Use the given function to find the
-coordinate of
.
![x=2 \implies y = 10+8\cdot2+2^2-2^3 = 22](https://tex.z-dn.net/?f=x%3D2%20%5Cimplies%20y%20%3D%2010%2B8%5Ccdot2%2B2%5E2-2%5E3%20%3D%2022)
Find the equation of the line through the origin and
. This line has slope
![\mathrm{slope} = \dfrac{22-0}{2-0} = 11](https://tex.z-dn.net/?f=%5Cmathrm%7Bslope%7D%20%3D%20%5Cdfrac%7B22-0%7D%7B2-0%7D%20%3D%2011)
and passes through (0, 0), so its equation is
![y - 0 = 11 (x-0) \implies y = 11x](https://tex.z-dn.net/?f=y%20-%200%20%3D%2011%20%28x-0%29%20%5Cimplies%20y%20%3D%2011x)
Then the area of the shaded region is given by the definite integral
![\displaystyle \int_0^2 (y - 11x) \, dx = \int_0^2 (10 + 7x + x^2 - x^3) \, dx \\\\ ~~~~~~~~ = \left(10x + \frac72 x^2 + \frac13 x^3 - \frac14 x^4\right)\bigg|_0^2 \\\\ ~~~~~~~~ = 10\cdot2+\frac72\cdot2^2+\frac13\cdot2^3-\frac14\cdot2^4 = \boxed{\frac{98}3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E2%20%28y%20-%2011x%29%20%5C%2C%20dx%20%3D%20%5Cint_0%5E2%20%2810%20%2B%207x%20%2B%20x%5E2%20-%20x%5E3%29%20%5C%2C%20dx%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%20%5Cleft%2810x%20%2B%20%5Cfrac72%20x%5E2%20%2B%20%5Cfrac13%20x%5E3%20-%20%5Cfrac14%20x%5E4%5Cright%29%5Cbigg%7C_0%5E2%20%5C%5C%5C%5C%20~~~~~~~~%20%3D%2010%5Ccdot2%2B%5Cfrac72%5Ccdot2%5E2%2B%5Cfrac13%5Ccdot2%5E3-%5Cfrac14%5Ccdot2%5E4%20%3D%20%5Cboxed%7B%5Cfrac%7B98%7D3%7D)
Y is going to be equal to four
Step-by-step explanation:
Statements
1.RA equal RB
2.RP equal RP
3.RA is perpendicular to AP, RB is perpendicular to PB
4.right triangle RAP is congruent to Right triangle RBP
5.PA equal PB
Reasons
1.radii of same circle are equal
2.Reflexitive
3.Radius is perpendicular to tangent
4.HL
5 CPCTC
If you are trying to find the cost of the basket ball, it is $8.15.
Step 1: Find 20% of 10.95- which is 2.19- and subtract 2.19 from 10.95-which is 8.76.
Step 2: Find 7% of 8.76-which is 0.6132- and subtract 0.6132 from 8.76-which is 8.1468
Step 3: Round to the nearest hundredth, which gives you 8.15.
Thus, $8.15 is your answer.