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zloy xaker [14]
2 years ago
10

11. John puts a fence around his rectangular backyard. The width of his backyard is 10 feet. He

Mathematics
1 answer:
Lady_Fox [76]2 years ago
4 0

Length = 20 ft

If he uses 60 ft of fencing to line his rectangular backyard, then the perimeter is 60 ft.

Perimeter formula is ((Width × 2) + (Length × 2))

10 × 2 = 20

20 × 2 = 40

40 + 20 = 60

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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 recursive formula can be used to generate the sequence shown where f(1)=9.6 and n is greater than or equal to 1?
S_A_V [24]
The formula is f(x) = 10x + 5
3 0
3 years ago
Factor Completely: -3x - 9
uranmaximum [27]

Step-by-step explanation:

-3x-9

divide the equation by -1 so that the -1's are taken from -3x and -9. so the -1 goes on the outside of 3x+9

-1(3x+9)

then divide the equation by 3 since 3x and 9 is divisible by 3.

(-1)(3)(3/3x+9/3)

-3(x+3)

Now we can expand again to check the problem

-3 times x=-3x

-3 times 3=-9

and add

-3x-9

Hope that helps :)

7 0
3 years ago
Find the average of 2, 6, 12, 8, and 7
Crazy boy [7]

Answer:

7

Step-by-step explanation:

7 0
3 years ago
The opening balance of the March billing cycle for Bernice's credit card was $2374. If she makes a new purchase of $200 on the 2
Norma-Jean [14]

The opening balance of the March billing cycle for Bernice's credit card = $2374.

Amount of new purchase = $200 on the 20th of March.

She did purchase only of $200 in that March month.

We are given that she didn't do any payment.

So, still she has balance $2374 till end of the month.

Therefore, her average daily balance is $2374.00

So, the correct option is  B. $2374.00.

4 0
3 years ago
Read 2 more answers
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