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3 years ago

What are the solutions to x2 + 8x + 7 =0?

Mathematics

1 answer:

Nata [24]3 years ago

7 0

The chosen topic is not meant for use with this type of problem. Try the examples below.

y = x+4

y = 2x-5

y = x-1

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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

Which statement best describes the association between variable X and variable Y? Question 1 options: perfect negative associati

polet [3.4K]

The statement which best describes the association between the variables X and Y is the <em>moderate positive association</em>. It is observable that the values of X and Y are increasing, however, not in a perfect manner as there are some minor deviations. But nonetheless, the direction is clear and the values are close to each other so they have a moderate positive association.

5 0

3 years ago

Read 2 more answers

I need help which letter is it?

s2008m [1.1K]

It should be B If I am correct if I am not I am sorry

8 0

3 years ago

Solve 5 / 6 ÷ 1 / 12 ?

Tema [17]

Answer:

Step-by-step explanation:

5/6 ÷ 1/12 ➡ 5/6 × 12/1 = 60/6 ➡ 10

5 0

3 years ago

Read 2 more answers

A bowl has 9 green grapes and 13 grapes. Henry randomly chooses a grape, and eats it, and then choose a another grape What is th

Sunny_sXe [5.5K]

Answer:

$\frac{72}{462}$ or $\frac{12}{77}$ (simplified)

Step-by-step explanation:

Based on the information provided within the question it can be said that in order to calculate the probability of both grapes being green we need to find the probability of each grape being green separately and then multiply those probabilities together

In the first choice, there are a total of 22 grapes (9+13), 9 of which are green. Therefore the probability of the first chosen grape being green is $\frac{9}{22}$

In the second choice,since we removed one grape there is now a total of 21 grapes (22-1), 8 of which are green. Therefore the probability of the second chosen grape being green is $\frac{8}{21}$

Now we multiply both probabilities together to calculate the probability that both grapes are green in a sequence.

$\frac{9}{22} * \frac{8}{21} = \frac{72}{462} or \frac{12}{77}$

7 0

3 years ago