macro-environment or in industry and competitive conditions.o functional strategies (R&D, supply chain management, production, sales and marketing, HR, and finance) employed by the company.o efforts to expand or narrow geographic coverage. .a missing-person emergency action plan should include a specific signal, how responders will be staged, and how searchers will be assinged.true or false? Select potential new antimicrobial therapies that are under investigation. Check all that apply.Use of probiotics to contribute healthy microbes to the GI tractBacteriophage therapyUse of prebiotics to feed normal inhabitants of the GI tractIntroduction of healthy biota through fecal transplantation Select the correct answer. Circle O is represented by the equation (x + 7)2 + (y + 7)2 = 16. What is the length of the radius of circle O? A. 3 B. 4 C. 7 D. 9 E. 16 Could I get some assistance with the question below please.Find dy/du, du/dx, and dy/dx. y=u, u = 5x - 8 dy / du = du / dx = dy / dx = which of the following would not be a tacticused by a services provider to aid in scheduling an appointmentsystemA. a reservation systemB. cyclical schedulingC. yield managementD. shortest proce The model of customer-initiated interactive communication includes ______. (Check all that apply.)a. a message channelb. the receiverc. the source messaged. a search What is the value of x in the systems: 5x + 2y = 3 2x + 3y = -1