at 111111:55\text{ p.m.}55 p.m.55, start text, space, p, point, m, point, end text, thomas ties a weight to the minute hand of a clock. the clockwise torque applied by the weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be modeled by a trigonometric function. the torque peaks 151515 minutes after each whole hour, when the minute hand is pointing directly to the right, at 3\text{ nm}3 nm3, start text, space, n, m, end text (newton metre, the si unit for torque). the minimum torque of -3\text{ nm}−3 nmminus, 3, start text, space, n, m, end text occurs 151515 minutes before each whole hour, when the minute hand is pointing directly to the left. find the formula of the trigonometric function that models the torque \tauτtau applied by the weight ttt minutes after thomas attached the weight. define the function using radians.

Answers

Answer 1

The trigonometric function's formula, which simulates the torque (tau) that the weight applied t minutes after Thomas attached it is

[tex]3 Sin (\frac{2\frac{22}{7} }{60} (t-51))[/tex]

The angular speed of the minutes hand is

[tex]w = \frac{2 (\frac{22}{7}) }{60}[/tex] rad/min

Following the application of weight, the torque as a function of time t is,

[tex]t= t_{0} sin (w (t-5) min)\\ = (3 Nm) sin ((\frac{2 (\frac{22}{7} }{60} ) rad/min (t-5) min)[/tex]

[tex]= (3 Nm) sin ( \frac{2 (\frac{22}{7} }{60} (t-5) rad ) \\= 3 sin (\frac{2 \frac{22}{7} }{60} (t-5)[/tex]

What is torque ?

Torque, which is also known as the moment of a force, is the propensity of a force to rotate the body to which it is applied. Force (F) x Distance (r) = Torque is how torque is calculated. The distance (r) between the pivot point and the force's action point. A vector quantity is a torque. As a vector quantity, torque always has a direction that is perpendicular to the plane that contains the vectors of force and displacement.

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Related Questions

2[-3^(2)-(5)/(4-9)]+3(4-2^(3))

Answers

Answer:

-28

Step-by-step explanation:

Divide. 5/6 ÷ −2/3



−5/4

negative fraction 5 over 4


​−5/9​

​, negative fraction 5 over 9, ​


5/9

5 over 9


​5/4

5 over 9

Answers

Answer:

[tex] \frac{ - 5}{4} [/tex]

Step-by-step explanation:

[tex] \frac{5}{6} \div \frac{ - 2}{3} [/tex]

When dividing two fractions, we turn the second fraction upside-down and multiply two expressions instead.

[tex] \frac{5}{6} \times \frac{ - 3}{2} = \frac{ - 15}{12} [/tex]

Now simplify the fraction by dividing it with biggest common divisor which is 3 in this case.

[tex] \frac{ - 5}{4} [/tex]

is the final result.

an equation that is true for all values of the variable is called an

Answers

Answer:

an identity............

Answer:

An identity

Step-by-step explanation:

An identity is an equation, which is true for all values of the variables in the equation.

mav is older than justin. Their ages are consecutive integers find mavs age if the product of their age is 42

Answers

Answer:

7

Step-by-step explanation:

hope this works :)

consecutive numbers means 2 numbers next to eachother like 8 and 9 or 3 and 4

product means basically the result of numbers multiplying together, e.g. the product of 8×9 = 72

so if you use trial and error you will find 6 × 7 = 42 and since mav is older she must be 7 years old

Answer:

mav is 7

Step-by-step explanation:

let justin's age be n then mav is n + 1 and the product is

n(n + 1) = 42

n² + n = 42 ( subtract 42 from both sides )

n² + n - 42 = 0 ← in standard form

(n + 7)(n - 6) = 0 ← in factored form

equate both factors to zero and solve for n

n + 7 = 0 ⇒ n = - 7

n - 6 = 0 ⇒ n = 6

since n > 0 then n = 6

mav is n + 1 = 6 + 1 = 7

how many calories would you consume if you were to eat a large size pizza (16 inches) by yourself? give your answer to the nearest hundred.

Answers

So nearest hundred of calories of pizza is 3384.

As it is given that its an pizza of 16 inches .

