45 = (x) + (x + 1) + (x + 2)
45 = 3x + 3
- 3
42 = 3x
/3
14 = x
45 = 14 + (14 + 1) + (14 + 2)
45 = 14 + 15 + 16
The ages of the 3 friends are 14, 15, and 16.
The answer is 0.29 because that would be equal to 29%
Answer:
-10
Step-by-step explanation:
Substitute
and
. Then the integral transforms to
![\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \int \frac{du}{u^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bx%5C%2Cdx%7D%7B%28x%5E2%2B4%29%5E3%7D%20%3D%20%5Cfrac12%20%5Cint%20%5Cfrac%7Bdu%7D%7Bu%5E3%7D)
Apply the power rule.
![\displaystyle \int \frac{du}{u^3} = -\dfrac1{2u^2} + C](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bdu%7D%7Bu%5E3%7D%20%3D%20-%5Cdfrac1%7B2u%5E2%7D%20%2B%20C)
Now put the result back in terms of
.
![\displaystyle \int \frac{x\,dx}{(x^2+4)^3} = \frac12 \left(-\dfrac1{2u^2} + C\right) = -\dfrac1{4u^2} + C = \boxed{-\dfrac1{4(x^2+4)^2} + C}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%5Cfrac%7Bx%5C%2Cdx%7D%7B%28x%5E2%2B4%29%5E3%7D%20%3D%20%5Cfrac12%20%5Cleft%28-%5Cdfrac1%7B2u%5E2%7D%20%2B%20C%5Cright%29%20%3D%20-%5Cdfrac1%7B4u%5E2%7D%20%2B%20C%20%3D%20%5Cboxed%7B-%5Cdfrac1%7B4%28x%5E2%2B4%29%5E2%7D%20%2B%20C%7D)
The correct answer is D. NURSING AIDES HAD FEWER PEOPLE IN 2002.
<span>Employment Projections
Job Number of People (2002) Projection (2012) Percent Change
Nursing Aides 1,375,000 1,718,000 25
Customer Service 1,894,000 2,354,000 24
(1,718,000 - 1,375,000) / 1,375,000 = 343,000 / 1,375,000 = 0.249 or 0.25 or 25%
(2,354,000 - 1,894,000) / 1,894,000 = 460,000 / 1,894,000 = 0.242 or 0.24 or 24%
The base number is the number of people in 2002. There is a higher percent change in number for nursing aides despite having lesser people added because its base number is lower than those in customer service. </span>