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At a sand and gravel plant, sand is falling off a conveyor, and onto a conical pile at a rate of 10 cubic feet per minute. The d

kherson [118]

Answer:

dh/dt=9.82x10^-3 ft/min

Step-by-step explanation:

1. You have that the rate is10 ft³/min. Then:

dV/dt=10

2. The formula for calculate the volume of a cone, is:

V=1/3(πr²h)

"r" is the radius and "h" is the height.

3. The diameter of the base of the cone is approximately 3 times the altitude. Then, the radius is:

r=diameter/2

diameter=3h

r=3h/2

4. When you susbstitute r=3h/2 into the formula V=πr²h/3, you have:

V=1/3(πr²h)

V=1/3(π(3h/2)²(h)

V=1/3(π9h²/4)(h)

V=9πh³/12

5. Therefore:

dV/dt=(9πh²/4)dh/dt

h=12

dV/dt=10

6. When you substitute the values of dV/dt and h into dV/dt=(9π(12)²/4)dh/dt, you have:

dV/dt=(9π(12)²/4)dh/dt

10=(1017.876)

7. Finally, you obtain:

dh/dt=10/1017.876

dh/dt=9.82x10^-3 ft/min

5 0

3 years ago

Help please! I got the answer wrong the first timee and im having trouble understanding!!!

andreyandreev [35.5K]

Answer:

the answer is 30 because if x = 3 they you would do 8x3 and get 24 then add the 6 to get 30

Step-by-step explanation:

Plz give brainly

5 0

3 years ago

Read 2 more answers

Choose the graph of y = 2cosx

valentinak56 [21]

Answer:

B

Step-by-step explanation:

Because C, Is greater than, X.

5 0

3 years ago

**Spam answers will not be tolerated**

Morgarella [4.7K]

Answer:

$f'(x)=-\frac{2}{x^\frac{3}{2}}$

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

3 years ago

Bill spent $42 on fruit at the grocery store. He spent a total of $60 at the store. What percentage of the total did he

Neporo4naja [7]

Answer:

70%

Step-by-step explanation:

To find the total percentage of his $60 dollars that he spent on fruit, we simply take the amount of money spent on fruit divided by the total spent.

% spent on fruit = 42 / 60

% spent on fruit = 0.7

% spent on fruit = 70 %

Cheers.

3 0

3 years ago

Read 2 more answers

Plzzzz answer fast......​

Plzzzz answer fast......