Let R be the region in the first quadrant bounded by the graph of y=x, the vertical line x = 9, and the x-axis, as shown in the figure.
a) Write, then evaluate (show all of your work), an integral expression that gives the volume of the solid generated when R is rotated about the x-axis.
b) Write, then evaluate (show all of your work), an integral expression that gives the volume of the solid generated when R is rotated about the vertical line x = 9.

Let R Be The Region In The First Quadrant Bounded By The Graph Of Y=x, The Vertical Line X = 9, And The

Answers

Answer 1

The volume of the solid generated when R is revolved about the

x

-axis is

848

15

π

or approximately

177.6

.

The area of a circle with a radius equal to

8

x

3

2

at any given

x

is

π

(

8

x

3

2

)

2

.

= 848

15

π

177.6


Related Questions

Jazz emerged as musicians combined elements of

A. bluegrass, hip-hop, and concert band music
B. classical, ragtime, and blues
C. folk, rap, and movie music
D. classical, lullabies, and rock 'n' roll

Answers

Answer:

B

Step-by-step explanation:

Answer:

The person above is correct.

Step-by-step explanation:

Don't have proof I just know, trust\( ̄︶ ̄*\))

Ahamd wants to cover a box that is 6 cm long 4 cm high and 4 cm wide with material on all the sides how much material does he need​

Answers

Answer:

128cm²

Step-by-step explanation:

To find out how much material he needs, you need to find the surface area of the box. Each box has 6 sides, 2 of 3 different sides.

Surface area = 2(6 × 4) + 2(6 × 4) + 2(4 × 4)

                      = 128cm²

A carpenter is creating two new templates for his designs. One template will be in the shape of a right triangle, where the longer leg is 4 inches more than six times the shorter leg. The second template will be in the shape of a rectangle, where the width is 5 inches more than the triangle’s shorter leg, and the length is 3 inches. The carpenter needs the areas of the two templates to be the same. Write a system of equations to represent this situation, where y is the area, and x is the length of the shorter leg of the triangle. Which statement describes the number and viability of the system’s solutions?
A. The system has two solutions, but only one is viable because the other results in negative side lengths.
B. The system has only one solution, and it is viable because it results in positive side lengths.
C. The system has only one solution, but it is not viable because it results in negative side lengths
. D. The system has two solutions, and both are viable because they result in positive side lengths.

Answers

Answer:

The system has two solutions, but only one is viable because the other results in negative side lengths.

Step-by-step explanation:

Took the plato test and passed it, I don't know what the purpose of the first answer is, but here is the correct answer.

all numbers that have an absolute vlue of -3

Answers

Answer:

No numbers have an absolute value of -3

Step-by-step explanation:

hippity hoppity your pints are my property

absolute value cannot be negative tho

I know I just fill in -1 with x but I’m stuck with 2 different answers and this is an exam sooooo I don’t wanna risk it. Can someone please tell me the answer?

Answers

Answer:

g(-1) = 4

Step-by-step explanation:

Given:

g(x) = [tex] \frac{3x^2 - 2x + 7}{2x + 5} [/tex]

To find g(-1), substitute x = -1

Thus:

g(-1) = [tex] \frac{3(-1)^2 - 2(-1) + 7}{2(-1) + 5} [/tex]

g(-1) = [tex] \frac{3 + 2 + 7}{-2 + 5} [/tex]

= [tex] \frac{3 + 2 + 7}{-2 + 5} [/tex]

= [tex] \frac{12}{3} [/tex]

g(-1) = 4

Express the shaded area as a fraction, a decimal, and a percent of the whole

Answers

Answer:

Fraction : 3/9

Decimal : 0.33333333 (the .3 continues)

Percent : 33.33333%

Step-by-step explanation:

Dividing 3 by 9 will give you a continous set of 3.

3 I think will be your answer

Simplify the radical

Answers

Answer:

4

Step-by-step explanation:

4 to the 4th power is 256

2x - 15 = x + 5

Plz I need it now ​

Answers

Answer:

[tex]2x - 15 = x + 5 \\ 2x - x = 15 + 5 \\ x = 20[/tex]

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

Answer:

x=20

Step-by-step explanation:

2x-15=x+5

-x          -x

x-15=5

+15     +15

x=20

Help me plzzzz??!!! Anyone??

