Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = √x, y = 2, x = 0.

a. the x-axis
b. the line y = 2
c. the y-axis
d. the line x = -1

Answers

Answer 1

Answer:

a) 8π

b) 8/3 π

c) 32/5 π

d) 176/15 π

Step-by-step explanation:

Given lines :  y = √x, y = 2, x = 0.

a) The x-axis

using the shell method

y = x = , x = y^2

h = y^2 , p = y

vol = ( 2π ) [tex]\int\limits^2_0 {ph} \, dy[/tex]

     = [tex]( 2\pi ) \int\limits^2_0 {y.y^2} \, dy[/tex]  

Vol = 8π

b) The line y = 2  ( using the shell method )

p = 2 - y

h = y^2

vol = ( 2π ) [tex]\int\limits^2_0 {ph} \, dy[/tex]

     = [tex]( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy[/tex]

     = ( 2π ) * [ 2/3 * y^3  - y^4 / 4 ] ²₀

Vol  = 8/3 π

c) The y-axis  ( using shell method )

h = 2-y  = h = 2 - √x

p = x

vol = [tex](2\pi ) \int\limits^4_0 {ph} \, dx[/tex]

     = [tex](2\pi ) \int\limits^4_0 {x(2-\sqrt{x} ) } \, dx[/tex]

     = ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀

vol = ( 2π ) ( 16/5 ) = 32/5 π

d) The line x = -1    (using shell method )

p = 1 + x

h = 2√x

vol = [tex](2\pi ) \int\limits^4_0 {ph} \, dx[/tex]

Hence   vol = 176/15 π

attached below is the graphical representation of P and h

Use The Disk Method Or The Shell Method To Find The Volumes Of The Solids Generated By Revolving The

Related Questions

Brainliest, 10 Points, & Thanks if answer to these questions!!!!!!!!

Answers

Answer:

D

Step-by-step explanation:

+1 and -1 change the x postion

Dave wants to build a rectangular screened-in porch that is 20 feet long, and it will extend 6 feet out from the backside of his house.


Dave sketches a scale drawing of the porch. Choose a reasonable size and scale for Dave’s drawing of the porch. How should Dave label the dimensions of the model?

Answers

Answer:

Scale of the drawing would be 20/12 inch and 0.6 (6/12) inch

Step-by-step explanation:

For most of the residential buildings an scale of 1 inch = 12 feet can be used to draw the residential units.

In that case the scale of the drawing would be 20/12 inch and 0.6 (6/12) inch

Dave should label the dimensions in inches

Don’t save the answer and I really need help

Answers

9514 1404 393

Answer:

  zero solutions

Step-by-step explanation:

The first inequality has a boundary line with a slope of 3 and a y-intercept of 9. Shading is above the boundary line.

The second inequality has a parallel boundary line with a slope of 3 and a y-intercept somewhat lower, at -1. Shading is below this boundary line.

There is a gap between the shaded areas, so no points will be solutions to both inequalities.

Please help, please no links or websites

Answers

Answer:

12

Step-by-step explanation:

Just substitute 3 for n and solve.

Solve the expression [tex]2+(3-1)5\\[/tex]

Use PEMDAS and solve.

(3-1) = 2 so it becomes 2 + (2)5

Then multiply 2 and 5 to get 10.

Then add 2 so you get 12.

[tex]a_{3}[/tex]=12

need help with these table

Answers

Tens: 73,650
Hundreds: 73,700
Thousands: 74,000

Mary plants roseas in 1/4 of her garden. She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. What fraction of Mary's garden has tulips?

Answers

Let x represent the full area if Mary's garden.

Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4

She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12

The portion of the garden on which she planted tulips would be

x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12

x - x/3 = (3x - x)/3 = 2x/3

Therefore, the fraction of Mary's garden that has tulips would be

(2x/3) /x = 2/3

A car that is normally $4200 is on sale for 80% of its original cost.
what is the sale price of the car? ​

Answers

Answer:

$3360

Step-by-step explanation:

4200(.80) = 3360

anything less than 1.00 will be a decreasing amount, so i just took the 80% and put it as a decimal and multiplied to find the current cost of the car

HELP PLSSS I WILL GIVE YOU BRAINLYEST
i suck at math this is easy

Answers

OPTION C is the correct answer.

