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3 years ago

Factorise this expression as fully as possible: 9x²y + 12xy²

Mathematics

1 answer:

finlep [7]3 years ago

6 0

First you can take out a 3. And an x and a y. Thus, 3xy(3x+4y) is the answer.

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How do I find the integral<br> ∫10(x−1)(x2+9)dxint10/((x-1)(x^2+9))dx ?

defon

$\int\frac{10}{(x-1)(x^2+9)}\ dx=(*)\\\\\frac{10}{(x-1)(x^2+9)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+9}=\frac{A(x^2+9)+(Bx+C)(x-1)}{(x-1)(x^2+9)}\\\\=\frac{Ax^2+9A+Bx^2-Bx+Cx-C}{(x-1)(x^2+9)}=\frac{(A+B)x^2+(-B+C)x+(9A-C)}{(x-1)(x^2+9)}\\\Updownarrow\\10=(A+B)x^2+(-B+C)x+(9A-C)\\\Updownarrow\\A+B=0\ and\ -B+C=0\ and\ 9A-C=10\\A=-B\ and\ C=B\to9(-B)-B=10\to-10B=10\to B=-1\\A=-(-1)=1\ and\ C=-1$

$(*)=\int\left(\frac{1}{x-1}+\frac{-x-1}{x^2+9}\right)\ dx=\int\left(\frac{1}{x-1}-\frac{x+1}{x^2+9}\right)\ dx\\\\=\int\frac{1}{x-1}\ dx-\int\frac{x+1}{x^2+9}\ dx=\int\frac{1}{x-1}-\int\frac{x}{x^2+9}\ dx-\int\frac{1}{x^2+9}\ dx=(**)\\\\\#1\ \int\frac{1}{x-1}\ dx\Rightarrow\left|\begin{array}{ccc}x-1=t\\dx=dt\end{array}\right|\Rightarrow\int\frac{1}{t}\ dt=lnt+C_1=ln(x-1)+C_1$

$\#2\ \int\frac{x}{x^2+9}\ dx\Rightarrow \left|\begin{array}{ccc}x^2+9=u\\2x\ dx=du\\x\ dx=\frac{1}{2}\ du\end{array}\right|\Rightarrow\int\left(\frac{1}{2}\cdot\frac{1}{u}\right)\ du=\frac{1}{2}\int\frac{1}{u}\ du\\\\\\=\frac{1}{2}ln(u)+C_2=\frac{1}{2}ln(x^2+9)+C_2$

$\#3\ \int\frac{1}{x^2+9}\ dx=\int\frac{1}{x^2+3^2}\ dx=\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3\\\\therefore:\\\\\#1;\ \#2;\ \#3\Rightarrow(**)=ln(x-1)+C_1-\frac{1}{2}ln(x^2+9)+C_2-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3$

$\boxed{=ln(x-1)-\frac{1}{2}ln(x^2+9)-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C}$

4 0

3 years ago

Nine is more than twice n.

ella [17]

I hope this helps you

9=n.n

3.3=n.n

n=3

6 0

3 years ago

one number is three more than four time another if the sum of the two number is 23 then find both numbers

zloy xaker [14]

<h3><u>The value of x is 19.</u></h3><h3><u>The value of y is 4.</u></h3>

x = 3 + 4y

x + y = 23

Because we have a value for x we can plug it directly into the second equation.

3 + 4y + y = 23

Subtract 3 from both sides.

4y + y = 20

Combine like terms.

5y = 20

Divide both sides by 5.

y = 4

Plug this value for x back into the original equation.

x = 3 + 4(4)

x = 3 + 16

x = 19

8 0

3 years ago

What is the answer to this question 800×900= ?<br>

dezoksy [38]

Answer:

720,000

Step-by-step explanation:

800 × 900 = 720,000

8 0

3 years ago

Read 2 more answers

Corinne made apple jam and strawberry jam. She made enough apple jam to

Ne4ueva [31]

Answer:

Step-by-step explanation:

1 ×3 =3

apple jam times strawberry

6 0

3 years ago