Yes it's exactly due to symmetry. Specifically, symmetry about the x axis.
Simply writing ![\displaystyle \int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-8%7D%5E%7B-4%7D%5Cleft%5B%5Csqrt%7Bx%2B8%7D%20%5C%20%5Cright%5Ddx)
, without the 2 out front, will only get you the area of the portion shown in red (see diagram below).
The blue region has equal area of the red region due to symmetry.
So,
![\displaystyle 2\int_{-8}^{-4}\left[\sqrt{x+8} \ \right]dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%202%5Cint_%7B-8%7D%5E%7B-4%7D%5Cleft%5B%5Csqrt%7Bx%2B8%7D%20%5C%20%5Cright%5Ddx)
represents the red and blue regions combined.
The portion in green is ![\displaystyle \int_{-4}^{8}\left[\sqrt{x+8} - \frac{x}{2} \ \right]dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-4%7D%5E%7B8%7D%5Cleft%5B%5Csqrt%7Bx%2B8%7D%20-%20%5Cfrac%7Bx%7D%7B2%7D%20%5C%20%5Cright%5Ddx)
which is the integral of the difference of the upper and lower curves over the interval 
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In all honesty, it's probably easier to integrate with respect to y since the given functions are in terms of y initially. Also, there isn't a junction point in which the curves swap places in terms of which one is larger. However, it doesn't hurt to have practice in integrating with respect to x.
If you're curious about what the y integral looks like, then it would be
![\displaystyle \int_{-2}^{4} \bigg[ (2y) - (y^2-8)\bigg] dy](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-2%7D%5E%7B4%7D%20%5Cbigg%5B%20%282y%29%20-%20%28y%5E2-8%29%5Cbigg%5D%20dy)
You can use a tool like WolframAlpha to check that both integral expressions result in 36 to help confirm that they represent the same overall area (just in different ways of course).
Answer:
A
Step-by-step explanation:
V=B+15
V+2B=180
Therefore:
3B+15=180
B=55
V=70
Check:
V+2B=180
70+2(55)=180
70+110=180
180=180. Checks.
Answer:
A literal equation is an equation that consists of multiple variables or letters.
A linear equation is an equation that consists of one variable
Step-by-step explanation:
Literal EX:
a = 1/2h(a + b)
ax + b = c
u = ak/b
Linear EX:
5(3a + 8) = 12a
4a = 8
11(3a - 18) = 12a
Measurement is the numerical quantitation of the attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependent on the context and discipline
