Given conditions are :
In 1980's, a typical middle-income household earned= $34,757
In 2009, a similar middle-income household earned= $38,550
And we have to find relative increase in income for these households from 1980 to 2009.
So first we will find the total increase in amounts.
![38550-34757=3793](https://tex.z-dn.net/?f=38550-34757%3D3793)
Relative increase = ![\frac{3793}{34757}*100](https://tex.z-dn.net/?f=%5Cfrac%7B3793%7D%7B34757%7D%2A100)
= 10.91% or rounding it off we get approx 11%.
Hence, the answer is 11%.
nwere ike nwa osisi poop pusi ibu onu nkita meow n'anya papa 46721
Length (L): 2w + 6
width (w): w
Perimeter (P) = 2L + 2w
240 = 2(2w + 6) + 2(w)
240 = 4w + 12 + 2w
240 = 6w + 12
228 = 6w
38 = w
Length (L): 2w + 6 = 2(38) + 6 = 76 + 6 = 82
Answer: width = 38 ft, length = 82 ft
Answer:
D. Undefined
Step-by-step explanation:
4-4 = 0, 10-6 = 4
Change of x = 0
Change of y = 4
Since the change of x is 0 (a horizontal line), it is undefined.
Answer:
The area of the region is 25,351
.
Step-by-step explanation:
The Fundamental Theorem of Calculus:<em> if </em>
<em> is a continuous function on </em>
<em>, then</em>
![\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}](https://tex.z-dn.net/?f=%5Cint_%7Ba%7D%5E%7Bb%7D%20f%28x%29dx%20%3D%20F%28b%29%20-%20F%28a%29%20%3D%20F%28x%29%20%7C%20%20%7B_a%5Eb%7D)
where
is an antiderivative of
.
A function
is an antiderivative of the function
if
![F^{'}(x)=f(x)](https://tex.z-dn.net/?f=F%5E%7B%27%7D%28x%29%3Df%28x%29)
The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
To find the area of the region between the graph of the function
and the x-axis on the interval [-6, 6] you must:
Apply the Fundamental Theorem of Calculus
![\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx](https://tex.z-dn.net/?f=%5Cint%20_%7B-6%7D%5E6%28x%5E5%2B8x%5E4%2B2x%5E2%2B5x%2B15%29dx)
![\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%5C%3ARule%7D%3A%5Cquad%20%5Cint%20f%5Cleft%28x%5Cright%29%5Cpm%20g%5Cleft%28x%5Cright%29dx%3D%5Cint%20f%5Cleft%28x%5Cright%29dx%5Cpm%20%5Cint%20g%5Cleft%28x%5Cright%29dx%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E6x%5E5dx%2B%5Cint%20_%7B-6%7D%5E68x%5E4dx%2B%5Cint%20_%7B-6%7D%5E62x%5E2dx%2B%5Cint%20_%7B-6%7D%5E65xdx%2B%5Cint%20_%7B-6%7D%5E615dx)
![\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2](https://tex.z-dn.net/?f=%5Cint%20_%7B-6%7D%5E6x%5E5dx%3D0%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E68x%5E4dx%3D%5Cfrac%7B124416%7D%7B5%7D%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E62x%5E2dx%3D288%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E65xdx%3D0%5C%5C%5C%5C%5Cint%20_%7B-6%7D%5E615dx%3D180%5C%5C%5C%5C0%2B%5Cfrac%7B124416%7D%7B5%7D%2B288%2B0%2B18%5C%5C%5C%5C%5Cfrac%7B126756%7D%7B5%7D%5Capprox%2025351.2)