Answers

Answer:

12

Step-by-step explanation:

Answer:

we have a same question bro TwT

Step-by-step explanation:

i also doesn't know the answer TwT but i thought its 12

An icosahedron has twelve faces, the most of any Platonic solid.

Answers

Answer:

Step-by-step explanation:

True

hey,need the answer.Have a nice Easter ❤️❤️

Answers

Answer:

(B)-4

Step-by-step explanation:

Hey happy Easter how’s your day


What is the possible number of solutions to a system of linear equations in three variables? Select the three
correct answers.
a) 4
b) 1
c) infinitely many
d) 3
e) 2

Answers

a and d and ehxgfhsy eyehe74vd surge

a new desk cost (d) dollars. A bookshelf cost $114 less than the desk. A new lamp cost twice as much as the bookshelf

Answers

Answer: what are you looking for (d)?  there isnt enough info

Step-by-step explanation:

2. The numbers from 101 to 150 are written as, 101102103104105.146147148149150.
What will be the remainder when this total number is divided by 3?​

Answers

Answer:

We know that a number is divisible by 3 if the sum of its digits is a multiple of 3.

if the sum is a multiple of 3 + 1  (like 3*n + 1) the remainder is 1

if the sum is a multiple of 3 + 2 (like 3*n + 2) the remainder is 2.

Then we need to find the sum of all the single digits in the number:

101102103104...149150

the sum of all the single digits is:

( 1 + 1) + (1 + 2) + (1 + 3) + ... + (1 + 4 + 9) + ( 1 + 5)

The method i used is:

(from 101 to 110)

first we sum the hundreds digit 10 times, and then we add the unit digits for each case, this is:

1*10 + (1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 + 1) = 10 + 46

From (111 to 119)

first we add the sum of the hundreds and tens digits 10 times, and then the units:

2*9 + ( 1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 )

now if we also add the number 120 (so we have the range 111 to 120)

the sum becomes:

2*9 + ( 1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 ) + 1 + 2

2*10 + (1 + 2+ 3 + 4+ 5+ 6+ 7+ 8 + 9 + 1 ) = 20 + 46

You already can see the pattern here.

in the range from (121 to 130) we will have the sum equal to 30 + 46

in the range from (131 to 140) we will have the sum equal to 40 + 46

in the range from (141 to 150) we will have the sum equal to 50 + 46

Then the total sum is:

(10 + 20 + 30 + 40 + 50) + 5*46 = 380

We know that 380 is multiple of 3 (because 3 + 8+ 0 = 12)

Then the remainder is 0.

If <2 = <6, which must be true about <2?

Answers

Answer:

If 2 6, which must be true about 2? 2 is complementary to 5.

Step-by-step explanation:

Welcome for the answer. This answer is for good intentions only, report if necessary. Thank you and have a good rest of your day!

Which equation is a linear function?
y= 1 - 5
3m2 - 3
y = 22 - 1
y= 22 +7

Answers

Answer:

None

Step-by-step explanation:

I think

the relative extrema of f(×)=x³-x+1​

Answers

Hope this helps?!!!!

ASAP ASAP ASAP ASAP please please help ASAP ASAP please please ASAP ASAP please ASAP help please please ASAP please

Answers

Step-by-step explanation:

The lateral area is

[tex]42\pi[/tex]

The surface area is

[tex]60\pi[/tex]

The volume is

[tex]63\pi[/tex]

From a 18-foot roll of rubber hose, a person cuts lengths of 23 feet, 2 22 feet, and 6 61 feet. How much hose is left on the roll?​

Answers

Answer:

Trick question? You can't cut 23 feet from an 18 foot roll.

Did you leave out the decimal points?

Step-by-step explanation:

Answer:

You can't cut 23 or 24 feet from 18 foot roll.

If Johnny caught 2 out of 5 catfish on his first fishing trip how many catfish can he expect to catch if he caught a total of 60 fish?



