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ankoles [38]
3 years ago
9

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

Mathematics
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)
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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
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