Find the interest rate implied by the following combinations of present and future values: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

Present Value Years Future Value Interest Rate
$340 12 611 %
153 5 225 %
240 8 240 %
British government 3.6% perpetuities pay £3.6 interest at the end of each year forever. Another bond, 2.1% perpetuities, pays £2.10 a year forever.

a. What is the value of 3.6% perpetuities if the long-term interest rate is 5.6%? (Round your answer to 2 decimal places.)

b. What is the value of 2.1% perpetuities? (Round your answer to 2 decimal places.)

Suppose that the value of an investment in the stock market has increased at an average compound rate of about 5% since 1901. It is now 2019.

a. If your great grandfather invested $1,000 in 1901, how much would that investment be worth today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Investment

b. If an investment in 1901 has grown to $1 million, how much was invested in 1901? (Enter your answer in dollars. Do not round intermediate

Present value

Answer:

6 pepper fruits

Step-by-step explanation:

Given the following :

Fraction of pepper in terms of tomato = 2/3

Number of fruits on pepper plant = 9

Therefore number of pepper fruits on pepper plant:

2/3 * number of tomato fruits

2/3 * 9

(2 * 3) = 6

6 pepper fruits.

Answer: 4.1 feet : 4 feet

Step-by-step explanation:

From the question, we are informed that Bradley estimated the height of a tree at 2.5 meters. Carla estimated that tree's height at 8 feet.

The conversion ratio be used to compare Bradley's and Carla's estimates of the tree's height when measured in feet goes thus:

Since 1 feet = 0.305 meters

2.5 meters will be = 2.5/0.305 = 8.2 feet

Therefore the conversion ratio will be:.

= 8.2 : 8

Reducing to lowest term will be

= 4.1 feet : 4 feet.

= 4.1 : 4

To find the position function s(t) of a particle given the acceleration function a(t) and initial conditions, we need to integrate the acceleration function twice with respect to time.

Given the acceleration function a(t) = t^2 - 8t + 7, we can integrate it once to find the velocity function v(t):

v(t) = ∫(t^2 - 8t + 7) dt

= (1/3)t^3 - 4t^2 + 7t + C1

Using the initial condition s(0) = 0, we can find the constant of integration C1:

s(0) = (1/3)(0)^3 - 4(0)^2 + 7(0) + C1

= C1

Therefore, C1 = 0, and the velocity function becomes:

v(t) = (1/3)t^3 - 4t^2 + 7t

Now, we can integrate the velocity function v(t) to find the position function s(t):

s(t) = ∫((1/3)t^3 - 4t^2 + 7t) dt

= (1/12)t^4 - (4/3)t^3 + (7/2)t^2 + C2

Using the initial condition s(1) = 20, we can find the constant of integration C2:

s(1) = (1/12)(1)^4 - (4/3)(1)^3 + (7/2)(1)^2 + C2

= 20

Therefore, C2 = 20, and the position function becomes:

s(t) = (1/12)t^4 - (4/3)t^3 + (7/2)t^2 + 20

Hence, the position of the particle is given by the function s(t) = (1/12)t^4 - (4/3)t^3 + (7/2)t^2 + 20.

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The angle of depression of the fish from the given height to the bottom of the lake is 60° .

The bird caught the fish at site A, flew it 100 yards to location B, and then dropped it off at location C. (which is horizontally 50 yards from A).

The right angled triangle BAC is equal to the length of the perpendicular and base .

The angle the bird creates with the water piques our interest (horizontal). This angle is BAC. We can claim to be knowledgeable about the "hypotenuse" and "adjacent" side of the right triangle to angle BAC. Since the cosine relationship between the hypotenuse and its neighbors exists, we can write:

cos BAC = 50/100

BAC = cos ⁻¹ 1/2

BAC = 60 °

Here, our goal is to determine the length (distance) of segment BC. We can say that BC is "opposite" to the angle BAC, which we discovered to be 60 degrees. The hypotenuse is known to be 100. So let's utilize sine since sine is the ratio of the hypotenuse's opposite.

