Answer:
2x - 3 = 6
Step-by-step explanation:
solve for 'x':
2x - 3 = 6
2x = 9
x = 9/2 or 4 1/2
Check:
2(9/2) - 3 = 6
9 - 3 = 6
6 = 6
4.
first one, since the lower bound is y=0
so what we do is just inetgrate from x=0 to x=8
![\int\limits^8_9 { \frac{16x}{x^2+1} } \, dx](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E8_9%20%7B%20%5Cfrac%7B16x%7D%7Bx%5E2%2B1%7D%20%7D%20%5C%2C%20dx%20)
find an antiederivitive
use u subsitution
u=x²+1
du=2x dx
so factor out the 8
![8 \int\limits^8_9 { \frac{2x}{x^2+1} } \, dx](https://tex.z-dn.net/?f=%208%20%5Cint%5Climits%5E8_9%20%7B%20%5Cfrac%7B2x%7D%7Bx%5E2%2B1%7D%20%7D%20%5C%2C%20dx%20)
![8 \int\limits^8_9 { \frac{1}{u} } \, du](https://tex.z-dn.net/?f=%208%20%5Cint%5Climits%5E8_9%20%7B%20%5Cfrac%7B1%7D%7Bu%7D%20%7D%20%5C%2C%20du%20)
and we know that the antideritivitve of 1/u is ln|u|
8ln|x²+1| is an antideritivive
now
![[8ln|x^2+1|]^8_0](https://tex.z-dn.net/?f=%5B8ln%7Cx%5E2%2B1%7C%5D%5E8_0)
![8ln|8^2+1|-8ln|0^2+1|](https://tex.z-dn.net/?f=8ln%7C8%5E2%2B1%7C-8ln%7C0%5E2%2B1%7C)
![8ln|65|+8ln|1|](https://tex.z-dn.net/?f=8ln%7C65%7C%2B8ln%7C1%7C)
![8ln65+0](https://tex.z-dn.net/?f=8ln65%2B0)
the aera is 8ln65
A is the answer
6.
find where they intersect to find the area bounded
f(x)=g(x) at x=-6 and x=2
and g(x) is on top (we can see that because g(0)>f(0))
so we integrate from -6 to 2
![\int\limits^2_{-6} {g(x)-f(x)} \, dx](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E2_%7B-6%7D%20%7Bg%28x%29-f%28x%29%7D%20%5C%2C%20dx%20)
![\int\limits^2_{-6} {8x+48-(x^2+12x+36)} \, dx](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E2_%7B-6%7D%20%7B8x%2B48-%28x%5E2%2B12x%2B36%29%7D%20%5C%2C%20dx%20)
![\int\limits^2_{-6} {8x+48-x^2-12x-36)} \, dx](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E2_%7B-6%7D%20%7B8x%2B48-x%5E2-12x-36%29%7D%20%5C%2C%20dx%20)
![\int\limits^2_{-6} {-x^2-4x+12)} \, dx](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E2_%7B-6%7D%20%7B-x%5E2-4x%2B12%29%7D%20%5C%2C%20dx%20)
this is easy
use reverse power rules
remember that
![\int\limits^a_b {f(x)+g(x)} \, dx = \int\limits^a_b {f(x)} \, dx + \int\limits^a_b {g(x)} \, dx](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5Ea_b%20%7Bf%28x%29%2Bg%28x%29%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5Ea_b%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%5Ea_b%20%7Bg%28x%29%7D%20%5C%2C%20dx%20)
the antiderivitive is
![\frac{-x^3}{3} -2x^2+12x](https://tex.z-dn.net/?f=%5Cfrac%7B-x%5E3%7D%7B3%7D%20-2x%5E2%2B12x)
so
![[\frac{-x^3}{3} -2x^2+12x]^2_{-6}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B-x%5E3%7D%7B3%7D%20-2x%5E2%2B12x%5D%5E2_%7B-6%7D)
=
![(\frac{-2^3}{3} -2(2)^2+12(2))-(\frac{-(-6)^3}{3} -2(-6)^2+12(-6))](https://tex.z-dn.net/?f=%28%5Cfrac%7B-2%5E3%7D%7B3%7D%20-2%282%29%5E2%2B12%282%29%29-%28%5Cfrac%7B-%28-6%29%5E3%7D%7B3%7D%20-2%28-6%29%5E2%2B12%28-6%29%29)
=
![({-8}{3} -8+24)-(72 -72-72)](https://tex.z-dn.net/?f=%28%7B-8%7D%7B3%7D%20-8%2B24%29-%2872%20-72-72%29)
=
![({-8}{3}+ 16)-(-72)](https://tex.z-dn.net/?f=%28%7B-8%7D%7B3%7D%2B%2016%29-%28-72%29)
=
![{-8}{3}+ 16+72](https://tex.z-dn.net/?f=%7B-8%7D%7B3%7D%2B%2016%2B72)
=
![{-8}{3}+ 88](https://tex.z-dn.net/?f=%7B-8%7D%7B3%7D%2B%2088)
=
![\frac{-8}{3} + \frac{264}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-8%7D%7B3%7D%20%2B%20%5Cfrac%7B264%7D%7B3%7D%20)
=
![\frac{256}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B256%7D%7B3%7D%20)
answer is C
Add them all up and then divide by 5. The answer is 1.493
Step-by-step explanation: If we want to put this in standard form, we first want to add 2x² to both sides of the equation to get 2x² + 5x - 17 = 0.
Notice that I have set up the left side of the equation in descending order of powers. In other words, first the x² term, then the x term, then the constant term.
Answer:
A. Option 1
Sign up cost = 0
1 Month = 125
2 Months = 150
3 Months = 175
4 Months = 200
Step-by-step explanation:
For every option simply write what the starting cost is in the top box for every option. Then multiply the monthly cost by how many months for each box and then add the starting cost. The result of the multiplication and addition will be what you put in each box.