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)
Both rooms share a common side whose dimension is unknown. Call it x.
Then, the area of both squares have x as common factor.
So, x is the greatest common factor of 104 and 130.
You should know how to calculate the greatest common factor of two integers.
Just find the prime factors and choose the common factors raised to the lowest exponent.
104 = (2^3) (13)
130 = (2) (5)(13)
=> the greatest common factor is 2 * 13 = 26, and that is the greatest possible integer length of the shared wall.
Answer: 26
The stem and leaf plot will look like:
6 | 1 5 8 - 3 scores
7 | 1 7 7 9 - 4 scores
8 | 2 3 4 5 7 9 - 6 scores
9 | 0 1 4 7 9 - 1 score
To total up the number of students who scored less than 90, we have 3 under 60-69, 4 under 70-79, and 6 under 80-89, so this is 3 + 4 + 6. This is the third choice.
Answer:
b) -9.25
Step-by-step explanation:
-1/4 = -0.25
-9 + -0.25 = -9.25
-10, -9.75, -9.5, -9.25, -9, -8.75, -8.5, -8.25, -8, -7.75, -7.5, -7.25, -7
Hope this helps!
Answer:
5x + 45
Step-by-step explanation:
distribute 5 to both x and 9 so multiply them both