Express 6x-9≤3x-11 in interval notation

Answers

Answer:

(-∞, - 2/3)

Step-by-step explanation:

Given the inequality :

6x-9≤3x-11

Collect like terms :

6x - 3x ≤ - 11 + 9

3x ≤ - 2

Divide both sides by 3

3x/3 ≤ - 2/3

x ≤ - 2/3

(-∞, - 2/3)

-3 to the 3rd power + 2

Answers

Answer:-7

Step-by-step explanation: -3^3+ 2

-9+2= -7

I got -25 with the 3^3 in parenthesis and without them.

Find f(x) and g(x) so that the function can be described as y = f(g(x)).
y=[tex]\frac{9}{x^2} + 2[/tex]

Answers

Hope this help!!!

Have a nice day!!!

PLWASE HELP GEOMETRY
A hot-air balloon is tied to the ground with two taut ropes. One rope is directly under the balloon and makes a right
angle with the ground. The other rope forms an angle of 60° with the ground. Which statements are correct?

Answers

Using trigonometry solve for h and d.

H :

Sin(60) = h/120

H = 120 x sin(60)

H = 103.9 = 104 feet

D:

Cos(60) = d/120

D = 120 x cos(60)

D = 60 feet

The correct answers:

A. D = 60 ft.

C. H = 104 ft

Find the area of the polygon.
is this right?
ERGENT

Answers

Answer:

The answer is in the picture.

15cm²

45 is what percent of 82
what percent of 5 is 26
Round each answer to the nearest TENTH!

HELP FINALS TODAY :(

Answers

Answer:

45 is 54.9 percent of 82.

26 is 520% of 5.

Answer:

45 is 55% of 82 and 520% of 5 is 26.

Step-by-step explanation:

First you want to set up a proportion, using the is over of formula (Is/of= %/100). In the first problem, 45 will be the is, 82 will be the of, for % will be the x, and 100 will go on the bottom (it will look something like this: 45/82=x/100). When you solve it, you get around 55 (45x100/82.) Same thing for the next equation, use the same formula (is/of=%/100) which turns into: 5/26= x/100 and you get 520%.

Without graphing, determine the range of the function f(x) = -5|x-7|+2 over
the interval (-5,10).
A. [2 -62
B. [2, 17]
C. (17, 62]
D. (-7, 2]

Answers

A [2 -62] is the correct answer

simplify x^0 y^-3/x^2y^-1

Answers

The answer is 1/x^2y^2

The given expression is [tex] \frac{ {x}^{0} y { - }^{3} }{ {x}^{2}y { - }^{1} } [/tex]

We know that any number raised with zero power equals 1. Thus, [tex] {x}^{0} = 1[/tex]

Hence, the expression becomes

[tex] \frac{y { - }^{3} }{ {x}^{2} y { - }^{1} } [/tex]

Now, apply the quotient rule,[tex] \frac{ {x}^{ \alpha } }{ {x}^{b} } = {x}^{ \alpha - b} [/tex]

Using this rule, we have

[tex] \frac{1}{ {x}^{2} y { - }^{1 - ( - 3)} } [/tex]

[tex] = \frac{1}{ {x}^{2} y { - }^{1 + 3} } [/tex]

[tex]= \frac{1}{ {x}^{2} {y}^{2} } [/tex]

Hence, the simplified expression is [tex] \frac{1}{ {x}^{2} {y}^{2} } [/tex]

Select the correct answer.
What is the approximate value of the correlation coefficient for the given graph



Answers

Answer:

x = -5

Step-by-step explanation:

the answer is -5 sussy baka

Answer:  D)  -1

This is because all points are on, or nearly on, the same straight line that has a negative slope. We consider this close to or nearly perfect negative linear correlation.

Side note: The r value and slope are both negative, but they aren't equal to one another.

What is the next term of this sequence? -5,5,-6,6,-7,7,-8,..

Answers

Answer:

8,-9,9

Step-by-step explanation:

Find the value of x.

Answers

Answer:

[tex]4/12=x/18[/tex]

[tex]x=4*18/12[/tex]

[tex]x=6[/tex]

--------------------------

hope it helps...

have a great day!!

A sample of 260 students enrolled at a university were asked what they intended to do after graduation. The results are shown below.

Bar Graph of Type of Employment


What percentage of students intend to go into state or local government after graduation?

Answers

Hi my name is Fabian and 69% because 69 is a man which is multi colour hair

A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the second row, 23 in thethird row. How many seats are there in total? Show explain all work.

Answers

Answer:

There are 54 in total because if you add them all it gets you 54

State if the two triangles are congruent. If they are, prove by using a two column proof!!!

