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3 years ago

I need help on this problem please help me.

Mathematics

1 answer:

a_sh-v [17]3 years ago

3 0

Answer:

150 mL

Step-by-step explanation:

Let x represent the quantity of 75% solution needed. The total amount of alcohol in the 60% mixture will be ...

75%·x + 10%·45 = 60%·(x+45) . . . . . there will be x+45 mL of solution in the end

0.15x = 22.5 . . . . . . . . . . . . . . . . . . . . simplify, subtract .60x+4.5

22.5/0.15 = x = 150 . . . . . . . . . . . . . . mL of 75% solution needed

You will need 150 mL of the 75% solution.

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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

Show work how you know it’s a function or not a function for each problem. PLEASE SOMEONE HELP ME OUT

Fudgin [204]

Answer: Function, not a function, Function, not a function

Step-by-step explanation:

For it to be a function, each value of x has to map onto one value of y.

This is a function.
Not a function since x=-1 has more than one y value.
This is a function
Not a function since x=-6 has more than one y value.

7 0

1 year ago

The price of a microwave oven went up from $75 to $90; then went on sale for $57. What is the percent decrease from the original

Arisa [49]

Answer:

<u>The percent decrease of the microwave from the original price to the sale price is 24%</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Original price of a microwave = $ 75

Mark-up price of the microwave = $ 90

Sale price of the microwave = $ 57

2. What is the percent decrease from the original price to the sale price?

For answering this question we will use the Direct Rule of Three this way:

Price Percentage

75 100%

57 x

75x = 57 * 100

75x = 5,700

x = 5,700/75

x = 76

76 = 100 - 24

<u>The percent decrease of the microwave from the original price to the sale price is 24%</u>

5 0

3 years ago

Read 2 more answers

How could you use coordinate geometry to prove that segment BD and segment AC bisect one another?

____ [38]

Answer:

I think it's prove the midpoints are the same

Step-by-step explanation:

I'm not completely sure but I'm taking it right now and I believe that's the most logical answer because if they meet up at the same midpoint then they could bisect each other.

3 0

3 years ago

Convert to a fraction 12 3\100

sashaice [31]

Answer:

1203/100

Step-by-step explanation:

12 times 100 equals 1200 plus three equals 1203/100

8 0

3 years ago