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Llana [10]
2 years ago
13

For the region bounded by y=2x​, the​ x-axis, and x=1​, determine which of the following is​ greater: the volume of the solid ge

nerated when the region is revolved about the​ x-axis or about the​ y-axis.When the region is revolved about the​ x-axis, the volume is​(Type an exact​ answer, using piπ as​ needed.)When the region is revolved about the​ y-axis, the volume is​(Type an exact​ answer, using piπ as​ needed.)Which volume is​ greater?A.The volume about the y dash axis is greater.The volume about the y-axis is greater.B.The volumes are equal.The volumes are equal.C.The volume about the x dash axis is greater.
Mathematics
1 answer:
telo118 [61]2 years ago
7 0

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,

\int\limits^1_0 {(pi)y^{2} } \, dx

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,

\int\limits^2_0 {pi - pix^{2} } \, dy = \int\limits^2_0 {1 - y^{2}/4 } \, dy

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.

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A dilation has center (0,0). Find the image of the point L(-4,0) for the scale factor 9.
Andreyy89

Answer:

L' = (-36, 0)

Step-by-step explanation:

If the point (x, y) is dilated by a scale factor of k about the center (0, 0), then its image is the point (kx, ky)

∵ A dilation has a center (0, 0)

∵ The point L is (-4, 0)

∴ x = -4 and y = 0

∵ The scale factor of dilation is 9

∴ k = 9

→ By using the rule above

∵ kx = 9(-4) = -36

∵ ky = 9(0) = 0

∵ The image of the point L is (kx, ky)

∴ L' = (kx, ky)

∴ L' = (-36, 0)

8 0
2 years ago
Your reading material states that many banks pay interest that is calculated
Step2247 [10]
Carry on... There is not sufficient information to answer
3 0
3 years ago
What are the x and y intercept of c = 0.75m + 2.25?
lakkis [162]
The y intercept is 2.25 and x intercept is -3
6 0
3 years ago
Read 2 more answers
Heyy pls help! worth 20 points, and please only help if you know the answer. also no links those r kinda annoying lol
iragen [17]

Step 1: Find the slope:

    m= \dfrac{y_2-y_1}{x_2-x_1}= \dfrac{-2-7}{4-(-2)} =  \dfrac{-9}{6}= -\dfrac{3}{2}

This gives you y=-\dfrac{3}{2}x+b, but we need to find b.

To find b, substitute in one (x,y) pair and it doesn't matter which one.  I'll go with (4,-2):

    \begin{aligned}-2&=-\dfrac{3}{2}(4)+b\\[0.5em]-2&=-6+b\\[0.5em]4&=b\end{aligned}

Now take that b-value and plug in into the slope-intercept form:

     y=-\dfrac{3}{2}x+4

It's always a good idea to toss in the other x-value from the other point, to make sure it checks out.

7 0
3 years ago
Elena bought a backpacking tent to take with her on hiking trips.
Masteriza [31]

Answer:

Question 1 = c) Medium: 88 ft²

Question 2 = d) 46.7 ft³

Step-by-step explanation:

Question 1

We would be solving this question by finding the surface area of the tent. The shape of the tent is a square based pyramid.

The surface area of a square based pyramid(tent) =

a² + 2ah

Where in the diagram,

a = base length = 4 ft

h = height of the pyramid (tent ) = 9ft

Surface area = 4² + 2 × 4 × 9

= 16 + 72

= 88ft²

Therefore, the size tarp should she purchase is Medium: 88 ft²

Question 2

For question 2, from the attached diagram, we can see that the diagram is a square based pyramid.

To calculate the amount of water that would fill the square based pyramid, we would have to find the Volume of the tent(square based pyramid).

The formula for the Volume of the tent(square based pyramid) = 1/3(a²h)

Where a = base edge

h = height of the pyramid.

From the diagram,

a = base edge => 4ft.

From the question,

h = height of the tent is given as how tall the tent is = 8.75ft.

Therefore, 1/3(a²h)

1/3 × (4ft)²× 8.75ft

= 46.67ft³

Approximately = 46.7ft³

Therefore, the amount of water it would it take to fill the tent, if the tent is 8.75 ft tall is 46.7ft³

3 0
3 years ago
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