Answers

Answer:

Step-by-step explanation:

There are four axioms to prove the triangles are contruent.They are

SSS(side side side axiom)

SAS(side angle side axiom)

AAS(angle angle side axiom)

ASA(angle side angle axiom)

RHS (right angle hypotenuse side axiom)

here two triangles are congruent by RHS axiom

Hi! Could someone check this questions for me and if I have anything wrong tell what I have wrong please? That would be highly appreciated!!

Answers

Answer:

Both are correct

I'm only checking the first page

Step-by-step explanation:

Answer:

Step-by-step explanation:

The 3rd page both are wrong the correct answers are 6 degrees C and Ice would form on the top of the lake like it does now.

The 4th page the bottom one is wrong the correct answer is -22.

Evaluate the expression 53 ÷ (13 − 8) × 2.

Numerical Answers Expected!

Answers

53 ÷(13-8)x2
53 ÷5x2
10.6x2
21.2
Hope this helps

Answer:

21.2

Step-by-step explanation:

BODMAS : First bracket, then Division then multiplication.

[tex]53 \div (13-8) \times 2\\53 \div 5 \times 2\\10.6 \times 2\\21.2[/tex]

PLEASE PLEASE HELP!!!!

Find the volume of the triangular pyramid to the nearest whole number

A) 170in³
B) 340in³
C) 680in³
D) 1,020³

Answers

V=(l x w x h) / 3 ———> (10 x 12 x 17) / 3 ———> 2040/3 = 680 in^3, it’s C

What is the area of this???

Answers

9.09(m2)??
I think so

Determine whether the vectors u and v are parallel, orthogonal, or neither.
u = <2,-4>, v = <6,3> (5 points)

Answers

Answer:  orthogonal

===========================================================

Explanation:

For any two vectors defined as follows

u = <a,b>

v = <c,d>

the dot product is computed by

u dot v = a*c + b*d

If the dot product of the vectors is 0, then the vectors are orthogonal. Meaning they are perpendicular to one another.

-------------------

Let's find the dot product of these two given vectors

u = < 2, -4 >

v = < 6, 3 >

u dot v = 2*6 + (-4)*3

u dot v = 12 - 12

u dot v = 0

Therefore, these two vectors form a right angle and are orthogonal

-------------------

Extra info:

If we can show that u = <a, b> and v = <ka, kb> for some real number k, then we have shown that vectors u and v are parallel.

Find the value of x

Answers

Answer:

x = 40

Step-by-step explanation:

Two triangles are similar so we can use similarity ratio to find x

x/16 = 35/14 cross multiply expressions

14x = 560 divide both sides by 14

x = 40

The dean of a major university claims that the mean number of hours students study at her University (per day) is at most 4.9 hours. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis

Answers

Answer:

If the null hypothesis is rejected, the interpreatation is that there is significant evidence at the desired significance level to conclude that the mean time the students study at her university is of more than 4.9 hours.

Step-by-step explanation:

The dean of a major university claims that the mean number of hours students study at her University (per day) is at most 4.9 hours.

At the null hypothesis, we test if the mean is of at most 4.9 hours, that is:

[tex]H_0: \mu \leq 4.9[/tex]

At the alternative hypothesis, we test if the mean is more than 4.9 hours, that is:

[tex]H_1: \mu > 4.9[/tex]

Accepting the null hypothesis:

If the null hypothesis is accepted, the interpretation is that there is not significant evidence to conclude that the mean time the students study at her university is of more than 4.9 hours.

Rejecting the null hypothesis:

As is the case in this question, if the null hypothesis is rejected, the interpreatation is that there is significant evidence at the desired significance level to conclude that the mean time the students study at her university is of more than 4.9 hours.

please help me i’m begging!!

i need to match them

Answers

An angle of depression is measured from the horizon downwards and an angle of elevation is measured from the horizon upwards.

When solving for the sides or angles of a right triangle you can use trigonometry. The sine of an angle is found by the ratio of the opposite side and the hypotenuse. The cosine of an angle is found by the ratio of the adjacent side and the hypotenuse. The tangent of an angle is found by the ratio of the opposite side and the adjacent side.

The opposite side is always the leg opposite the angle that you are using. The adjacent side is the leg that forms one of the sides of the angle you are talking about and the hypotenuse is always across from the right angle.

If you know two lengths you can find the third leg length by using the Pythagorean Theorem.

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