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nignag [31]
2 years ago
6

Question 3

Mathematics
1 answer:
vitfil [10]2 years ago
8 0

Answer:

Step-by-step explanation:

No there parallel

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Evaluate the integral ∫2−1|x−1|dx
defon

I think you might be referring to the definite integral,

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx

Recall the definition of absolute value:

|x| = \begin{cases}x&\text{if }x\ge0\\-x&\text{if }x

Then |x-1|=x-1 if x\ge1, and |x-1|=1-x is x. So spliting up the integral at <em>x</em> = 1, we have

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \int_{-1}^1(1-x)\,\mathrm dx + \int_1^2(x-1)\,\mathrm dx

The rest is simple:

\displaystyle \int_{-1}^2|x-1|\,\mathrm dx = \left(x-\dfrac{x^2}2\right)\bigg|_{-1}^1 + \left(\dfrac{x^2}2-x\right)\bigg|_1^2 \\\\ = \left(\left(1-\frac12\right)-\left(-1-\frac12\right)\right) + \left(\left(2-2\right)-\left(\frac12-1\right)\right) \\\\ = \boxed{\frac52}

5 0
3 years ago
What is the sum of 347+645=
iren [92.7K]

Answer:

347 + 645 = 992

Step-by-step explanation:

 347

<u>+645</u>

 922

7 0
3 years ago
Suppose two variables are positively correlated. Does the response variable increase or decrease as the explanatory variable inc
matrenka [14]

Answer:

Option A

Step-by-step explanation:

Positive correlation describes a relationship between two variables where both variables move in the same direction. In this case, the response variable will increase as the explanatory variable increases.

3 0
3 years ago
Jan's gas tank is nearly empty, at 1/12 full. she doesn't have enough cash to fill the tank, she adds enough gas to reach 2/3 fu
Ira Lisetskai [31]

Answer:

7/12

Step-by-step explanation:

well first you have subtract 2/3 from 1/12 how you do that is that you have to change the denominator into twelve by multiplying 3 times 4 and 2 times for which you get 8/12 them subtract 8/12 from 1/12 which is 7/12

8 0
3 years ago
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Please help me with geometry :(
eimsori [14]

Answer:

I think it's C is true but make sure

3 0
3 years ago
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