Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(6x), y = 4, y = 6, x = 0; about the y-axis step 1 we will use horizontal strips. such a strip has a vertical span of δy. sketch the region.

V = 2219.08π

Step-by-step explanation:

If you use the washer/disk method as you indicated you were going to in the statement "we will us horizontal strips", you have to solve that equation for x.  The equation solved for x is

The bounds are y-intervals from 4 to 6, and we are rotating about the y-axis.  I cannot sketch the graph for you here, but if you need it, graph y = ln(6x) and you'll see what it looks like.  I can only help you with the calculus of it, not the drawing of it.

The volume formula then for this is

Squaring what's inside the parenthesis gives you:

To make this a tiny bit simpler we can pull out the fraction:

The antiderivative of e to the 2y power is found:

from 4 to 6

We can then pull out the 1/2:

from 4 to 6.

Evaluating that antiderivative using the First Fundamental Theorem of calculus gives you:

which simplifies to

If you leave your answer in terms of pi it is:

2219.08π or if you multiply pi in it is:

6971.44863

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".