Find the volume generated by rotating the region in the first quadrant bounded by y =e" and the X-axis from = 0 to x = ln(3) about the y-axis. Express your answer in exact form. Volume =

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Answer 1

Answer:

The volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3.

To find the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis, we can use the disk method. The disk method involves slicing the region into thin disks and adding up their volumes.

The volume of each disk is πr2h, where r is the radius of the disk and h is the thickness of the disk. In this case, the radius of each disk is x and the thickness is dx.

So, the volume of the region is:

V = ∫0ln(3)πx2dx

We can use the power rule for integration to solve this integral:

V = π∫0ln(3)x2dx = π[(x3)/3]0ln(3) = π[(ln(3)3)/3 - (03)/3] = (πln(3)3)/3

Therefore, the volume generated by rotating the region in the first quadrant bounded by y = ex and the x-axis from x = 0 to x = ln(3) about the y-axis is (πln(3)3)/3. This is the exact form of the volume.

To know more about disk method refer here:

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What is the average rate of change of h over the interval 5 ≤ t ≤ 9 ?

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Answer:

5 because its greatest

Answer:

8!-4!

6!+6?+72817#8288288#+287228282272777337

Can anyone tell me how to graph 7x+y=5

Answers

You have the equation 7x+y=5
But you must rearrange this into y=mx+b form
to do this subtract 7x from both sides

y= -7x+5

On the y axis plot a dot on 5 because that is the y intercept.

To find the x intercept let y=0
0= -7x+5
1. Subtract 5 to both sides
-5=-7x
2. Divide by -7 to both sides
x= -5/-7
x=5/7
The x intercept is 5/7, so on the x axis mark a dot on 5/7 which is approximately at 0.7
Once you have marked one dot on the y axis at 5 and another dot on the x-axis at 0.7 then you draw a straight line through these points and you have graphed the function 7x+y=5

To graph an equation, you first need to solve it for y. This means turning the equation into this form: Y=.......

For your equation, once you solve it for Y, you get this:

$y = -7x +5$

Now, the coefficient of X is a very crucial part of graphing an equation. Once the equation is solved for Y, the coefficient of X is going to be the slope of the line you are graphing. The slope of a line is how much Y goes up every time X is increased by 1.

To graph an equation, you need to put in a number for X and find the matching value for Y and then graph that point. To do this, you will need a coordinate plane. I can't show you what that looks like on here. But, I will do my best to explain how it is done.

Now, for your equation:

$y = -7x +5$

Simply chose a number for X and find the matching value for Y. I'll try 0 for an example:

$y = -7(0) +5$

-7 * 0 is 0. Therefore, your new equation looks like this:

$y =+5$

Therefore, one "Solution pair" to this equation is (X=0,Y=5)

Simply repeat this process and plot the solution pairs on the coordinate plane and then connect the dots.

What is the scale factor for the set of similar figures?

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$k=(7)/(20)$

Toilet rolls come in packs of 4 and 9the 4 pack is priced at 2.04 pound
the 8 pack is prices at 3.68 pound
by calculating the price per roll, determine which pack is better value.
show your working

Answers

Answer:

8 pack.

Step-by-step explanation:

For the 4 pack, price per roll = 2.04 / 4 = £0.51

For the 8 pack, price per roll = 3.68 / 8 = £0.46.

What is 6,000 in word form?

Answers

six thousand, is the answer in word form

it is six thousand ^~^

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