A Calorie is unit of heat used to indicate the amount of energy foods produce in the human body that is equal to 1000 calories.

Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

So as we all know pizza of 16 inches contains 3384.00 calories

And its been asked to the nearest hundred so divide it by 100And we get 3384 calorie. So a 16 inch pizza contains 3384 calories.

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4x = 0.5(2x- 12) solve for x

Answers

Answer: x = -2

Step-by-step explanation:

4x=0.5(2x−12)

Use the distributive property to multiply 0.5 by 2x−12.

4x=x−6

Subtract x from both sides.

4x−x=−6

Combine 4x and −x to get 3x.

3x=−6

Divide both sides by 3.

x= 3−6

Divide −6 by 3 to get -2.

Joel is buying packs of baseball cards to add to his collection. He wants to have at least 65 total. He already has 15 and each pack has 5 cards, c, in it. How many packs will Joel need to buy in order to have at least 65 total cards?​

Answers

Answer:

10 cards

Step-by-step explanation:

In order to find how many packs Joel needs to buy we need Make an equation

Equation = 5c + 15 = 65

where,

c = cards

5c+15=65

Step 1: Subtract 15 from both sides.

5c+15−15=65−15

5c=50

Step 2: Divide both sides by 5.

5c/5 = 50/5

c=10

Therefore, Joel need to buy total of 10 cards in order to have at least 65 total cards

write equation in the standard form then identify the terms and the values of a,b and c

Answers

I’m fine with over the phone and you can just text back and forth with me if you want you to text text

What is 9+9?
Easy points and brainliest if 2 ppl answer

Answers

Answer:

18

Step-by-step explanation:

which is equivalent to the following expression 4p^2+5.5m+2.5p^2-m+3m

Answers

The equivalent expression of 4p^2 + 5.5m + 2.5p^2 - m + 3m is 6.5p^2 + 7.5m

How to determine the equivalent expression?

The expression is given as

4p^2+5.5m+2.5p^2-m+3m

Rewrite properly as

4p^2 + 5.5m + 2.5p^2 - m + 3m

Collect the like terms in the above equation

4p^2 + 5.5m + 2.5p^2 - m + 3m = 4p^2 + 2.5p^2 + 5.5m - m + 3m

Evaluate the like terms in the above equation

4p^2 + 5.5m + 2.5p^2 - m + 3m = 6.5p^2 + 7.5m

Hence, the equivalent expression of 4p^2 + 5.5m + 2.5p^2 - m + 3m is 6.5p^2 + 7.5m

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If m∠j=91 m∠l=16 and m∠k=73 list the sides of ∆JLK in order from smallest to largest

Answers

Answer:

ikj

Step-by-step explanation:

In a triangle:

The shortest side is opposite the smallest angle.The longest side is opposite the biggest angle.

When labeling angles and sides of triangles, it is convention to label the side opposite an angle with the same letter but in lower case.  

Therefore in ∆JLK:

Side j is opposite angle J.Side l is opposite angle L.Side k is opposite angle K.

As 16 < 73 < 91

⇒ m∠I < m∠K < m∠J

As the angles of ∆JLK in order from smallest to largest are IKJ, then the sides of ∆JLK in order from smallest to largest are ikj.

In a food court there are people eating hamburgers, burritos & pizza. P(h) = 0. 38 and P(b) = 0. 31. If there are 35 people eating pizza, what is the total number of people in the food court?


Answer should be rounded to the nearest WHOLE NUMBER

Answers

The total number of people in the food court eating pizza, burritos, and hamburgers is 113 (Approximate) or (Whole number)

People eating hamburger P(h) =0.38

People eating burritos P(b) = 0.31

Number of people eating pizza = 35

    Let's suppose the total number of people is 1

So,

    By adding the total number of people eating hamburgers and burritos                                          

                                                           = 0.38+0.31

                                                            = 0.69

    The ratio of the total number of people eating pizza = 1.00 - 0.69

                                                                                            = 0.31

   So total number of people eating pizza = 0.31 = 35

   By solving :

              1 = 35 / 0.31

                = (35*100)/31

                = 3500/31

                 = 112.9 (we have to write it down in the nearest whole number)

Here we writing the approximate value of 112.9 = 113 (Approximate)

Hence, the total number of people in the food court in the nearest whole number is 113

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Evaluate.
Quickly please!

