Answer:

Step-by-step explanation:

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:
1/3
Step-by-step explanation:
<span>It might be helpful to remember that the definitions of R2 and R3 are not geometric at all. R2 is the set of all ordered pairs of real numbers, whereas R3 is the set of all ordered triples of real numbers. W is a subspace fo R3, and so it still consists of elements which are triples, not pairs.
The fact that R2 and W can be visualized with the same geometric picture, namely the xy plane, is one way to see in a concrete way the isomorphism which the second poster refered to.</span>