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:
The corresponding point is (5,8)
Step-by-step explanation:
In this problem we know that
The rule of the transformation is equal to
(x,f(x)) ------> (x,f(x)+4)
so
for the point (5,4)
x=5, f(x)=4
substitute
(5,4) ------> (5,4+4)
(5,4) ------> (5,8)
therefore
The corresponding point is (5,8)
This is what the test said so option D
Considering High School level question, answer can be written as:
A system of 2 linear equations is [two] dimensional. It is a graph of [two] lines. The solutions can be [unique] solution if the graph intersects. [No] solution if the lines are parallel - meaning they have the same slope, or [Infinitely many] solutions if they are the same line.
Explanation:
when two lines are drawn on a two-dimensional plane then there are only three possible cases:
Case1: lines will intersect
In that case you will get a unique solution at the intersection point.
Case2: lines are parallel but don't touch each other
In that case there will be no point which lies on both lines so No solution.
Case3: lines are overlapping.
In that case all the points lies on both lines so infinitely many solutions.
The answer to the first one is 15.6 and the second one is 1.76
