Answer:
4
Step-by-step explanation:
set

constrain:

Partial derivatives:

Lagrange multiplier:

![\left[\begin{array}{ccc}1\\1\end{array}\right]=a\left[\begin{array}{ccc}2x\\2y\end{array}\right]+b\left[\begin{array}{ccc}3x^2\\3y^2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C1%5Cend%7Barray%7D%5Cright%5D%3Da%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2x%5C%5C2y%5Cend%7Barray%7D%5Cright%5D%2Bb%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3x%5E2%5C%5C3y%5E2%5Cend%7Barray%7D%5Cright%5D)
4 equations:

By solving:

Second mathod:
Solve for x^2+y^2 = 7, x^3+y^3=10 first:

The maximum is 4
Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,

which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,

If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.
Answer:
l >= 60
Step-by-step explanation:
l greater than or equal to 60