Answer:
The volume is 
Step-by-step explanation:
The General Slicing Method is given by
<em>Suppose a solid object extends from x = a to x = b and the cross section of the solid perpendicular to the x-axis has an area given by a function A that is integrable on [a, b]. The volume of the solid is</em>
Because a typical cross section perpendicular to the x-axis is a square disk (according with the graph below), the area of a cross section is
The key observation is that the width is the distance between the upper bounding curve 
and the lower bounding curve 
The width of each square is given by
This means that the area of the square cross section at the point x is
The intersection points of the two bounding curves satisfy 
, which has solutions x = ±1.
Therefore, the cross sections lie between x = -1 and x = 1. Integrating the cross-sectional areas, the volume of the solid is
![V=\int\limits^{1}_{-1} {(2-2x^2)^2} \, dx\\\\V=\int _{-1}^14-8x^2+4x^4dx\\\\V=\int _{-1}^14dx-\int _{-1}^18x^2dx+\int _{-1}^14x^4dx\\\\V=\left[4x\right]^1_{-1}-8\left[\frac{x^3}{3}\right]^1_{-1}+4\left[\frac{x^5}{5}\right]^1_{-1}\\\\V=8-\frac{16}{3}+\frac{8}{5}\\\\V=\frac{64}{15}](https://tex.z-dn.net/?f=V%3D%5Cint%5Climits%5E%7B1%7D_%7B-1%7D%20%7B%282-2x%5E2%29%5E2%7D%20%5C%2C%20dx%5C%5C%5C%5CV%3D%5Cint%20_%7B-1%7D%5E14-8x%5E2%2B4x%5E4dx%5C%5C%5C%5CV%3D%5Cint%20_%7B-1%7D%5E14dx-%5Cint%20_%7B-1%7D%5E18x%5E2dx%2B%5Cint%20_%7B-1%7D%5E14x%5E4dx%5C%5C%5C%5CV%3D%5Cleft%5B4x%5Cright%5D%5E1_%7B-1%7D-8%5Cleft%5B%5Cfrac%7Bx%5E3%7D%7B3%7D%5Cright%5D%5E1_%7B-1%7D%2B4%5Cleft%5B%5Cfrac%7Bx%5E5%7D%7B5%7D%5Cright%5D%5E1_%7B-1%7D%5C%5C%5C%5CV%3D8-%5Cfrac%7B16%7D%7B3%7D%2B%5Cfrac%7B8%7D%7B5%7D%5C%5C%5C%5CV%3D%5Cfrac%7B64%7D%7B15%7D)
Answer:
Last one:
The probability of the spinner not landing on A and rolling a prime number is 1/3
Step-by-step explanation:
The probability of the spinner not landing on A: 2/3
Prime outcomes on a dice:
2, 3, 5
The probability of rolling a prime number: 3/6 = 1/2
The probability of the spinner not landing on A and rolling a prime number is:
2/3 × 1/2
1/3
<h2>
Step-by-step explanation:</h2>
Interest, is an additional money paid for borrowing money. it could be simple or compound interest.
simple interest= p×T×R/100
when interest is compounded annually
F= p(1+r)^t
F= future value
p= principal
r= rate
t= time
compound interest is calculated based on the initial and accumulated interest.
<h2>interest Linda earns</h2><h3>fist year</h3>
F= p(n+r)^n
F= 10000(1+0.02)^1
F= 10000×1.02= $10200
interest= 10200-10000
interest = $200
second year
F = 10200(1+0.02)^1
F=10200×1.02= $10404
Interest= 10404-10200
interest= $204
third year
F= 10404(1+0.02)^1
F= 10404(1.02)
F = $10612.08
interest= 10612.08-10404
interest= $208.08
<h2>Bob's interest</h2><h2>I= p×t×R/100</h2>
first year
I=10000×1×0.02/100
interest= $2
second year
I= 10000×2×0.02/100
interest= $4
for the third year
I =10000×3 × 0.02/100
interest= $6
<h2>check answer above for final computation</h2>
Answer:
it would be three
Step-by-step explanation:
Answer:
9x-3
Step-by-step explanation:
To do this, we can make an equation and add like terms.
The equation is 2x+3x-1+4x-2=p. P stands for perimeter.
Now, simplify. Add like terms.
9x-1-2=p
9x-3=p
9x-3
The answer is D. 9x-3
Hope this helps!
