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meriva
3 years ago
12

Use a change of variables to find the indefinite integral xe^(x^2) dx

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
3 0
\displaystyle\int xe^{x^2}\,\mathrm dx=\frac12\int2xe^{x^2}\,\mathrm dx

If we take y=x^2, then \mathrm dy=2x\,\mathrm dx, and we can write the above integral as


\displaystyle\frac12\int e^y\,\mathrm dy=\frac12e^y+C

and undoing the substitution, we end up with

\displaystyle\int xe^{x^2}\,\mathrm dx=\frac12e^{x^2}+C
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<h2>Explanation:</h2><h2></h2>

In this problem, we know that Harry saved $100 each week for 8 weeks. In other words, he saved a total amount of money:

\text{Amount of money saved}=8\times 100=\$800

We know that he earned $48 on his savings of $800, so for every $100 the interest (I) he earns is:

I=\frac{48}{8}=\$6

So, in conclusion Harry did earn $6 in interest for every $100

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5 0
3 years ago
Find The Value Of X When 6-2x = 6x-10x+6. The Value Is
Natasha_Volkova [10]

Answer:

x = 0

Step-by-step explanation:

6 - 2x = 6x - 10x + 6

1. Isolate the variable (x)

  • Add 2x to both sides

    6 - 2x = 6x - 10x + 6 -> 6 = 6x - 10x + 2x + 6

  • Subtract 6 from both sides

    6x - 10x + 2x + 6 -> 0 = 6x - 10x + 2x

2. Combine like terms

      0 = 6x - 10x + 2x -> 0 = -2x

3. Solve

  • Divide both sides by -2

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*Note: 0 divided by anything is 0 so 0/-2 is 0

(unless it is 0/0 which equals 1)

6 0
3 years ago
Which property is illustrated by the following statement? If ZXY= FDE, and FDE= CAB, then ZXY=CAB
blagie [28]

Answer:

Transitive property of equality

Step-by-step explanation:

By the definition of transitivity, a relation R is said to be transitive if (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.

If p = q, q = r then p = r.

Here, we have given that if ZXY = FDE and FDE = CAB, then, ZXY = CAB.

Therefore, it shows the transitive property of equality.

5 0
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sladkih [1.3K]

Answer:

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Step-by-step explanation:

A non-response bias would mean that there are some non-response surveys, which will create a bias in the survey results. Because the survey didn't include information from those who are not responded.

If there will be 860 surveys back, this would prevent non-response bias

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