Answers

Answer:

819,200

Step-by-step explanation:

First start by raising all the numbers to the power indicated:

5^4 = 625

8^5 = 32768

2^9 = 512

5^2 = 25

Then divide the numerators by the denominators:

625 / 8 = 78.125

32768 / 64 = 512

512 / 25 = 20.48

Finally, multiply all the numbers together

78.125 * 512 * 20.48 = 819200

The quotient of a number and negative six plus eight is twenty-four

Answers

Answer:

the number is ..let X

X/-6+8=24X/2=24criss cross the number and we get 48

Use the diagram shown to answer the question. What
are the sine and cosine values of a 60° angle?

Answers

Answer: sin(60°)= [tex]\frac{\sqrt{3}} 2[/tex] and cos(60°)=[tex]\frac{1} 2[/tex]

Step-by-step explanation:

sine means opposite/hypothenus (SOH)

opposite=[tex]\frac{\sqrt{3}} 2[/tex] and hypothenus is 1

sin(60°) = [tex]\frac{\sqrt{3}} 2[/tex] ÷ [tex]\frac{1} 1[/tex]

              =  [tex]\frac{\sqrt{3}} 2[/tex] × [tex]\frac{1} 1[/tex]

              =  [tex]\frac{\sqrt{3}} 2[/tex]

cosine means adjacent/hypothenus (CAH)

adjacent= [tex]\frac{1} 2[/tex] and hypothenus is 1

cos(60°) =  [tex]\frac{1} 2\\[/tex] ÷ [tex]\frac{1} 1[/tex]

              =  [tex]\frac{1} 2[/tex] × [tex]\frac{1} 1[/tex]

              =  [tex]\frac{1} 2[/tex]

find the area of the polygon with the given points A (-5,-2) B (4,-2) C (4, -7) D (-5, -7)

Answers

Answer is 45 units squared

Step by step

It’s a rectangle!

9 units long (x axis) by 5 units tall (y axis)
= 45 units squared

What is the scale factor from the drawing to the actual airplane

the scale factor is _

Answers

Answer: 2

Step-by-step explanation: I just did this lesson

A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.

If the height of the actual airplane is 20m and the in the scale drawing the height is 10m.

The scale factor of the airplane is 200.

What is a scale factor?

A scale factor is a ratio between the scale of the original object in an actual sense and the prototype figure of the same object.

We have

The height of the plane in scale drawing:

= 10 cm

The height of the plane in an actual airplane.

= 20 m

The scale factor of the height of the airplane:

= 20m / 10 cm

[ 1 m = 100 cm ]

= (20 x 100) cm / 10 cm

= 200

Thus,

The scale factor of the airplane is 200.

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Kyle asks his friend Jane to guess his age and his grandmother’s age. Kyle says his grandmother is not more than 80 years old. He says his grandmother’s age is, at most, 3 years less than 3 times his own age.

Jane writes this system of inequalities to represent k, Kyle’s age, and g, Kyle’s grandmother’s age.

Inequality 1: g > 80
Inequality 2: g ≤ 3k – 3
Which inequality did Jane write incorrectly, and how could it be corrected?

Inequality 1 is incorrect; it should be g ≤ 80.
Inequality 1 is incorrect; it should be g ≥ 80.
Inequality 2 is incorrect; it should be g < 3k – 3.
Inequality 2 is incorrect; it should be g ≥ 3k – 3.

Answers

Answer:

Inequality 1 is incorrect; it should be g ≤ 80.

Step-by-step explanation:

Kyle's grandmother is not more than 80. This means that she is either equal to 80 or less than 80.

This gives us the inequality: g ≤ 80

Systems of equations with graphing

Answers

For the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.

