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3 years ago

7

Show the expression as the base to one power.

1 answer:

Usimov [2.4K]3 years ago

8 0

16*16*4 . 16*4

solvong it

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Quotient of 120 and 10

saw5 [17]

Quotient is the result of division
120 divided by 10 = 12

therefore your quotient would be 12

5 0

3 years ago

Read 2 more answers

First make a substitution and then use integration by parts to evaluate the integral. (Use C for the constant of integration.) x

e-lub [12.9K]

Answer:

$(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

Step-by-step explanation:

Ok, so we start by setting the integral up. The integral we need to solve is:

$\int x ln(5+x)dx$

so according to the instructions of the problem, we need to start by using some substitution. The substitution will be done as follows:

U=5+x

du=dx

x=U-5

so when substituting the integral will look like this:

$\int (U-5) ln(U)dU$

now we can go ahead and integrate by parts, remember the integration by parts formula looks like this:

$\int (pq')=pq-\int qp'$

so we must define p, q, p' and q':

p=ln U

$p'=\frac{1}{U}dU$

$q=\frac{U^{2}}{2}-5U$

q'=U-5

and now we plug these into the formula:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int \frac{\frac{U^{2}}{2}-5U}{U}dU$

Which simplifies to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\int (\frac{U}{2}-5)dU$

Which solves to:

$\int (U-5)lnUdU=(\frac{U^{2}}{2}-5U)lnU-\frac{U^{2}}{4}+5U+C$

so we can substitute U back, so we get:

$\int xln(x+5)dU=(\frac{(x+5)^{2}}{2}-5(x+5))ln(x+5)-\frac{(x+5)^{2}}{4}+5(x+5)+C$

and now we can simplify:

$\int xln(x+5)dU=(\frac{x^{2}}{2}+5x+\frac{25}{2}-25-5x)ln(5+x)-\frac{x^{2}+10x+25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}-\frac{5x}{2}-\frac{25}{4}+25+5x+C$

$\int xln(x+5)dU=(\frac{x^{2}-25}{2})ln(5+x)-\frac{x^{2}}{4}+\frac{5x}{2}+C$

notice how all the constants were combined into one big constant C.

7 0

3 years ago

Quadrilateral ABCD?<br>

Mashutka [201]

The given quadrilateral is a kite.

Given: Point A (2, 4), B (-2, -5), C (7, -1) and D (7, 4)

Firstly, we find the distance between AD and DC

AD = $\sqrt{(7 - 2)^{2} + (4 - 4)^{2} }$

⇒ AD = $\sqrt{5^{2} }$

⇒ AD = 5

DC = $\sqrt{(7 - 7)^{2} + (4 - (-1))^{2} }$

⇒ DC = $\sqrt{5^{2} }$

⇒ DC = 5

Hence, AD = DC = 5

Now, find the distance between AB and BC

AB = $\sqrt{(-2 - 2)^{2} + (-5 - 4)^{2} }$

⇒ AB = $\sqrt{(-4)^{2} + (-9)^{2} }$

⇒ AB = $\sqrt{16 + 81}$

⇒ AB = $\sqrt{97}$

BC = $\sqrt{(7 - (-2))^{2} + (-1 - (-5))^{2} }$

⇒ BC = $\sqrt{9^{2} + 4^{2} }$

⇒ BC = $\sqrt{81 + 16}$

⇒ BC = $\sqrt{97}$

Hence, AB = BC = √97

In the given quadrilateral, the two pair is of equal length and these sides are adjacent to each other.

Hence, it follows the property of kite.

For more questions on quadrilateral, visit:

brainly.com/question/23935806

#SPJ9

6 0

1 year ago

WHat is the y- intercept of the quadratic function f(x)=(x-6)(x-2)?

aleksandrvk [35]

I think it's (0, -12)

7 0

3 years ago

Read 2 more answers

Simplify: <br>5√3+4√12-2√75

svlad2 [7]

Answer:

8 + $5\sqrt{3}$ $-10\sqrt{7}$

Step-by-step explanation:

i just wrote $5\sqrt{3}$ as a decimal

times 2 with $4\sqrt{1}$ and

times 5 with $-2\sqrt{7}$

i might be wrong but hope this helps

3 0

3 years ago