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VladimirAG [237]

3 years ago

15

Write an expression equivalent to 10+2m by factoring out the greatest common factor from the two terms

1 answer:

Rina8888 [55]3 years ago

5 0

The greatest common factor is 2. So you have to factor out 2 from the equation. So it is (5+m)2.

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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

W+1/8 =8 plzz help me i need it

Marina CMI [18]

Answer:

w = 7 7/8

Step-by-step explanation:

w + 1/8 = 8

First, subtract 1/8 from both sides of the equation

w + 1/8 = 8

- 1/8 - 1/8

w = 7 7/8

8 0

3 years ago

Read 2 more answers

Two plants, plant A and B, are being grown in a science experiment. Plant A is 6 cm tall and growing at a rate of 4 cm/day. Plan

Irina18 [472]

By the second day of growth

6 0

3 years ago

What is the length of QR?

Elena L [17]

Answer:

C

Step-by-step explanation:

Since the triangle is right with hypotenuse QR

Use Pythagoras' identity to solve for QR

The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is

QR² = 8² + (8 $\sqrt{3}$ )²

= 64 + 192

= 256 ( take the square root of both sides )

QR = $\sqrt{256}$ = 16

7 0

3 years ago

What is the equation shown in the graph? Explain your answer.

Yuliya22 [10]

Answer:

y=x

Step-by-step explanation:

The graph is going 1 up and 1 to the right. You can plug in a value for x and get y. So if you plug in 1 for x, you get 1 for y and if u plug in 2 for x, you get 2 for y, so when you graph (1, 1) and (2, 2) you know the graph is y=x.

(can I get brainliest please)

4 0

3 years ago