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3 years ago

9

The Jones family is building a circular swimming pool. If the radius of the pool is 14 feet, what is its circumference? Use π =

3.14 to solve.

1 answer:

Katyanochek1 [597]3 years ago

5 0

Answer:

87.96 ft

Step-by-step explanation:

In order to find the circumference given the radius we use 2 pi r so it would be 2xpix14 which comes out to be 87.96

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Evaluate the integral of the quantity x divided by the quantity x to the fourth plus sixteen, dx . (2 points) one eighth times t

Anika [276]

Answer:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

Step-by-step explanation:

Given

$\int\limits {\frac{x}{x^4 + 16}} \, dx$

Required

Solve

Let

$u = \frac{x^2}{4}$

Differentiate

$du = 2 * \frac{x^{2-1}}{4}\ dx$

$du = 2 * \frac{x}{4}\ dx$

$du = \frac{x}{2}\ dx$

Make dx the subject

$dx = \frac{2}{x}\ du$

The given integral becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{x}{x^4 + 16}} \, * \frac{2}{x}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{1}{x^4 + 16}} \, * \frac{2}{1}\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

Recall that: $u = \frac{x^2}{4}$

Make $x^2$ the subject

$x^2= 4u$

Square both sides

$x^4= (4u)^2$

$x^4= 16u^2$

Substitute $16u^2$ for $x^4$ in $\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{x^4 + 16}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16u^2 + 16}} \,\ du$

Simplify

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \int\limits {\frac{2}{16}* \frac{1}{8u^2 + 8}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{2}{16}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

In standard integration

$\int\limits {\frac{1}{u^2 + 1}} \,\ du = arctan(u)$

So, the expression becomes:

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}\int\limits {\frac{1}{u^2 + 1}} \,\ du$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(u)$

Recall that: $u = \frac{x^2}{4}$

$\int\limits {\frac{x}{x^4 + 16}} \, dx = \frac{1}{8}*arctan(\frac{x^2}{4}) + c$

4 0

3 years ago

How does one solve this?

Tresset [83]

The answer is a. $x\sqrt{7}$

3 0

4 years ago

Read 2 more answers

Dafna11 [192]

Answer:

C. 2x^2-7x+7

Step-by-step explanation:

(3x^2-2x+2)-(x^2+5x-5) <em>Given</em>

From the given you will subtract like terms from both parenthesis.

3x^2-x^2=2x^2

-2x-5x=-7x

2-(-5)=7

6 0

3 years ago

Math Help? Please! : )

Ray Of Light [21]

1/2 is the probability, or 50%. There are 4 teams of S and B n the Y, 2 are B. so its 2/4

5 0

3 years ago

Brainliest + Points!<br><br> I need help please explain

Simora [160]

Answer:

C. Symetrey

If you cut the picture in half, both sides are Exaactly the same.

Hope this helped!

~Lunar Rose. Moon

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers