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Pepsi [2]
3 years ago
7

The radius of the base of a cylinder is decreasing at a rate of 9 millimeters per hour and the height of the cylinder is increas

ing at a rate of 2 millimeters per hour. At a certain instant, the base radius is 8 millimeters and the height is 3 millimeters. What is the rate of change of the surface area of the cylinder at that instant in square millimeters per hour?
a) 310pi
b) 155pi
c) -155pi
d) -310pi
Mathematics
1 answer:
ivann1987 [24]3 years ago
4 0

Answer:

<em>Answer: d) -310pi</em>

Step-by-step explanation:

<u>Instantaneous Rate of Change</u>

Is the change in the rate of change of a function at a particular instant. It's the same as the derivative value at a specific point.

The surface area of a cylinder of radius r and height h is:

A=2\pi r^2+2\pi r h

We need to calculate the rate of change of the surface area of the cylinder at a specific moment where:

The radius is r=8 mm

The height is h=3 mm

The radius changes at r'=-9 mm/hr

The height changes at h'=+2 mm/hr

Find the derivative of A with respect to time:

A'=2\pi (r^2)'+2\pi (r h)'

A'=2\pi 2rr'+2\pi (r' h+rh')

Substituting the values:

A'=2\pi 2(8)(-9)+2\pi ((-9) (3)+(8)(2))

Calculating:

A'=-288\pi +2\pi (-27+16)

A'=-288\pi +2\pi (-11)

A'=-288\pi -22\pi

A'=-310\pi

Answer: d) -310pi

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I think it would take 24 hours or 10 hours

explanation: if you have 4 hours from Erin, and 6 hours from Cathy, it’ll most likely be 10 hours because you’re trying to find out the total amount. (keyword: together & how many)
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3 years ago
A cone-shaped tent has a diameter of 12 ft and a height of 6 ft. What is the approximate volume of the tent? Question 2 options:
inessss [21]

Answer:

Step-by-step explanation:

The formula of volume of cone is

V=\frac{1}{3}\pi r^{2} h

where, r is the radius

we have given diameter = 12 =2r

r=6 ft

h is the height h=6 ft

\pi =3.14

Substitute the value in the formula,

V=\frac{1}{3}\pi r^{2} h

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V=\frac{1}{3}\times 3.14\times 36\times 6

V=226.08 ft^3

Therefore, The volume of cone is 226.08 cubic ft.

Read more on Brainly.com - brainly.com/question/9177514#readmore

3 0
3 years ago
Find the measure of the indicated angle
emmasim [6.3K]
I think the answer is 23
8 0
3 years ago
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AlekseyPX

Answer:

D. 220.16 Square feet

Step-by-step explanation: The shaded area is the space in the square not filled by the circle. So we need to find the area of the circle. The formula for area of a circle is A=\pi r^{2}. So we fill in this equation with the information we already know:

A=\pi 16^{2}

A=3.14*16^{2} Simplify the exponents

A=3.14*256 Multiply

A=803.84

So now we know the area of the circle we have to find the area of the square because the circle is inside the square. It is a simple 32*32 which is 1,024. Since we are looking for the shaded area we will subtract the area of the circle from the area of the square because the circle is not shaded.

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3 years ago
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Identify the constant of<br> proportionality (k)<br> 8Y = 16x<br> k=
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Answer:

JUST WRITE THIS AS YOUR ANSWER

Step-by-step explanation:

Step 1: Put together the general equation.

Step 2: Solve for the constant of proportionality.

Step 3: Plugging the constant into the equation, solve for the unknown variable.

Let's solve a few problems to see how this works, shall we?

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

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So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

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We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

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Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

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3 years ago
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