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4 years ago

Consider this composite figure.

Mathematics

2 answers:

Feliz [49]4 years ago

8 0

Answer:

$V=39\pi\ cm^3$

Step-by-step explanation:

we know that

The volume of a cone is given by the formula

$V=\frac{1}{3}\pi r^{2} h$

where

r is the radius of the circular base of cone

h is the height of the cone

step 1

Find the volume of the top cone

we have

$r=3\ cm\\h=5\ cm$

substitute

$V=\frac{1}{3}\pi (3)^{2} (5)$

$V=15\pi\ cm^3$

step 2

Find the volume of the bottom cone

we have

$r=3\ cm\\h=8\ cm$

substitute

$V=\frac{1}{3}\pi (3)^{2} (8)$

$V=24\pi\ cm^3$

step 3

Find the exact volume of the composite figure

Adds the volume of the top cone plus the volume of the bottom cone

$V=(15\pi+24\pi)=39\pi\ cm^3$

Nana76 [90]4 years ago

5 0

Answer: The answer is 39. It's correct:)

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4 years ago

One serving of soybeans contains 14 grams of protein and 8 grams of fat. One serving of rice contains 4 grams of protein and 1/2

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Answer: 1.8 servings of soybean and 1.2 servings rice will be needed.

Step-by-step explanation:

Let x be the number of soybeans and y be the number of rice.

Then , According to the question , we have

$14x+4y=30\\\Rightarrow\ 7x+2y=15..................................(1)\\\\ 8x+\frac{1}{2}y = 15\\\Rightarrow\ 16x+y=30.............................(2)$

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$32x+2y=60................................(3)$

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4 years ago

Determine whether each of the following functions is a solution of laplace's equation uxx uyy = 0.

ratelena [41]

Both functions are the solution to the given Laplace solution.

Given Laplace's equation: $u_{x x}+u_{y y}=0$

We must determine whether a given function is the solution to a given Laplace equation.
If a function is a solution to a given Laplace's equation, it satisfies the solution.

(1) $u=e^{-x} \cos y-e^{-y} \cos x$

Differentiate with respect to x as follows:

$u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x$

Differentiate with respect to y as follows:

$u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x$

Supplement the values in the given Laplace equation.

$e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0$

The given function in this case is the solution to the given Laplace equation.

(2) $u=\sin x \cosh y+\cos x \sinh y$

Differentiate with respect to x as follows:

$u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y$

Differentiate with respect to y as follows:

$u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y$

Substitute the values to obtain:

$-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0$
The given function in this case is the solution to the given Laplace equation.

Therefore, both functions are the solution to the given Laplace solution.

Know more about Laplace's equation here:

brainly.com/question/14040033

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The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)

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2 years ago