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murzikaleks [220]

3 years ago

9

Please help! ASAP will give brainiest

2 answers:

katen-ka-za [31]3 years ago

8 0

I got a decimal,10.66.

Zanzabum3 years ago

7 0

I got 10.66 as a decimal

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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

2 years ago

What is 92119 rounded to the nearest thousand

Leokris [45]

Answer:

92000

Step-by-step explanation:

2119 is less then 500

6 0

2 years ago

Read 2 more answers

A 8 ft tall cardboard box standing next to a man casts a 20 ft shadow. If the man casts a shadow that is 15 ft long, then how ta

Nataliya [291]

Answer:

The answer is that he would be 27 ft tall

7 0

2 years ago

At the city museum, child admission is 6.10 and adult admission is 9.40. On wednesday, 125 tickets were sold for a total sales o

murzikaleks [220]

55 adult tickets. Set up 2 equations: c+a=125 and 6.1c+9.4a=944. Isolate either variable from first equation and plug into second to find that 55 adult tickets were sold and 70 children’s tickets

7 0

2 years ago

Help me please help pleaseeeeeeeeeeeee

LenaWriter [7]

Answer:

(8,3)

Step-by-step explanation:

Point c is seven units away from the line x = 1

So we move seven units to the right of the line x = 1

the x value = 8

y value = 3

Coordinates = (8,3)

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

3 0

2 years ago