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Answer: 1 batch

Step-by-step explanation:

1 batch = 24 - 36 cookies

So here we have 23 cups of sugar, and we know that each chocolate chip cookie uses 1 cup, so we can only make 23 cookies

Which is only 1 batch of cookies can be made.

Answer:

23 batches of cookies

Step-by-step explanation:

I think this problem is kind of straightforward:

1 bag = 23 cups

1 batch = 1 cup

We need to find how many batches = 1 bag

To find that out, we have to divide bags by batches, but we don't know the number of batches yet. (Also, they're not the same units)

Instead, we can use the respective cups of sugar to divide (because they do have the same units)

So we divide the number of cups of sugar in a bag (23) by the number of cups in a batch (1):

23 ÷ 1 = 23 batches

I hope this explanation was simple enough

The radius of the base of the cone-shaped block is approximately 10.69 inches.

We can use the formula for the volume of a cone to find the radius of its base. The volume of a cone is given by the formula  :

V = (1/3)πr^2h

Where

We know that the volume of the cone-shaped block is 125 cubic inches, and we know the height is the same for all blocks. So we can solve for the radius:

125 = (1/3)πr^2h

125 = (1/3)πr^2h

375 = πr^2h

r^2 = 375/π

r ≈ 10.69

So we can conclude that the radius of the base of the cone-shaped block is approximately 10.69 inches.

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The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5

(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

Given: Function f(x) is (x - 5)3(x + 2)2

If a curve touches the x-axis then f(x) = 0

⇒ (x - 5)3(x + 2)2 = 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ (x - 5)3 = 0 and (x + 2)2 = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

x1 =1.317

x2=-5.317

Step-by-step explanation:

(a) The ratio of the areas, A2/A1, is: A2/A1 =\((16πr1^2)/(4πr1^2) = 4\)

(b)  The ratio of the areas A2/A1 is 4, and the ratio of the volumes V2/V1 is 8.

(a) To find the ratio of the areas, A2/A1, we need to substitute the radii of sphere 2 and sphere 1 into the formula for surface area.

Let's denote the radius of sphere 1 as r1 and the radius of sphere 2 as r2, where r2 = 2r1.

For sphere 1:

A1 =\(4πr1^2\)

For sphere 2:

A2 = \(4πr2^2 = 4π(2r1)^2 = 4π(4r1^2) = 16πr1^2\)

Therefore, the ratio of the areas, A2/A1, is:

A2/A1 =\((16πr1^2)/(4πr1^2) = 4\)

(b) Similarly, to find the ratio of the volumes, V2/V1, we substitute the radii into the formula for volume.

For sphere 1:

V1 = \((4/3)πr1^3\)

For sphere 2:

V2 = \((4/3)πr2^3 = (4/3)π(2r1)^3 = (4/3)π(8r1^3) = (32/3)πr1^3\)

Therefore, the ratio of the volumes, V2/V1, is:

V2/V1 = \(((32/3)πr1^3)/((4/3)πr1^3) = 8\)

So, the ratio of the areas A2/A1 is 4, and the ratio of the volumes V2/V1 is 8.

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Answer:

Step-by-step explanation:

Equation of the line for container O and container P will be in the form of,

y = mx + b

Here m = slope of the line = Change in amount of water per minute

b = y-intercept

From the graph attached,

y-intercept 'b' represents the initial amount of water in the container.

For container O, initial amount of water in the container is 1000 mL.

Similarly, initial amount in the container is 900 mL.

Answer: The expression 3/4÷ 1/12 has the highest value

Step-by-step explanation: We examine the value of all the 4 terms and compare them.

