Refer to the figure and find the volume V generated by rotating the given region about the specified line. R3 about AB

QUESTION POSTED AT 15/01/2020 - 03:09 AM

Answered by admin AT 15/01/2020 - 03:09 AM

Answer:

Hence, volume is: \dfrac{34\pi}{45} cubic units.

Step-by-step explanation:

We will first express our our equation of the curve and the line bounded by the region in terms of the variable y.

i.e. the curve is rex=\dfrac{1}{16}y^4

and the line is given as:  x=\dfrac{1}{2}y

Since after rotating the given region R_{3} about the line AB.

we see that for the following graph

the axis is located at x=1.

and the outer radius(R) is: \dfrac{1}{16}y^4

and the inner radius(r) is:  \dfrac{1}{2}y

Now, the area of the graph= area of the disc.

Area of graph=\pi(R^2-r^2)

Now the volume is given as:

Volume=\int\limits^2_0 {Area} \, dy

On calculating we get:

Volume=\dfrac{34\pi}{45} cubic units.

Post your answer

Related questions

The image of a point after a –90° rotation about the origin is (–4, 7). What are the coordinates of the preimage?

The point (-4, 7) is in the 2nd quadrant. The coordinate of the preimage of a -90 degrees rotation that resulted to point (-4, 7) will be in the third quadrant. (i.e. both x and y is negative). Hence, answer is (-7, -4).

ANSWERED AT 29/01/2020 - 05:41 PM


QUESTION POSTED AT 29/01/2020 - 05:41 PM

A given line has the equation 10x 2y -2.What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?)x 12O Submitted

10x + 2y = -2
2y = -10x - 2
y = (-10/2)x - 2/2
y = -5x - 1...the slope here is -5...a parallel line will have the same slope.

y = mx + b
slope(m) = -5
(0,12)...x = 0 and y = 12
now we sub...we r looking for b, the y intercept
12 = -5(0) + b
12 = b

so ur parallel line is : y = -5x + 12

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

A given line has the equation 10x -2.2y What is the equation, in slope-intercept form, of the line that is parallel to given line passes through the point (0, 12)?the and )x 12submitted

10x + 2y = -2

2y = -10x - 2

y = -(10/2)x - 2/2

y = -5x  - 1    y = mx + c,   slope m = -5.

If it is parallel, then the slope of the second line ought to be -5 as well.

So you should fill -5 in the bracket.

ANSWERED AT 29/01/2020 - 05:36 PM


QUESTION POSTED AT 29/01/2020 - 05:36 PM

John wants to buy a new bike that costs $337 and he already has saved $103. Estimate to find about how much more John needs to save to buy the bike

John needs 234 dollars more for the bike.  About 235

336-103=234

ANSWERED AT 29/01/2020 - 05:35 PM


QUESTION POSTED AT 29/01/2020 - 05:35 PM

Which of the following is an example of perpendicular lines? I'm thinking it's B, but not sure

Answer:

Second figure is an example of perpendicular lines.

Step-by-step explanation:

The perpendicular lines are those that forms 90^{\circ} at the base of the vertical line.

The straight lines denotes the  90^{\circ} angle

The first figure is not correct both are intersecting tilted lines.

The second figure is correct since they form right angle that is 90^{\circ} angle.

The third figure is again tilted lines hence, not correct.

The fourth figure is again tilted lines hence, not correct.

therefore, second figure is correct.

ANSWERED AT 29/01/2020 - 05:35 PM


QUESTION POSTED AT 29/01/2020 - 05:35 PM

Check all of the values that have three significant figures

They're just the numbers that are not a zero. For example, If i wanted to round 12.034 to three significant figures, then it would be 12.03, as three digits are not zeros!

ANSWERED AT 29/01/2020 - 05:34 PM


QUESTION POSTED AT 29/01/2020 - 05:34 PM

A cylindrical container is packaged inside a prism-shaped box. The box has a volume of 96 cubic units. If the container has a diameter of 4 units and a height of 6 units, what is the volume of the empty space between the cylinder and the box? Round the answer to two decimal places.

