Answer:
Step-by-step explanation:
Consider the graphs of the 
and 
.
By equating the expressions, the intersection points of the graphs can be found and in this way delimit the area that will rotate around the Y axis.
then 
o 
. Therefore the integration limits are:
and 
The inverse functions are given by:
and 
. Then
The volume of the solid of revolution is given by:
![\int\limits^{64}_ {0} \, [2\sqrt{y} - \frac{y}{4}]^{2} dy = \int\limits^{64}_ {0} \, [4y - y^{3/2} + \frac{y^{2}}{16} ]\ dy = [2y^{2} - \frac{2}{5}y^{5/2} + \frac{y^{3}}{48} ]\limits^{64}_ {0} = 546.133 u^{2}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B2%5Csqrt%7By%7D%20-%20%5Cfrac%7By%7D%7B4%7D%5D%5E%7B2%7D%20%20dy%20%3D%20%5Cint%5Climits%5E%7B64%7D_%20%7B0%7D%20%5C%2C%20%5B4y%20-%20y%5E%7B3%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B2%7D%7D%7B16%7D%20%5D%5C%20%20dy%20%3D%20%5B2y%5E%7B2%7D%20-%20%5Cfrac%7B2%7D%7B5%7Dy%5E%7B5%2F2%7D%20%2B%20%5Cfrac%7By%5E%7B3%7D%7D%7B48%7D%20%5D%5Climits%5E%7B64%7D_%20%7B0%7D%20%3D%20546.133%20u%5E%7B2%7D)
First thing you should do is reduce coefficients.
1st equation has all multiples of '2'. Divide by 2
---> x +3y = -6
2nd equation has multiples of 5. Divide by 5.
---> x - y = 2
Now elimination part is easier.
Eliminate 'x' variable by subtracting 2nd equation from 1st.
x + 3y = -6
-(x - y = 2)
----------------------
4y = -8
Solve for 'y'
4y = -8
y = (-8)/4 = -2
Substitute value for 'y' back into 2nd equation:
x - (-2) = 2
x + 2 = 2
x = 0
Solution to system is:
x=0, y =-2
4/572
divide top and bottom by 4
1/143
or in decimal form
.006993007
Y =
x + 3
y = x - 4
Since both equations are equal to y, you can set the two values equal to each other and solve for x.
x + 3 = x - 4 Multiply both sides by 2
x + 6 = 2x - 8 Add x to both sides
6 = 3x - 8 Add 8 to both sides
14 = 3x DIvide both sides by 3
4
= x
Now, plug the x value into one of the original equations, I'll plug it into y = x - 4.
y = x - 4 Plug in the x value
y = 4
- 4 Subtract
y =
x = 4 and
y =
Answer:-p-30
Step-by-step explanation: First to get rid of the parantheses we have to multiply 5 times everything inside it.
4p-5(p+6)
4p-5p-30
Now combine like terms.
4p-5p-30
-1p-30
or
-p-30
Hope this helps!