We are given the equations:

7 x - y = 7   … (1)

x + 2 y = 6

x = 6 - 2 y   … (2)

Substitute equation (2) in equation (1), we get that:

7 ( 6 - 2 y ) - y = 7

42 - 14 y - y = 7

15 y = 35

y = 35 / 15

y = 7 / 3

x = 6 - 2 ( 7 / 3)

x = 18 - 14 / 3

x = 4 / 3

Therefore, for the equations 7 x - y = 7 and x + 2 y = 6, we get the solution as x = 4 / 3 and y = 7 / 3.

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[tex] {x}^{2} + 70 = 17x[/tex]
solve

I really neeed this done asap​

Answers

Answer: x=7     x=10

Step-by-step explanation:

[tex]x^2+70=17x\\x^2+70-17x=17x-17x\\x^2-17x+70=0\\x^2-7x-10x+70=0\\x(x-7)-10(x-7)=\\(x-7)(x-10)=0\\x-7=0\\x=7\\x-10=0\\x=10[/tex]

Answer:

x = 7, x = 10

Step-by-step explanation:

x² + 70 = 17x ( subtract 17x from both sides )

x² - 17x + 70 = 0 ← in standard form

consider the factors of the constant term (+ 70) which sum to give the coefficient of the x- term (- 17)

the factors are - 10 and - 7 , since

- 10 × - 7 = + 70 and - 10 - 7 = - 17 , then

(x - 10)(x - 7) = 0 ← in factored form

equate each factor to zero and solve for x

x - 7 = 0 ⇒ x = 7

x - 10 = 0 ⇒ x = 10

Please help and please hurry I have to submit it soon: The price of Stock A at 9 A.M. was ​$15.01. Since​ then, the price has been increasing at the rate of ​$0.13 each hour. At noon the price of Stock B was ​$15.76. It begins to decrease at the rate of ​$0.09 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

Answer: 8.3 hours

Step-by-step explanation: 15.76-15.01 is 0.75

Now just divide 0.75 from 0.09 and you get 8.3

Answer:

Step-by-step explanation:

Stock A= $15.01 increases by $0.13 an hour. $15.14

Stock B =$15.76 decreases by $0.09 an hour $15.65

15.65-15.14= 0.51

write the equation for a parabola with a focus at (6,-4)(6,−4)left parenthesis, 6, comma, minus, 4, right parenthesis and a directrix at y

Answers

The equation of the parabola is (x - 6)² = 6(y + 5.5).

Given that, a focus at (6,-4) and a directrix at y= -7.

We need to find the equation for a parabola.

What are focus and directrix?

Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).

The standard form of the equation of the parabola is  (x - h)² = 4p(y - k), where

The vertex of the parabola is (h , k)

The focus is (h, k + p)

The directrix is at y = k - p  

∵ The focus of the parabola is at (6, -4)

The coordinates of the focus are (h, k + p)

∴ h = 6

∴ k + p = -4 ⇒ (1)

∵ The directrix of the parabola is at y = -7

The directrix is at y = k - p

∴ k - p = -7 ⇒ (2)

Solve the system of equations to find k and p

Add equations (1) and (2) to eliminate p

∴ 2k = -11

Divide both sides

∴ k = -5.5

Substitute the value of k in equation (1) to find p

∵ -5.5 + p = -4

Add 5.5. to both sides

∴ p = 1.5

∵ The form of the equation is (x - h)² = 4p(y - k)

Substitute the values of h, k, and p in the form

∴ (x - 6)² = 4(1.5)(y - -5.5)

∴ (x - 6)² = 6(y + 5.5)

Therefore, the equation of the parabola is (x - 6)² = 6(y + 5.5).

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Your question is incomplete, probably the complete question/missing part is:

Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

solve (x-3)(x+8)+(2x-x^2)

Answers

The required solution of the given expression is 7x-24.

What is expression?

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.

Given:

The given expression is

[tex](x-3)(x+8)+(2x-x^{2} )[/tex]

According to given question we have

By the expansion theorem we have

The expression is

[tex](x-3)(x+8)+(2x-x^2)\\\\=x^{2} +8x-3x-24+2x-x^{2} \\\\=7x-24[/tex]

Therefore, the required solution of the given expression is 7x-24.

