Answer:![A=\frac{14}{9}\cdot \sqrt{2}\ unit^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B14%7D%7B9%7D%5Ccdot%20%5Csqrt%7B2%7D%5C%20unit%5E2)
Step-by-step explanation:
Given
Two curves are given
![y=10 x^2](https://tex.z-dn.net/?f=y%3D10%20x%5E2)
and ![y=x^2+2](https://tex.z-dn.net/?f=y%3Dx%5E2%2B2)
the two curves intersect at
![10x^2=x^2+2](https://tex.z-dn.net/?f=10x%5E2%3Dx%5E2%2B2)
![x=\pm \frac{\sqrt{2}}{3}](https://tex.z-dn.net/?f=x%3D%5Cpm%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D)
to get the we need to integrate the curves over x axis
![A=\int_{-\frac{\sqrt{2}}{3}}^{\frac{\sqrt{2}}{3}}\left ( x^2+3-10x^2\right )dx](https://tex.z-dn.net/?f=A%3D%5Cint_%7B-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D%7D%5E%7B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D%7D%5Cleft%20%28%20x%5E2%2B3-10x%5E2%5Cright%20%29dx)
![A=2\int_{0}^{\frac{\sqrt{2}}{3}}\left ( 3-9x^2\right )dx](https://tex.z-dn.net/?f=A%3D2%5Cint_%7B0%7D%5E%7B%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D%7D%5Cleft%20%28%203-9x%5E2%5Cright%20%29dx)
![A=2\left [ 3\left ( \frac{\sqrt{2}}{3}\right )-\frac{9}{3}\left ( \frac{\sqrt{2}}{3}\right )^3\right ]](https://tex.z-dn.net/?f=A%3D2%5Cleft%20%5B%203%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D%5Cright%20%29-%5Cfrac%7B9%7D%7B3%7D%5Cleft%20%28%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B3%7D%5Cright%20%29%5E3%5Cright%20%5D)
![A=2\sqrt{2}\left [ 1-\frac{2}{9}\right ]](https://tex.z-dn.net/?f=A%3D2%5Csqrt%7B2%7D%5Cleft%20%5B%201-%5Cfrac%7B2%7D%7B9%7D%5Cright%20%5D)
![A=\frac{14}{9}\cdot \sqrt{2}\ unit^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B14%7D%7B9%7D%5Ccdot%20%5Csqrt%7B2%7D%5C%20unit%5E2)
Answer:
the answer is about 8 cuz the answer shows 7.12 if you divide mentally
Answer: Last option.
Step-by-step explanation:
The total amount of concrete in the ramp (
) will be the sum of the volume of the rectangular prism (
) and the volume of the triangular prism (
)
![V_t=V_{rp}+V_{tp}](https://tex.z-dn.net/?f=V_t%3DV_%7Brp%7D%2BV_%7Btp%7D)
The formulas are:
![V_{rp}=lwh](https://tex.z-dn.net/?f=V_%7Brp%7D%3Dlwh)
Where "l" is the lenght, "w" is the width and "h" is the height.
![V_{tp}=\frac{bhl}{2}](https://tex.z-dn.net/?f=V_%7Btp%7D%3D%5Cfrac%7Bbhl%7D%7B2%7D)
Where "l" is the lenght, "b" is the base and "h" is the height.
Substituting, we get:
![V_t=V_{rp}+V_{tp}\\\\V_t=lwh+\frac{bhl}{2}\\\\V_t=(18in)(6in)(6in)+\frac{(8in)(6in)(18in)}{2}\\\\V_t=1,080in^3](https://tex.z-dn.net/?f=V_t%3DV_%7Brp%7D%2BV_%7Btp%7D%5C%5C%5C%5CV_t%3Dlwh%2B%5Cfrac%7Bbhl%7D%7B2%7D%5C%5C%5C%5CV_t%3D%2818in%29%286in%29%286in%29%2B%5Cfrac%7B%288in%29%286in%29%2818in%29%7D%7B2%7D%5C%5C%5C%5CV_t%3D1%2C080in%5E3)
Answer:
option (B).
Step-by-step explanation:
it's really simple....
just replace the (n) near the 3 with 1,2,3,4,5 and 6 and then solve the maths and when you're done , you add the answers all up.
sooo...
3(1)-2 = 1
3(2)-2 = 4
3(3)-2 = 7
3(4)-2 = 10
3(5)-2 = 13
3(6)-2 = 16
now we add them all up...
1+4+7+10+13+16 = <u>5</u><u>1</u><u>.</u>
Hope this helps.
Good luck.