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Whitepunk [10]
1 year ago
9

evaluate the integral by reversing the order of integration. $ \displaystyle\int {0}^{{\color{red}4}} \displaystyle\int {\sqrt{x

}}^{{\color{red}2}}\, \dfrac{{\color{red}3}}{y^3 1}\,dydx$
Mathematics
1 answer:
almond37 [142]1 year ago
4 0

The integral by reversing the order of integration \frac{1}{2}

  • Performing u-substitution with definite integrals is very similar to how it's done with indefinite integrals, but with an added step: accounting for the limits of integration.
  • The limit and summation that we examined in the previous section to get the net area between a function and the x-axis are exactly what is characterized as the definite integral.

Now, Use u-substitution by given integration

$$\mathrm{u}=4+8 \mathrm{x}^2$$

du $=16 \mathrm{x}$...now back substitute,

\begin{aligned}&\int_0^2 \frac{x}{\sqrt{4+8 x^2}} \mathrm{~d} x=\frac{1}{16} \int_0^2 \frac{1}{\sqrt{4+8 x^2}} \mathrm{~d}\left(4+8 x^2\right)=\left.\frac{1}{8} \sqrt{4+8 x^2}\right|_0 ^2 \\&=\frac{1}{8}(\sqrt{4+8 * 4}-\sqrt{4})=\frac{4}{8}=\frac{1}{2}\end{aligned}

Therefore,

The integration is \frac{1}{2}

To learn more about the u-substitution visit: brainly.com/question/1407154

#SPJ4

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Answer:

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nata0808 [166]

Answer:

The length of the other leg of this right angled triangle is 30 inches.

Step-by-step explanation:

We are given the following in the question:

A right angles triangle with the hypotenuse of 34 inches and the length of one of its legs is 16 inches.

Pythagoras theorem:

  • The sum of of square of two sides of a triangle is equal to the square of the hypotenuse.

Let x inches be the length of the other leg of this right triangle.

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3 years ago
 Sandra sells necklaces at a school craft fair. She uses the equation P= 7.5n - (2.25n + 15) to determine her total profit at th
gregori [183]
The way you find profit is to subtract the revenue and the cost
Profit = Revenue - Cost
The revenue is the amount of money coming in, the cost is the amount of money going out. The goal of course is to have the revenue larger than the cost so that the profit is positive. 

So the equation given is
P = 7.5n - (2.25n+15)
and its in the form
P = R - C
where...
R = 7.5n is the revenue equation
C = 2.25n+15 is the cost equation

Focus on the revenue equation
R = 7.5n
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This tells us that Sandra pulls in a total of 7.50*n dollars where n is some positive whole number. It represents the number of necklaces sold. For example, if she sold n = 10 necklaces, then
R = 7.50*n
R = 7.50*10
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meaning that Sandra has made $750 in revenue

As you can see above, the revenue is computed by multiplying the price per necklace ($7.50) by the number of necklaces sold (n) to get R = 7.50*n

So that's why the answer is $7.50

Note: The 2.25 is part of the cost equation. This is known as the variable cost. It is the cost to make one necklace ignoring the fixed cost (eg: rent). The variable cost often doesn't stay the same, but algebra textbooks often simplify this aspect. 
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RUDIKE [14]

Answer:

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Step-by-step explanation:

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