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Delicious77 [7]
3 years ago
15

Consider the following. y = 2xe−x, y = 0, x = 3; about the y-axis (a) Set up an integral for the volume V of the solid obtained

by rotating the region bounded by the given curve about the specified axis. V = 0 dx (b) Use your calculator to evaluate the integral correct to five decimal places.
Mathematics
1 answer:
IrinaK [193]3 years ago
7 0

Using the shell method, the volume would be

\displaystyle2\pi\int_0^3x(2xe^{-x})\,\mathrm dx=4\pi\int_0^3x^2e^{-x}\,\mathrm dx

Each shell contributes a volume of approximately 2πrh, where r is the distance from the axis of revolution to the shell (<em>x</em>) and h is the height of the shell given by the vertical distance between <em>y</em> = 2<em>x</em> e^(-<em>x</em>) and <em>y</em> = 0.

If you go on to use your calculator, you'll find the volume is approximately 14.49681.

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Can you explain to me the answers in a and b?
Hoochie [10]

a. The constant of proportionality is k = 2

b. If Micah saves $150, his parents will give him $300

<h2>Explanation:</h2>

<h3>PART A.</h3>

From mathematics, we know that y varies directly as x or y is directly proportional to x if and only if:

y=kx for some nonzero constant k.

Here we know some facts:

  • For every $5 that Micah saves, his parents give him $10.

In other words:

Let y be the money his parents give him.

Let x be the money that Micah saves.

We \ know \ that: \\ y=kx \\ \\ \\ Solving \ for \ k: \\ \\ k=\frac{y}{x} \\ \\ k=\frac{10}{5} \\ \\ \boxed{k=2}

So,<em> the constant of proportionality is k = 2</em>

<h3>PART B.</h3>

In this case, we know that Micah saves $150. So we need to find the amount of his parents will give him. So what we know here is the value of x, because x represents the amount of money Micah saves. Therefore, by knowing x and k, we can calculate the value of y, which is the amount of money his parents will give him. Hence:

For \ x=150 \ and \ k=2: \\ \\ y=2(150) \\ \\ \boxed{y=300}

Finally, <em>if Micah saves $150, his parents will give him 300$</em>

<h2>Learn more:</h2>

Cost of pizzas: brainly.com/question/12878495

#LearnWithBrainly

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4 years ago
If the length of two sides of a triangle are 7 and 10 the length of the third side may be?
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Marta_Voda [28]
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Martin modeled the distance, y, that runners traveled during a race a function of the time, that they ran. Which would best desc
Mama L [17]

Answer:

All positive real numbers

Step-by-step explanation:

Given

The model can be represented as:

y = f(x)

y = distance

x = time

Required

Determine the domain

This means that we list out possible values of x.

If x represents time, then it is impossible for x to be negative.

This implies that x can take any value as long as it is greater than or equal to 0.

<em>Hence, the domain is all positive real numbers</em>

4 0
3 years ago
Lydia owns a food truck that sells tacos and burritos. She only has enough supplies to make 115 tacos or burritos. She sells eac
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Answer:

She must sell 82 burritos

Step-by-step explanation:

81.77 (round it up)

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