Ooh, fun
what I would do is to make it a piecewise function where the absolute value becomse 0
because if you graphed y=x^2+x-12, some part of the garph would be under the line
with y=|x^2+x-12|, that part under the line is flipped up
so we need to find that flipping point which is at y=0
solve x^2+x-12=0
(x-3)(x+4)=0
at x=-4 and x=3 are the flipping points
we have 2 functions, the regular and flipped one
the regular, we will call f(x), it is f(x)=x^2+x-12
the flipped one, we call g(x), it is g(x)=-(x^2+x-12) or -x^2-x+12
so we do the integeral of f(x) from x=5 to x=-4, plus the integral of g(x) from x=-4 to x=3, plus the integral of f(x) from x=3 to x=5
A.

B.
sepearte the integrals
![\int\limits^{-5}_{-4} {x^2+x-12} \, dx = [\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-5}_{-4}=(\frac{-125}{3}+\frac{25}{2}+60)-(\frac{64}{3}+8+48)=\frac{23}{6}](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E%7B-5%7D_%7B-4%7D%20%7Bx%5E2%2Bx-12%7D%20%5C%2C%20dx%20%3D%20%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%2B%5Cfrac%7Bx%5E2%7D%7B2%7D-12x%5D%5E%7B-5%7D_%7B-4%7D%3D%28%5Cfrac%7B-125%7D%7B3%7D%2B%5Cfrac%7B25%7D%7B2%7D%2B60%29-%28%5Cfrac%7B64%7D%7B3%7D%2B8%2B48%29%3D%5Cfrac%7B23%7D%7B6%7D)
next one
![\int\limits^{-4}_3 {-x^2-x+12} \, dx=-1[\frac{x^3}{3}+\frac{x^2}{2}-12x]^{-4}_{3}=-1((-64/3)+8+48)-(9+(9/2)-36))=\frac{343}{6}](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E%7B-4%7D_3%20%7B-x%5E2-x%2B12%7D%20%5C%2C%20dx%3D-1%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%2B%5Cfrac%7Bx%5E2%7D%7B2%7D-12x%5D%5E%7B-4%7D_%7B3%7D%3D-1%28%28-64%2F3%29%2B8%2B48%29-%289%2B%289%2F2%29-36%29%29%3D%5Cfrac%7B343%7D%7B6%7D)
the last one you can do yourself, it is

the sum is

so the area under the curve is
Answer:
y=29x+50; 30 months
Step-by-step explanation:
$920-50=870
870/29=30
Answer:
U it is DG if jug chuchi DG u want u back to the u and composition
Answer:
z=-21
Step-by-step explanation: (9-3)/2=(6+z)/5
We move all terms to the left:
(9-3)/2-((6+z)/5)=0
We add all the numbers together, and all the variables
-((z+6)/5)+6/2=0
We add all the numbers together, and all the variables
-((z+6)/5)+3=0
We multiply all the terms by the denominator
-((z+6)+3*5)=0
We calculate terms in parentheses: -((z+6)+3*5), so:
(z+6)+3*5
We add all the numbers together, and all the variables
(z+6)+15
We get rid of parentheses
z+6+15
We add all the numbers together, and all the variables
z+21
Back to the equation:
-(z+21)
We get rid of parentheses
-z-21=0
We add all the numbers together, and all the variables
-1z-21=0
We move all terms containing z to the left, all other terms to the right
-z=21
z=21/-1
z=-21
The answer is 720 mph, since we make time the x and distance y. We use the slope formula (y2 - y1)/(x2 - x1)
(179-23)/(17-4)
156 miles/13 mins
12 miles per min
Since the answer is in hours instead of minutes, we multiply 12 by 60 to get 720 mph