3/4÷1/3=(3/4)*3=9/4

1 7/8÷ 1/2=(17/8)*(2)=17/4

3/4÷ 1/12=(3/4)*(12)=9

7/8÷1/3=(7/8)*3=(21/8)

Taking all the denominators as 8 we get

18/8 34/8 72/8 21/8

So clearly the 3rd expression is the largest one

The value of (gof)(x) is \(3x^2\) - 12x + 17

The first function is

g(x) = \(3x^2\) + 5

The second function is

f(x) = x - 2

The function is the mathematical statement that shows the relationship between one variable and another variable. If one variable is independent variable and another variable is dependent variable. The function consist of the different variable, numbers and mathematical operators

Then the value of (gof)(x) is

g(f(x) = g(x-2)

Then,

g(x - 2) = 3 × \((x-2)^2\) + 5

Expand the terms

g(x - 2) = 3 × (\(x^2\) - 4x + 4) +5

g(x - 2) = \(3x^2\) - 12x + 12 +5

Add the terms

g(x - 2) = \(3x^2\) - 12x + 17

Hence, the value of (gof)(x) is \(3x^2\) - 12x + 17

The complete question is

If g(x) = 3x^2+ 5

f(x) = x - 2

Find the value of (gof)(x)

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Answer:

47

Step-by-step explanation:

Remember triangle always equal to 180

180=70+4x-5+6x-15

x=13

4(13)-5

47

Angle A is 47

The correct option is 9 feet.

The height from the ground the white plank after the motion is 9 feet.

Anything that spins or moves in a circular route is said to be in rotational motion. It's also referred to as angular motion and circular motion. The motion can be uniform (— in other words, the velocity v remains constant) and non-uniform, but it must be circular.

Now, according to the question;

The wheel's radius is 4 feet.

The height of a bottom of a wheel from the ground equals 1 foot.

π/3 radians is the angle where the wheel is rolled.

The following relationship describes the height of a revolving wheel.

f(t) = A·sin(B·t + C) + D

Where,

D = Mid line =  4 + 1 = 5 feet

B·t = π/3

C = 0

amplitude; A = 4

Substituting the values in the function;

f(t) = 4×sin(π/3) + 5 = 8.464 ft

f(t) = 9 (approx)

Therefore, the plank's height after the /3π/3 rotation motion = 9 ft.

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Answer:

(C) 7 Feet


Just did it :)

Answer:

Pentagon - 5 sides = 5 x 4 = 20

Hexagon - 6 sides = 6 x 5 = 30

Nanagon - 9 sides = 9

20 + 30 + 9 = 59 IN TOTAL

Step-by-step explanation:

The expression (3) (15) + (8) (9) is equivalent to 45 + 72 using the GCF and the distributive property.

To find an expression equivalent to 45 + 72 using the greatest common factor (GCF) and the distributive property, you can use the option:

(3) (15) + (8) (9).

Here's the breakdown:

Step 1: Find the GCF of 45 and 72.

The GCF of 45 and 72 is 9.

Step 2: Express 45 and 72 as multiples of their GCF.

45 can be expressed as 9 * 5.

72 can be expressed as 9 * 8.

Step 3: Apply the distributive property.

Using the distributive property, you can rewrite the expression as follows:

(9) (5) + (9) (8).

Step 4: Simplify.

Evaluating the expression, you get:

45 + 72 = (9) (5) + (9) (8).

Therefore, the expression (3) (15) + (8) (9) is equivalent to 45 + 72 using the GCF and the distributive property.

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For minima,

C'(x) = 0

6x-30 = 0

x = 5

If C"(x) >0, then minima

So, C"(x) = 6 > 0

So, for x = 5 , thr value of C(x) will be minimum.

Option C is correct

By writing all the numbers as decimals, we can see that the correct option is D, the correct inequality is:

23% < 0.85 < four and one fourth

Here we have 3 numbers, which are:

0.85

23%

4 + 1/4.

So we have a decimal number, a percentage number, and a mixed number, let's write all of them as decimal numbers.

For the percentage, to get the decimal form we just need to divide it by 100%, so we will get:

23%/100% = 0.23

For the mixed number we have:

4 + 1/4 = 4 + 0.25 = 4.25

Then our 3 numbers are:

0.85

23% = 0.23

4 + 1/4 = 4.25

Then the correct order is:

23% < 0.85 < 4 and 1/4.

So the correct inequality is the one in option D.

