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3 years ago

What is the exact volume of the cone?

Mathematics

1 answer:

zlopas [31]3 years ago

4 0

Answer:

The third choice, (160/3)π cm³

Step-by-step explanation:

The formula for volume of a cone is

V = (1/3)πr²h where r is the radius of the base, and h is the height

Here, r = 4 and h = 10. plug those values in and simplify...

V = (1/3)π(4²)(10)

V = (1/3)π(16)(10)

V = (1/3)π(160)

V = (160π)/3

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How do i solve v=pi/3*r (squared)h for h

Colt1911 [192]

$V=\dfrac{\pi}{3}\cdot r^2h\ \ \ \ \ |multiply\ both\ sides\ by\ 3\\\\\pi r^2h=3V\ \ \ \ |\divide\ both\ sides\ by\ \pi r^2\\\\\boxed{h=\dfrac{3V}{\pi r^2}}$

3 0

3 years ago

Show that ( 2xy4 + 1/ (x + y2) ) dx + ( 4x2 y3 + 2y/ (x + y2) ) dy = 0 is exact, and find the solution. Find c if y(1) = 2.

fredd [130]

$\dfrac{\partial\left(2xy^4+\frac1{x+y^2}\right)}{\partial y}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

$\dfrac{\partial\left(4x^2y^3+\frac{2y}{x+y^2}\right)}{\partial x}=8xy^3-\dfrac{2y}{(x+y^2)^2}$

so the ODE is indeed exact and there is a solution of the form $F(x,y)=C$ . We have

$\dfrac{\partial F}{\partial x}=2xy^4+\dfrac1{x+y^2}\implies F(x,y)=x^2y^4+\ln(x+y^2)+f(y)$

$\dfrac{\partial F}{\partial y}=4x^2y^3+\dfrac{2y}{x+y^2}=4x^2y^3+\dfrac{2y}{x+y^2}+f'(y)$

$f'(y)=0\implies f(y)=C$

$\implies F(x,y)=x^2y^3+\ln(x+y^2)=C$

With $y(1)=2$ , we have

$8+\ln9=C$

$\boxed{x^2y^3+\ln(x+y^2)=8+\ln9}$

8 0

3 years ago

Help me please!!! help!

Alenkinab [10]

Answer:

234

Step-by-step explanation:

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3 years ago

A man walk 1/10 meters per second how long will it take him to walk in 5 minutes.

Stolb23 [73]

1 sec=1/10 m

5 min=300 sec

thus, 1/10 *300

=30 m

He will walk 30m in 5 min

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dusya [7]

Answer:

2.236

Step-by-step explanation:

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4 years ago

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