Answer:

The volume of the empty space is 20.57 unit³.

Step-by-step explanation:

Given,

The volume of the box = 96 cubic units,

Also, the cylindrical container is packed inside the box.

We know that,

The volume of a cylinder is,

V=\pi (r)^2 h

Where r is the radius of cylinder,

h is its height,

Here, r = \frac{4}{2} = 2 unit   ( Radius = Diameter / 2 )

And, h = 6 units

Thus, the volume of the cylindrical container is,

V=\pi (2)^2(6)

=\frac{22}{7}\times 4\times 6 = \frac{528}{7}\text{ cubic unit}

Hence, the volume of the empty space between the cylinder and the box = Volume of the box - Volume of the container

= 96 - \frac{528}{7}

=\frac{672-528}{7}

=\frac{144}{7}=20.5714285714\approx 20.57\text{ cubic unit}

ANSWERED AT 29/01/2020 - 05:33 PM


QUESTION POSTED AT 29/01/2020 - 05:33 PM

Which of the following figures is NOT a polygon?

The circle isn’t a polygon because it doesn’t have straight sides.

ANSWERED AT 29/01/2020 - 05:33 PM


QUESTION POSTED AT 29/01/2020 - 05:33 PM

Find the zeros of the function. f(x)= 3x^3- 12x^2- 15x a. 0, 1, and -5 b. -1 and 5 c. 0, -1, and 5 d. 1 and -5

F(x) = 3x³ - 12x² - 15x

1) Factor Outside: 3x( x² - 4x - 5)

Factor Inside: 3x(x + 1)(x - 5)

2) Set Equal To 0:
3x = 0
x + 1 = 0
x - 5 = 0

3) Solve:
x = 0, -1, 5

ANSWERED AT 29/01/2020 - 05:31 PM


QUESTION POSTED AT 29/01/2020 - 05:31 PM

What is the equation of a line that is perpendicular to y=3x-2 and passes through the point (6,8)

Answer:

APEX - y = -1/3x +10

Step-by-step explanation:

ANSWERED AT 29/01/2020 - 05:29 PM


QUESTION POSTED AT 29/01/2020 - 05:29 PM

The legs of a right triangle have lengths of 4 and 5 units. Find the length of the hypotenuse.

Answer:

\text{Length of hypotenuse is }\sqrt{41}units

Step-by-step explanation:

Given the legs of right angled triangle 4 and 5 units. we have to find the length of hypotenuse.

By Pythagoras theorem,

In right angled triangle the square of the length of the hypotenuse is equal to sum of squares of the lengths of other two sides

Hypotenuse&^2=Base^2+Height^2\\\\Hypotenuse^2=4^2+5^2\\\\H^2=16+25\\\\H=\sqrt{41}units=6.4units

Hence, \text{length of hypotenuse is }\sqrt{41}units

ANSWERED AT 29/01/2020 - 05:29 PM


QUESTION POSTED AT 29/01/2020 - 05:29 PM

How many significant figures will there be in the answer to the following 403.7*4.03

7 :). The answer is 1626.911. None of these digits are a zero, so therefore all 7 are sig figs :)

ANSWERED AT 29/01/2020 - 05:27 PM


QUESTION POSTED AT 29/01/2020 - 05:27 PM

The image of a point after a –90° rotation about the origin is (–4, 7). What are the coordinates of the preimage? A.(–7, –4) B.(–7, 4) C.(4, –7) D.(7, –4)

The point (-4, 7) is in the 2nd quadrant. The coordinate of the preimage of a -90 degrees rotation that resulted to point (-4, 7) will be in the third quadrant. (i.e. both x and y is negative). Hence, answer is (-7, -4).

