Answer:
V = 8.06 cubed units
Step-by-step explanation:
You have the following curves:
In order to calculate the solid of revolution bounded by the previous curves and the x axis, you use the following formula:
![V=\pi \int_a^b [(g(x))^2-(f(x))^2]dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_a%5Eb%20%5B%28g%28x%29%29%5E2-%28f%28x%29%29%5E2%5Ddx)
(1)
To determine the limits of the integral you equal both curves f=g and solve for x:
Then, the limits are a = -1 and b = 1
You replace f(x), g(x), a and b in the equation (1):
![V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint_%7B-1%7D%5E%7B1%7D%5B%28%5Cfrac%7B13%7D%7B9%7D-x%5E2%29%5E2-%28%5Cfrac%7B4%7D%7B9%7Dx%5E2%29%5E2%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2Bx%5E4-%5Cfrac%7B16%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5Cint_%7B-1%7D%5E1%20%5B%5Cfrac%7B169%7D%7B81%7D-%5Cfrac%7B26%7D%7B9%7Dx%5E2%2B%5Cfrac%7B65%7D%7B81%7Dx%5E4%5Ddx%5C%5C%5C%5CV%3D%5Cpi%20%5B%5Cfrac%7B169%7D%7B81%7Dx-%5Cfrac%7B26%7D%7B27%7Dx%5E3%2B%5Cfrac%7B65%7D%7B405%7Dx%5E5%5D_%7B-1%7D%5E1%5C%5C%5C%5CV%5Capprox8.06%5C%20cubed%5C%20units)
The volume of the solid of revolution is approximately 8.06 cubed units
Answer:
x= 8.00 Interest rate on $14000
y= 7.50 Interest rate on $7000
Step-by-step explanation:
Let interest rate of $14000 be x%
and Interest rate for $7000 be y %
According to the first condition
14000 * x% - 7000 * y% = 595
multiply by 100
14000x-7000y = 59500
/700
20x-10y=85.................(1)
II condition
x%=y%+0.5%
x=y+0.5
x-y=0.5..................................(2)
solve (1) & (2)
20 x -10 y = 85 .............1
Total value
1 x -1 y = 0.50 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -10
20.00 x -10.00 y = 85.00
-10.00 x + 10.00 y = -5.00
Add the two equations
10.00 x = 80.00
/ 10.00
x = 8.00
plug value of x in (1)
20.00 x -10.00 y = 85.00
160.00 -10.00 y = 85.00
-10.00 y = 85.00 -160.00
-10.00 y = -75.00
y = 7.50
x= 8.00 Interest rate on $14000
y= 7.50 Interest rate on $7000
You divide 33 by 113 and you get .29 times 9 and you get 2.63
Answer:
-3.125
Step-by-step explanation:
She paid $ 4 for renting a video game for 4 days...that means she paid $ 1 per day.
A horizontal axis is labeled days, a vertical axis is labeled cost of rental.
(x,y)...x is gonna be ur days and y is gonna be ur cost of rental
ur equation is gonna be y = x
points are plotted (1,1) , (2,2), (3,3)
^^ this is the graph u use ...graph B
