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2 years ago

Find the domain of this equation x+5/x+5 Will award brainliest BIG BOI POINTS

Mathematics

1 answer:

Otrada [13]2 years ago

7 0

Do you have what the equation is supposed to equal to?

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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

Find the size of angle X.

hodyreva [135]

Answer:

Because the sum of the interior angles of a triangle is 180,

X=180-(65+35)

X=180-100=80

3 0

2 years ago

1. On a number line, would you find −3 5/11 to the left or to the right of −3.4545? Explain how you know

AfilCa [17]

Answer:

<em> A number on the left is less than a number on the right. A number on the right is greater than a number on the left. You can also try the zoomable number line. Place these people on the number line to find who is poorest and who is richest.</em>

5 0

2 years ago

Ray is boiling water at 99°C. Which of the following best describes 99°C?<br> please help

kolezko [41]

99+99=198 so it is 198°C

7 0

3 years ago

Which scenario involves the value of greatest magnitude?

Sonbull [250]

Answer:

D. A withdrawal of $30 from a bank account

Step-by-step explanation:

When it says magnitude it doesn't matter if it's a positive or negative number.

So it's just asking which number is the greatest which is 30.

I hope my explanation makes sense and helps you out.

5 0

2 years ago