ANSWERED AT 29/01/2020 - 05:27 PM


QUESTION POSTED AT 29/01/2020 - 05:27 PM

What is the point-slope equation of the line with slope -13 that goes through the point (5,7)

Point slope formula: 
y-y_1=m(x-x_1)

We know that:
m=-13 
y1=7
x1=5
Plug those into the equation to get a final answer of:
y-7=-13(x-5)

ANSWERED AT 29/01/2020 - 05:23 PM


QUESTION POSTED AT 29/01/2020 - 05:23 PM

Scarlett is trying to find the height of a dam. She stands 90 meters away from the dam and records the angle of elevation to the top of the dam to be 26º. Scarlett's height is 1.65 meters, so what is the hight of the dam

The height of a dam:
h = x + 1.65 m,
where:
x = 90 m · tan 26°
x = 90 · 0.4877
x = 43.90
h = 43.90 m + 1.65 m = 45.55 m
Answer:
The height of the dam is 45.5 m.

ANSWERED AT 29/01/2020 - 05:23 PM


QUESTION POSTED AT 29/01/2020 - 05:23 PM

Point P (-3,-1) is the preimage. Point P’(3,-1) is the image after a reflection is performed. Give the line of reflection.

Answer with explanation:

⇒Position of Pre image = P (-3,-1)

This point  is lying in third Quadrant.

⇒Position of Image = P'(3, -1)

This Point is Lying in Fourth Quadrant.

The Preimage(-3, -1) is reflected along Negative Y axis to get Image (3,-1).

So, Line of Reflection = Y axis

ANSWERED AT 29/01/2020 - 05:23 PM


QUESTION POSTED AT 29/01/2020 - 05:23 PM

Find the slope of the line whose equation is 15 + 3x = 2y.

15+3x=2y
2y=3x+15
y= \frac{3}{2} x+ \frac{15}{2}
Gradient, m=  \frac{3}{2}

ANSWERED AT 29/01/2020 - 05:22 PM


QUESTION POSTED AT 29/01/2020 - 05:22 PM

Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Which equation represents the average of the x-intercepts for f(x) = 4x2 – 24x + 20?

To get the x-intercepts of the function, f(x) = 4x2 – 24x + 20

It has to be equated to zero and the values of x are the x-intercepts. So,

4x2 – 24x + 20 = 0

The resulting equation is a quadratic equation which can be solved by different methods. The solution is

x = 5, 1

The average therefore is:

(1+5/)2 = 3

ANSWERED AT 29/01/2020 - 05:22 PM


QUESTION POSTED AT 29/01/2020 - 05:22 PM

QT bisects ∠PQR. find ∠PQR if ∠RQT = (10x-13) and ∠PQT = (6x+1) i need to know angle PQR and the value of X.

The answer might be 
<PQR = 6x+1
X=3.5

ANSWERED AT 29/01/2020 - 05:21 PM


QUESTION POSTED AT 29/01/2020 - 05:21 PM

The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image? A.(–5, –4) B.(–4, 2) C.(2, 2) D.(2, 4)

Hint:
r_{y=k): (x,y)->(x,-(y-k)+k)
or simplified,
r_{y=k): (x,y)->(x,2k-y)

So in this case, k=-1, x=2, y=-4
(2,-4) -> (2, 2(-1)-(-4)
(2,-4) -> (2, -2+4)
(2,-4) -> (2, 2)

ANSWERED AT 29/01/2020 - 05:19 PM


QUESTION POSTED AT 29/01/2020 - 05:19 PM

Evaluate the expression 3.14(a2 + ab) when a = 4 and b = 3. (Input decimals only, such as 12.71, as the answer.)

Answer:

I got 65.94

Step-by-step explanation

3 x 3=9

3 x 4=12

12+9= 21

21 x 3.14 = 65.94

ANSWERED AT 29/01/2020 - 05:18 PM


QUESTION POSTED AT 29/01/2020 - 05:18 PM

Which statement describes the graph of the system of equations below? 1.5x + 0.2y = 2.68 1.6x + 0.3y = 2.98 The lines are parallel. The lines overlap at all points. The lines intersect at (1.6,1.4). The lines intersect at (3.1,0.5).

