4 years ago

????????????????????

Mathematics

1 answer:

Dmitry_Shevchenko [17]4 years ago

6 0

The answer is 1/9.

If you put it in a calculator you'll get 0.11111111.....
that's a repeating decimal.

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Use the definition of the derivative to differentiate v=4/2 pie r^3

nata0808 [166]

I suspect 4/2 should actually be 4/3, since 4/2 = 2, while 4/3 would make V the volume of a sphere with radius r. But I'll stick with what's given:

$\displaystyle \frac{dV}{dr} = \lim_{h\to0} \frac{2\pi(r+h)^3-2\pi r^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{(r^3+3r^2h+3rh^2+h^3)- r^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} \frac{3r^2h+3rh^2+h^3}{h}$

$\displaystyle \frac{dV}{dr} = 2\pi \lim_{h\to0} (3r^2+3rh+h^2)$

$\displaystyle \frac{dV}{dr} = 2\pi \cdot 3r^2 = \boxed{6\pi r^2}$

In Mathematica, you can check this result via

D[4/2*Pi*r^3, r]

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3 years ago

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pshichka [43]

Answer:

m^2-4m=-29

m^2-4m+4=-29+4

(m-2)^2=-25

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3 years ago

Kristin wants to make 12 ml of an 8% alcohol solution by mixing together a 32% alcohol solution and pure water. How much of each

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Answer:

6% of each

Step-by-step explanation:

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$\frac{1}{3}$

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