The answer is D. No relationship but there’s no question for it so it maybe wrong
so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check
so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.
![\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D~~%20-%20~~%5B%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D%5D%5Cimplies%202x%5E3-x%5E2-5x%2Bx%5E2-3x%20%5C%5C%5C%5C%5C%5C%202x%5E3-8x%5Cimplies%202%28x%5E3-4x%29%5Cimplies%20%5Cdisplaystyle%202%5Cint%5Climits_%7B-2%7D%5E%7B0%7D%20%28x%5E3-4x%29dx%20%5Cimplies%202%5Cleft%5B%20%5Ccfrac%7Bx%5E4%7D%7B4%7D-2x%5E2%20%5Cright%5D_%7B-2%7D%5E%7B0%7D%5Cimplies%20%5Cboxed%7B8%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}](https://tex.z-dn.net/?f=%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D~~%20-%20~~%5B%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D%5D%5Cimplies%20-x%5E2%2B3x-2x%5E3%2Bx%5E2%2B5x%20%5C%5C%5C%5C%5C%5C%20-2x%5E3%2B8x%5Cimplies%202%28-x%5E3%2B4x%29%20%5C%5C%5C%5C%5C%5C%20%5Cdisplaystyle%202%5Cint%5Climits_%7B0%7D%5E%7B2%7D%20%28-x%5E3%2B4x%29dx%20%5Cimplies%202%5Cleft%5B%20-%5Ccfrac%7Bx%5E4%7D%7B4%7D%2B2x%5E2%20%5Cright%5D_%7B0%7D%5E%7B2%7D%5Cimplies%20%5Cboxed%7B8%7D%20~%5Chfill%20%5Cboxed%7B%5Cstackrel%7B%5Ctextit%7Btotal%20area%7D%7D%7B8~~%20%2B%20~~8~~%20%3D%20~~16%7D%7D)
Answer:
B. 0.12
Step-by-step explanation:
To obtain this probability, you need to multiply the two probabilities.. since it's comprised of two events: one that he's in the brass section, one that he plays trombone. The probably of him playing trombone only happens if he's in the brass section.
So, you have the possibility he's in the brass section: 0.50
The possibility he's playing trombone, if he's in the brass section: 0.24
P = 0.5 * 0.24 = 0.12
Answer:
5
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
log 1/3 27= 1/3^x=27 this means we have to simplify it. 1/3= 3^-1 power. Thus, (3^-1)^x=3^3. This is equal to 3^-x=3^3 therefore x=-3