1.5x + 0.2y = 2.68....multiply by 0.3
1.6x + 0.3y = 2.98...multiply by - 0.2
------------------------
0.45x + 0.06y = 0.804 (result of multiplying by 0.3)
- 0.32x - 0.06y = - 0.596 (result of multiplying by - 0.2)
----------------------add
0.13x = 0.208
x = 0.208/0.13
x = 1.6

1.5x + 0.2y = 2.68
1.5(1.6) + 0.2y = 2.68
2.4 + 0.2y = 2.68
0.2y = 2.68 - 2.4
0.2y = 0.28
y = 0.28/0.2
y = 1.4

solution (they intersect at) (1.6,1.4)

ANSWERED AT 29/01/2020 - 05:18 PM


QUESTION POSTED AT 29/01/2020 - 05:18 PM

A cone has a diameter of 18 units and height of 8 units. What is its volume?


The radius of your cone is half of 18 units = 9 units.

The volume of any cone is      V = (1/3) · (pi) · (radius)² · (height)

-- Take that formula for the volume of any cone.
-- Write '8' in place of 'height'.
-- Write '9' in place of 'radius'.
-- Write '3.142' in place of 'pi'.
-- Complete the arithmetic.
-- Bada-bing, you've got the volume.

ANSWERED AT 29/01/2020 - 05:17 PM


QUESTION POSTED AT 29/01/2020 - 05:17 PM

The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image? A.(–5, –4) B.(–4, 2) C.(2, 2) D.(2, 4)

The coordinates of the image are : C ) ( 2, 2 )

ANSWERED AT 29/01/2020 - 05:17 PM


QUESTION POSTED AT 29/01/2020 - 05:17 PM

This figure shows the procedure for constructing a A. pair of parallel lines B. perpendicular bisector C. bisector of an angle D. perpendicular from a point on a line

In the question "This figure shows the procedure for constructing a" The correct answer is "bisector of an angle" (option C). To construct an angle bisector: Draw an arc that is centered at the vertex of the angle to intersect both sides of the angle. From the point of intersection of the previous arc and the both sides of the angle, draw two more arcs to intersect at a point. The radius for the two arcs must be equal. Then draw a straight line from the point of intersection of the later set of arcs and the vertex of the angle.

ANSWERED AT 29/01/2020 - 05:17 PM


QUESTION POSTED AT 29/01/2020 - 05:17 PM

A sphere has a diameter of 24 units. What is its volume in cubic units?

Ummm... I explained the whole process earlier, and was mistakenly issued for plagiarism. Which really sucks, because it took forever to type and format all of those formulas and steps.
Here's the shortened version...
V=4/3 \pi r^{3}
d (diameter) = 2r
so 24/2 = 12
plug in...
You should get approx. 7234.56, and don't forget to label it appropriately, it should be units cubed.

ANSWERED AT 29/01/2020 - 05:17 PM


QUESTION POSTED AT 29/01/2020 - 05:17 PM

Find S15 for the geometric series 72 + 12 + 2 + 1/3 +

Hello,

u_{1}=72\\&#10;&#10;u_{2}=\dfrac{72}{6}\\&#10;&#10;u_{3}=\dfrac{72}{6^{2}}\\&#10;&#10;u_{15}=\dfrac{72}{6^{14}}\\&#10;&#10;&#10;s=72*(1+\dfrac{1}{6^{1}}+\dfrac{1}{6^{2}}+\dfrac{1}{6^{3}}++...+\dfrac{1}{6^{14}})\\&#10;=72*(\dfrac{\frac{1}{6^{15}}-1}{\frac{1}{6}-1}})\\&#10;=72*(\dfrac{470184984576-1}{78364164095*5})\\&#10;&#10;=86,400...&#10;&#10;&#10;

ANSWERED AT 29/01/2020 - 05:16 PM


QUESTION POSTED AT 29/01/2020 - 05:16 PM