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Answer:

d

Step-by-step explanation:

Using the formula they gave us:

Cost of shipping = 2.79 + 0.38(8)

Cost of shipping = 2.79 + 3.04

Cost of shipping = 5.83(currency unit)

Answer:

x=10

Step-by-step explanation:

Answer:

(-1,3)

Step-by-step explanation:

Solve for x in the first equation

3x = 6 - 3y

9x - 5y= -24

Replace all occurrences of x with 2 - y in each equation

9(2 - y) - 5y = -24

x = 2 - y

Simplify the left side

18 - 4y = -24

x = 2 - y

Solve for y in the first equation

-14y = -42

x = 2 - y

y=3

x = 2- y

Replace all occurrences of y with 3 in each equation

x=-1

y=3

(-1,3)

Hope this helps!

Please give brainliest :)

If you need more help with these types of equations reach out to me!

Simplifying

3x + 6 = 9x + -24

Reorder the terms:

6 + 3x = 9x + -24

Reorder the terms:

6 + 3x = -24 + 9x

Solving

6 + 3x = -24 + 9x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9x' to each side of the equation.

6 + 3x + -9x = -24 + 9x + -9x

Combine like terms: 3x + -9x = -6x

6 + -6x = -24 + 9x + -9x

Combine like terms: 9x + -9x = 0

6 + -6x = -24 + 0

6 + -6x = -24

Add '-6' to each side of the equation.

6 + -6 + -6x = -24 + -6

Combine like terms: 6 + -6 = 0

0 + -6x = -24 + -6

-6x = -24 + -6

Combine like terms: -24 + -6 = -30

-6x = -30

Divide each side by '-6'.

x = 5

Simplifying

x = 5

The approximate change in surface area under the given condition if the radius increases by 0.01 cm is 3.54 cm².

The derived formula using the principles of surface area of a sphere is given as

A = 4πr²

staging the values to calculate the surface area before the increase in radius

A = 4 x π x (12)²

A = 4 x 3.14 x 144

A ≈ 1809.56 cm²

From the given question if the radius increases by 0.01 then new radius is 12.01cm

Therefore, the new surface area derived is

A' = 4π(12.01)²

A' = 4 x 3.14 x(12.01)²

A' ≈ 1813.1 cm²

considering the recent events the change in surface area

ΔA = A'-A ≈ 1813.1 - 1809.56 ≈ 3.54 cm²

The approximate change in surface area under the given condition if the radius increases by 0.01 cm is 3.54 cm².

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To verify the conditions of a binomial situation, there are three conditions that need to be met. These conditions are:
Fixed number of trials: The number of trials must be fixed, meaning that a specific number of experiments or observations are conducted. For example, flipping a coin 10 times or rolling a dice 20 times.

Independent trials: Each trial must be independent of each other, meaning that the outcome of one trial does not affect the outcome of the others. This ensures that each trial has the same probability of success or failure. For example, if we are flipping a fair coin, each coin flip is independent of the others. Two possible outcomes: There must be only two possible outcomes for each trial - success or failure. These outcomes must be mutually exclusive and exhaustive. For example, in a coin flip, the outcome can either be heads (success) or tails (failure). To provide evidence of whether these conditions are satisfied, we can look at the specific situation described in the post. If any of these conditions are not met or unclear, we need to identify and explain what is wrong or missing. It is important to carefully analyze the context and details provided to determine if the binomial conditions are satisfied. To verify the conditions of a binomial situation, we need to consider three conditions from the textbook. Firstly, the number of trials must be fixed. For example, if we are conducting an experiment of flipping a coin, we need to determine the specific number of flips. This ensures that there is a consistent number of trials in the situation. Secondly, each trial must be independent of each other. This means that the outcome of one trial should not affect the outcome of the others. For instance, if we are flipping a fair coin, each flip is independent, and the outcome of the previous flip does not impact the outcome of the next flip. Lastly, there must be two possible outcomes for each trial - success or failure. These outcomes should be mutually exclusive and exhaustive. In the case of flipping a coin, the possible outcomes are heads (success) or tails (failure). By verifying these conditions, we can ensure that the situation meets the criteria for a binomial scenario.

To verify the conditions of a binomial situation, it is important to check if the number of trials is fixed, if each trial is independent, and if there are only two possible outcomes. By ensuring that these conditions are met, we can confidently identify a situation as a binomial scenario.

