Please help<br><br> Select the expressions equivalent to 18 + 3r.

The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6

Arlecino [84]

Answer:

$\approx \bold{6544\ in^3/sec}$

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

$\dfrac{dr}{dt} = +7\ in/sec$

(This is increasing rate so positive)

Rate of change of height of cylinder:

$\dfrac{dh}{dt} = -6\ in/sec$

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

$V = \pi r^2h$

Differentiating it w.r.to 't':

$\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)$

Let us have a look at the formula:

$1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))$

$3.\ \dfrac{dx^n}{dx} = nx^{n-1}$

Applying the two formula for the above differentiation:

$\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}$

Now, putting the values:

$\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}$

So, the answer is: $\approx \bold{6544\ in^3/sec}$

3 0

3 years ago

What is the range of f(x)?

adoni [48]

Answer:

best ans is { f(x)| –∞ < f(x) ≤ 4}

Step-by-step explanation:

usually to find the range of a fn, u need to see what the value can be. the graph show only a small range of x values. but u can see f(x) is definitely <u><</u> 4. so the ans is { f(x)| –∞ < f(x) ≤ 4}

6 0

3 years ago

Read 2 more answers

You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12 equal slices. Before you

Karo-lina-s [1.5K]

Answer:

3.5355 inches

Step-by-step explanation:

Area should be same the concentric circle and rest piece .

let's consider the radius of concentric circle as r

so it's area is π r²

area of whole circle is π (5)" ( because diameter is 10 inches)

so the area of rest piece is π (5)² - π r²

π (5)² - π r² = π r²

5² = 2r²

r² = 25/2

r = √(25/2)

r = 3.5355 inches

4 0

2 years ago

Which quadratic equation has roots - 2 and 1/5 :

Sladkaya [172]

Answer:

$5 {x}^{2} \: + \: 8x \: - 2 \: = \: 0$

Step-by-step explanation:

$sum \: of roots = - 2 + \frac{1}{5} = - \frac{8}{5} \\ product \: of \: roots = - 2 \times \frac{1}{5} = - \frac{2}{5} \\ from \: general \: equation \\ a {x}^{2} + bx + c = 0 \\ {x}^{2} + \frac{8}{5} x \: - \frac{2}{5} = 0 \\ 5 {x}^{2} \: + \: 8x \: - 2 \: = \: 0$

7 0

2 years ago

Austin is building a miniature replica of the empire state building. the actual empire state building is 1,423 feet tall and 6,0

Fofino [41]

60/6000 = x/1423

100/1 = 1423/x

100x = 1423

x = 14.23 --> About 14 cm

6 0

3 years ago

Please help Select the expressions equivalent to 18 + 3r.