Answer:
x = 2, - 3/2.
Step-by-step explanation:
|4x - 1| = 7
4x - 1 = 7 or 4x - 1 = -7
4x = 8 or 4x = -6
x = 2 , x = -3/2.
Answer:
Step-by-step explanation:
Since x represents the length in feet, and the width is 2 ft shorter than 3 times the length, the width is 3x-2.
The perimeter is twice the sum of length and width, so we can write the equation ...
76 = 2(x + (3x-2))
38 = 4x -2 . . . . . divide by 2, simplify
40 = 4x . . . . . . . .add 2
10 = x . . . . . . . . . the length of the garden is 10 ft
The width of the garden is ...
3·10 -2 = 28 . . . feet
The width of the garden is 28 feet.
Looks like the integral is
The integration region is the upper half of a circle in the <em>x</em>-<em>y</em> plane centered at the origin with radius 8. So, in polar coordinates, the integral is
where we substituted 
and 
, which gives
Answer:
Step-by-step explanation:
a) about the line y = 3
⇒ 
is the intersection point
So,
b) about the line x = 5
⇒ 
So,
![V = \int\limits^3_0\pi([5-0]^2-[5-y^2/9]^2)\:dy=\pi\int\limits^3_0(25-25+10y^2/9-y^4/81)\:dy=\\\\=\pi(10y^3/27-y^5/405)|^3_0=\pi(10-3/5)=\frac{47}{5} \pi](https://tex.z-dn.net/?f=V%20%3D%20%5Cint%5Climits%5E3_0%5Cpi%28%5B5-0%5D%5E2-%5B5-y%5E2%2F9%5D%5E2%29%5C%3Ady%3D%5Cpi%5Cint%5Climits%5E3_0%2825-25%2B10y%5E2%2F9-y%5E4%2F81%29%5C%3Ady%3D%5C%5C%5C%5C%3D%5Cpi%2810y%5E3%2F27-y%5E5%2F405%29%7C%5E3_0%3D%5Cpi%2810-3%2F5%29%3D%5Cfrac%7B47%7D%7B5%7D%20%5Cpi)
