Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves and lines about the y-axis. =-x^2 , y=6 - 5 x, x=0, for x> =0

The two curves intersect when

The region bounded by and the two curves "ends" with a vertex where . So over the interval [0, 2], we have , so that the volume is

That is, each cylindrical shell has a radius of and height , and their contribution to the total volume is times the radius and height.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

step-by-step explanation: