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3 years ago

9

Factor 6y^2(y^2+6y+9) completely.

1 answer:

natali 33 [55]3 years ago

7 0

$6y^2(y^2+6y+9)\\\\=6y^2(y^2+2\cdot 3 \cdot y + 3^2)\\\\=6y^2(y+3)^2\\\\=6y^2(y+3)(y+3)$

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(2/9 v)-(-1/3v +5/9)

Alik [6]

2/9v +1/3v -5/9

2/9v + 3/9v-5/9

5/9v -5/9

6 0

3 years ago

Read 2 more answers

Help me please ! ASAP . . . .

salantis [7]

$\textbf{Answer:}$

$\medskip\newline{\int\limits_{0}^{\infty}{\bigl(\frac{1}{y^2+1}\bigr)tan^{-1}(x)\mid_{x=0}^{x=\infty}}dy=\frac{\pi^2}{4}}$

$\medskip\newline\textbf{Step-by-step explanation:}$

$\medskip\newline\text{It's been a very long time since I've seen a calculus question.}\newline{\text{It might be because I haven't visited this site in a while.}}$ $\text{Anyway, on to the answer.}$

$\medskip\newline\text{When doing 2 integrals, work inside to out and treat the variables}\newline\text{ that aren't the ones being integrated as constants and proceed like normal.}$ $\medskip\medskip\newline\int\limits_{0}^{\infty}{\int\limits_{0}^{\infty}{\frac{1}{(x^2+1)(y^2+1)}}dx}dy$

$\newline{\text{Work inner to outer. Therefore, treat all y's as constants for now.}}$ $\newline{\text{By the integration formula: }\int\frac{1}{x^2+a^2}dx=\frac{1}{a}tan^{-1}(\frac{x}{a})+C}$

$\newline{\int\limits_{0}^{\infty}{\int\limits_{0}^{\infty}{\frac{1}{(x^2+1)(y^2+1)}}dx}dy=}$

$\newline{\int\limits_{0}^{\infty}{\bigl(\frac{1}{y^2+1}\bigr)tan^{-1}(x)\mid\limits_{x=0}^{x=\infty}}dy=}$

$\newline{\int\limits_{0}^{\infty}{\bigl(\frac{1}{y^2+1}\bigr)(tan^{-1}(\infty)-tan^{-1}(0))}dy=}$

$\newline{\int\limits_{0}^{\infty}{\bigl(\frac{1}{y^2+1}\bigr)(\frac{\pi}{2}-0)}dy=}$

$\newline{\int\limits_{0}^{\infty}{\bigl(\frac{1}{y^2+1}\bigr)(\frac{\pi}{2})}dy}$

$\medskip\newline\text{Using the same integration formula as before.}$

$\medskip\newline{\int\limits_{0}^{\infty}{\bigl(\frac{1}{y^2+1}\bigr)(\frac{\pi}{2})}dy=}$

$\newline{(\frac{\pi}{2})tan^{-1}(y)\mid\limits_{y=0}^{y=\infty}=}$

$\newline{(\frac{\pi}{2})(tan^{-1}(\infty)-tan^{-1}(0))=}$

$\newline{(\frac{\pi}{2})(\frac{\pi}{2}-0)=}$

$\newline{(\frac{\pi}{2})(\frac{\pi}{2})=}$

$\newline{\frac{\pi^2}{4}}$

$\bigskip\newline{\text{Therefore, the answer is }\frac{\pi^2}{4}}$

4 0

3 years ago

Solve this problem 2/5=n/20

miss Akunina [59]

The answer of this question is n=8 .

5 0

3 years ago

Use the distributive property to write2(-5 + 3) as an equivalent expression what is the value of the expression

KiRa [710]

Answer:

-10+6=-4

Step-by-step explanation:

Here's why we use distributive property, so a(b+c) = ab+ac, therefore 2(-5+3) is -10+6, which is equal to -4.

4 0

4 years ago

What is the area of a regular pentagon with a side of 10 in.? round the answer to the nearest

german

The area of the regular pentagon given a side of 10 in is 172.0 in².

<h3>What is the area?</h3>

A pentagon is an object that is made up of five sides. The sum of the internal angles of a pentagon is 540 degrees.

Area of a pentagon = 1/4√ $\sqrt{5 ( 5 + 2 \sqrt{5} ) }$ a²

Where a = side = 10

A = 1/4√ $\sqrt{5 ( 5 + 2 \sqrt{5} ) }$ 10²

A = 172.02 in²

To learn more about pentagons, please check: brainly.com/question/17054992

#SPJ1

5 0

2 years ago