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Shalnov [3]
3 years ago
9

The triangles are similar. What is the value of x? Enter your answer in the box. x =

Mathematics
1 answer:
Radda [10]3 years ago
4 0
X = 13
using proportional reasoning, 48/12=4, and dividing 52 by 4 will give you the answer, 13.
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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
What is another way to write x 4/3
zloy xaker [14]

Answer:

1.3333333333333333 or 1 1/3

Step-by-step explanation:

What is the x?

4 0
3 years ago
Jack and jill went on their first date to chili's. Their food bill totaled $32.00 plus the 15% tip they needed to pay the waitre
Vlad1618 [11]
A) 15% of $32.00 is $4.80.
B) all together he will be paying $36.80.
i hope this helped, good luck!
5 0
3 years ago
Jean needs 1/3 cup of wulnuts for each serving of salad she makes.she has 2 cups of walnuts how many servings can she make
valentina_108 [34]
She can make 6 servings
5 0
3 years ago
Given the equation y = 2x - 8, what is the slope and the y-intercept? A.) m = 8 and b = 2 B.) m = 2 and b = 8 C.) m = 2 and b =
masha68 [24]

\tt\it\bf\it\LARGE\bm{\mathcal{\color{red}\underline\fcolorbox{red}{white}{\red{Answer}}}}

m=2b= -8

4 0
3 years ago
Read 2 more answers
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