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The average distance that the airplane covered in three flights is 2036 kilometers, time in trip from Hongkong to Manila is 1.468 hours, time in trip from Singapore to Manila is 3.146 hours, time in trip from Korea to Manila is 3.422 hours.

Given the distance that an airplane covered in three different trips:

Hongkong-Manila: 1116 kilometers, Singapore-Manila: 2391 kilometers,

Korea-Manila: 2601 kilometers.

We are required to find the average distance traveled by the airplane in the three trips, the time it took in each trip if the speed of airplane is 760 km/h and the trip that took the longest time to travel.

Average distance that airplane travelled in the three trips=(1116+2391+2601)/3

=6108/3

=2036 kilometers

We know that speed=distance/time.

Time=Distance/speed

Time in trip from Hongkong to Manila=1116/760=1.468 hours

Time in trip from Singapore to Manila=2391/760=3.146 hours

Time in trip from Korea to Manila=2601/760=3.422 hours

We can observe that the trip from Korea to Manila took longest time to travel.

Hence the average distance that the airplane covered in three flights is 2036 kilometers, time in trip from Hongkong to Manila is 1.468 hours, time in trip from Singapore to Manila is 3.146 hours, time in trip from Korea to Manila is 3.422 hours and the trip from Korea to Manila took longest time to travel.

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The numbers 31.3 sec, 41.05 sec, and 42.015 sec represent continuous data since time measurements can take on any value within a given range. Therefore, these numbers are not discrete but continuous.

The numbers, 31.3 sec, 41.05 sec, and 42.015 sec, represent the times taken by the runners to complete their runs. In this case, the numbers are continuous.

Continuous data refers to measurements that can take any value within a certain range or interval. In the context of measuring time, it is possible to have infinitely many possible values between any two given points. For example, between 31.3 sec and 31.31 sec, there can be an infinite number of additional decimal places.

Discrete data, on the other hand, consists of values that are separate and distinct with no intermediate values possible. Discrete data is typically based on counting or whole numbers, such as the number of runners or the number of wins in a competition.

In this scenario, the times of the runners are measured using a continuous scale, where the smallest unit of time can be divided further into smaller increments. Therefore, the times of the runners, 31.3 sec, 41.05 sec, and 42.015 sec, are considered continuous data.

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The length of the side opposite the angle of 53.1 degrees in a right triangle with a hypotenuse of 10 cm is 8 cm.  (A)

This can be found using trigonometry and the Pythagorean theorem. The trigonometric function sine can be used to find the ratio of the length of a side to the length of the hypotenuse given an angle in a right triangle.

In this case, the sine of the angle 53.1 degrees is the ratio of the length of the side opposite the angle to the length of the hypotenuse, which is 10 cm.

Therefore, the length of the side opposite the angle 53.1 degrees can be found by multiplying the sine of the angle by the length of the hypotenuse, which is 10 cm * sin(53.1) = 8 cm.

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Based on the numbers that Joe selected, the people selected were D) Alan, Eugene, Martin, Sam.

The 17th person was selected and if we assigned numbers from 1 to 20 to the alphabetized list, we would find that number 17 is Sam.

The 5th person is Eugene and the 1st person is Alan. The 12th person is Nathan.

In conclusion, option D is correct.

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Answer:

Trinomial: (2x² – 5x) + (4x – 10)

GCF: x (2x – 5) + 2 (2x – 5)

Step-by-step explanation:

2x² – x – 10

The equation above can be factorised as follow:

2x² – x – 10

Multiply the first term (i.e 2x²) and the last term (i.e –10) together.

2x² × (–10) = –20x²

Find two factors of –20x² such that when we add them together, it will result to the 2nd term in the equation (i.e –x).

The factors are 4x and –5x.

Next, replace –x in the equation above with 4x and –5x. This is illustrated below:

2x² – x – 10

2x² – 5x + 4x – 10

Next, factorise

2x² – 5x + 4x – 10

Trinomial: (2x² – 5x) + (4x – 10)

GCF: x (2x – 5) + 2 (2x – 5)

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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