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Llana [10]
3 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]3 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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Select the correct answer.
andrew-mc [135]

The prediction for average temperature is 53.06° F

Given: The equation for line of best fit:

y = -3.32x + 97.05

What is line of best fit?

Line of best fit is the line that is drawn through the points and it minimizes the error between the actual data and the predicted data.

In a regression graph, there are many scattered points and it becomes very difficult to predict a general equal if we focus on the coordinates and relations of each points. The line of best fit, is a line that passes through the center or from a position where the error between the point and the line is the minimum and it becomes easy to predict or a derive an equation or a relation.

What is a response variable?

A response variable is a variable that is dependent on one or more independent or dependent variables for it's value. So let's say in this equation y = mx + c, y is the response variable as on the change of variable x , y will have different values that is y will response differently for different values of x. Hence y is the dependent variable.

What is predictor variable?

A predictor variable is a variable that is independent of the influence from any other variable, and a change in this variable will give different outcomes. It is called predictor because or a change in it's value we can predict an outcome.

Let's solve the question that is given:

Now y is the response variable and x is the predictor variable.

From the given graph, we see

x = inches of rain

y = average temperature

To make the prediction for x = 13.25, we place the value of x in the equation of line of best fit, that is:

y(13.25) = -3.32*13.25 + 97.05 = 53.06

Hence our prediction or the response for average temperature is 53.06° F

Know more on "line of best fit" here: brainly.com/question/14279419

#SPJ1

4 0
1 year ago
Please help asap!!!
Tatiana [17]

Answer:

w = 6

Step-by-step explanation:

ST = w + 6,

PR = w

From the diagram given, we can deduce that PR is the midsegment of ∆QST. Therefore, according to the midsegment theorem:

PR = ½ of ST

Plug in the values into the equation and solve for w.

w = \frac{1}{2}(w + 6)

w = \frac{w}{2} + 3 (distributive property of equality)

w - 3 = \frac{w}{2} (subtraction property of equality)

2(w - 3) = \frac{w}{2}*2 (multiplication property of equality)

2w - 6 = w

2w - 6 - 2w= w - 2w (subtraction property of equality)

- 6 = - w

Divide both sides by -1

6 = w

w = 6

5 0
3 years ago
Find x. <br> 30 <br> 20 <br> Need help with this question asap
Molodets [167]
Cos=adjacent/hypotenuse
Cos30=x/20
x=cos30 *20

Sorry I don’t have a calculator right now
6 0
3 years ago
Read 2 more answers
Please help me I'm not sure what the answer is
gogolik [260]

Step-by-step explanation:

yes yours answer is correct .

4 0
3 years ago
PART A: A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the tr
Greeley [361]

Complete Question:

Johnny printed two maps of a walking trail near his home. The length of the walking trail on the first map is 8 cm.

(a) Choose a length between 5 cm and 15 cm for the walking trail on the second map: ________cm.  

(b) Determine the scale factor from the first map to the second map.

(c)  A landmark on the first map is a triangle with side lengths of 3 cm, 4 cm, and 5 cm. What are the side lengths of the triangle landmark on the second map?  

(d) Draw one of the triangles from part C. Label the side lengths and vertices accordingly. You may use this drawing tool or draw your triangle on paper:

Answer:

(a) Length = 4cm

(b) Scale factor = 0.5

(c) 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale

(d) See attachment for triangle

Step-by-step explanation:

(a) Choose a length between 5 cm and 15 cm

Length =4cm <em>--- This is solely up to you (you can make use of any length between 5 cm and 15 cm)</em>

(b) The scale factor

The scale factor (k) is calculated as:

k = \frac{New\ Length}{Old\ Length}

k = \frac{4cm}{8cm}\\

k = 0.5

(c) What are side lengths of 3 cm, 4 cm, and 5 cm on the second landmark

Using:

k = \frac{New\ Length}{Old\ Length}

The old lengths, in this case are: 3cm, 4cm and 5cm

Make New length the subject

New\ Length = k * Old\ Length

When Length = 3cm

New\ Length = 0.5 * 3cm = 1.5cm

When Length = 4cm

New\ Length = 0.5 * 4cm = 2cm

When Length = 5cm

New\ Length = 0.5 * 5cm = 2.5cm

So: 3cm, 4cm and 5cm are represented by 1.5cm, 2cm and 2.5cm respectively, on the second scale

(d) See attachment for triangle

7 0
3 years ago
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