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Find the surface area of the figure

Answers

Answer: 208 in^2

Step-by-step explanation:

4 2*8 rectangles

1 8*8 square

4 5*8/2 triangles

4(2*8)+8*8+4(5*8/2)=

4(16)+64+4(5*4)=

64+64+4(20)=

128+80=208 in^2

Which of the following equations has nosolution? B= -B+ 2 B + 2= b + 2 B+ b = 2 b + 2 = b-2

Answers

The equation which has no solution among the answer choices as given in the task content is; b + 2 = b-2.

Which equation has no solution?

It follows from the task content that the equation which has no solution is to identified.

On this note, the equation in which case, the variable diminishes and the equality does not hold represents that which has no solution.

Hence, the required equation is; b + 2 = b-2.

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32. XY, given X(7, 2) and Y(2, 0)
Domain
Range

Answers

Based on the coordinates of XY which are X(7, 2) and Y(2, 0), the domain and range are:

Domain : (2, 7)Range: (0, 2)

What are domain and range?

The domain of a line refers to all the points on that line that the value of the x-axis can take.

In line XY, the only two x-axis values are 7 and 2. This means that the domain is therefore (2, 7).

The range of a line on the other hand, are all the points that the value on the y-axis can take.

The range in this case is therefore (0, 2).

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Which of the following represents (picture)

Answers

The interval that represents the inequality 1 < x ≤ 6 is given by:

B. (1,6].

What is the standard interval notation?

The standard interval notation of an interval of lower bound a and upper bound b is given by:

[a,b].

The inequality notation is:

a ≤ x ≤ b

The set builder notation is:

{x | a ≤ x ≤ b}.

In this problem, we are given the inequality 1 ≤ x ≤ 6, hence a = 1 and b = 6, and open at x = 1 and closed at x = 6, hence the interval is:

B. (1,6].

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(b) Find the equation of the straight line which passes through 81 +88 (i) the point (3, 2) and makes an intercept on the x-axis is twice as long as that on the y-axis. (ii) the point (-1, 3) whose intercept on the y-axis is thrice that on x-axis.​

Answers

3x+y=0 and x+2y=7

i)

a= intercept on x axis

b= intercept on y axis

from the question

a=2b

x/2b+ y/b=1

x+2y=2b

since it passes through the point (3,2)

then 3+4=2b

7/2=b

x+2y=7     putting the value of b

ii) given b =3a

then x/a+ y/ 3a =1

3x+y=3a

it passes through ( -1,3) then

-3+3=3a

a=0

3x+y=0

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- The circles are identical. Find the circumference of each circle. Round your
answer to the nearest tenth.
4x
6x - 6

Answers

Answer:

Circumference = 75.4

Step-by-step explanation:

Since the circles are identical, that means that the radii must be equal.

4x=3x+3

x=3

That means that radius = 12

The formula for the circumference = 2pi × radius

2pi × 12 = 24pi ≈ 75.4

Answer:

75.4 (nearest tenth)

Step-by-step explanation:

The diameter of a circle is the distance from one side of the circle to the other through the center. The diameter is the widest part of the circle.

The radius of a circle is the distance from the center to the circumference.  The radius is half the diameter of a circle.

We have been given the radius of the circle on the left:  r = 4x.

Therefore, as the diameter is twice the radius, the diameter of the circle on the left is:  d = 2(4x) = 8x

We have been given the diameter of the circle on the right:  d = 6x + 6

Equate the two diameters and solve for x:

⇒ 8x = 6x + 6

⇒ 8x - 6x = 6x + 6 - 6x

⇒ 2x = 6

⇒ 2x ÷ 2 = 6 ÷ 2

⇒ x = 3

Substitute the found value of x into one of the diameter expressions to find the diameter of both circles:

⇒ d = 8x

⇒ d = 8(3)

⇒ d = 24

Circumference of a circle

C = πd

(where d is the diameter)

Substitute the found diameter into the circumference formula:

⇒ C = πd

⇒ C = 24π

⇒ C = 75.39822...

⇒ C = 75.4 (nearest tenth)

Therefore, the circumference of each circle is 75.4 units (nearest tenth).

HELP I LITTERALLY DO NOT UNDERSTAND

Answers

Answer: what are the options tho?

Step-by-step explanation:

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