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3 years ago

8

Which answer is correct ?

1 answer:

Radda [10]3 years ago

7 0

Answer:

C the table and the equation

Hope this helps :)

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The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

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

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

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

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

The height h in feet of a ball thrown vertically upward from the top of a 288-foot tall building is given by h=288+48t-16t^2 whe

mr Goodwill [35]

6 sec can take penny to strike the ground.

Solution:

Given data:

$H_0=288$ feet

$V_0=48$ feet

$h(t)=288+48t-16t^2$

Re-arrange the terms from greatest degree to smallest degree.

$h(t)=-16t^2+48t+288$

We can solve it by applying quadratic formula,

$$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here a = –16, b = 48, c = 288

$$t=\frac{-48\pm \sqrt{48^2-4(-16)(288)}}{2(-16)}$

$$t=\frac{-48\pm \sqrt{2304+18432}}{-32}$

$$t=\frac{-48\pm \sqrt{20736}}{-32}$

$$t=\frac{-48\pm144}{-32}$

Now, write find two t's using plus and minus operation.

$$t=\frac{-48+144}{-32},\ \ t=\frac{-48-144}{-32}$

$$t=\frac{96}{-32},\ \ t=\frac{-192}{-32}$

t = –3 (or) t = 6

We cannot write time is negative. so neglect t = –3.

Therefore t = 6.

Hence 6 sec can take penny to strike the ground.

8 0

3 years ago

Somebody please help. And be fr cause I’ll give that brainilest or whatever it’s called but please be the right answer.

bearhunter [10]

130 you multiply the left side by 13 to get the right side.

8 0

3 years ago

What is the area of a square if one side is 14 centimeters long?

natima [27]

Answer:

A=a2=142=196cm²

Answer: 196 cm²

hope this helps :)

5 0

2 years ago

Read 2 more answers

Marina correctly simplified the expression (-4a^-2 b^4)/(8a^-6b^-3) assuming that a does not equal 0 and b does not equal 0. Her

Elza [17]

For this case we have the following expression:
(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)
We can rewrite the expression using properties of exponents.
We have then:
(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))
Rewriting we have:
(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))
(-1/2) * ((a ^ 4) (b ^ 7))
-1 / 2a ^ 4b ^ 7
Answer:
The exponent of the variable b in Marina's solution should be 7

7 0

4 years ago

Read 2 more answers