60


24


600


6

Answers

Answer:

B, 24

Step-by-step explanation:

2 : 5 ratio of catching catfish

X : 60

2/5 = X/60

6 x (2/5) = (X/60) x 60

60 x (2/5) = X

X = 60 x (2/5)

X = 24

Therefore he can except to catch 24 catfish

The answer would be 24

Hi please help me with these questions asap.​

Answers

Step-by-step explanation:

A. r=42/2=21

B.

[tex] {21}^{2} \pi + 60 \times 42 = \\ = 441\pi + 2520[/tex]

C.

[tex]42\pi + 60 \times 2 = \\ = 42\pi + 120[/tex]

What is the vertex of y=5(x-1)^2+4

Answers

Answer:

the vertex is (1,4)

Step-by-step explanation:

your welcome :)

The distance around a circle is 69.08 feet. Determine the area of the circle.

Answers

Answer:

138.16

Step-by-step explanation:

An equation is shown, where 0 < x < 90 and 0 cos (x) = sin(yº)
Create an expression for x in terms of y.

Answers

The expression of x in terms of y for the case when  cos(xº) = sin(yº) is x° = cos^(-1)sin(y°)

What are the six trigonometric ratios?

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]

For this case, we have to express x in terms of y for [tex]\cos(x^\circ) = \sin(y^\circ)[/tex]

Since 0 < x < 90, and 0 < x < 90 so taking inverse cosine gives:

[tex]x^\circ= \cos^{-1}(\sin(y^\circ))[/tex]

Thus, the expression of x in terms of y for the case when  cos(xº) = sin(yº) is [tex]x^\circ= \cos^{-1}(\sin(y^\circ))[/tex]

Learn more about inverse trigonometric functions here:

https://brainly.com/question/12551115

Evaluate: show your work
Find the value of the variable.
102-8m=86

HELP. PLEASE HELP ME. I could really use your help. Please and thank you :))

Answers

M equals 2 in this equation
do this


102-8m=86
-86 -86
___________
16 -8m (0)
—- -8m
-8m
answer is -2 = m

8) Do these ratios form a proportion?
20 pedestrians : 5 years
7 pedestrians : 1 year
Please provide explanation.​

Answers

Answer:

Since the division of the number of pedestrians by the number of years yields different values for each ratio, these ratios do not form a proportion.

Step-by-step explanation:

They will form a proportion if the division of the number of pedestrians by the number of years yields the same results.

20 pedestrians : 5 years

20/5 = 4 pedestrians per year.

7 pedestrians : 1 year

7/1 = 7 pedestrians per year.

Since the division of the number of pedestrians by the number of years yields different values for each ratio, these ratios do not form a proportion.

Select the correct answer.
If a six-sided die is rolled 30 times, how many times can you expect to get a 6?
OA 3
OB.
5
OC. 6
OD 10
PL HELP WILL MARK BRAINLY 10 POINTS

Answers

Answer:

5 times

Step-by-step explanation:

1/6·30=5

so your answer is b)5

Can i have a brainliest please or 10 points?

Which characteristics describe the graph of (x – 6)2 + (y – 12)2 ≤ 196?

circle with solid boundary, center at (6, 12), bounded solution set
circle with solid boundary, center at (–6, –12), bounded solution set
circle with solid boundary, center at (6, 12), unbounded solution set
circle with solid boundary, center at (–6, –12), unbounded solution set

Answers

The characteristics describe in the graph of the circle inequality are a circle with a solid boundary, center at (6, 12), and bounded solution set option first is correct.

What is a circle?

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have a circle equation in the inequality form:

(x – 6)² + (y – 12)² ≤ 196

The center of the circle is at (6, 12)

The radius of the circle is:

r² = 196

r = 14 units

After drawing a circle on the coordinate plane.

We will see, a circle with a solid boundary, center at (6, 12), and bounded solution set.

Thus, the characteristics describe in the graph of the circle inequality are a circle with a solid boundary, center at (6, 12), and bounded solution set option first is correct.

Learn more about circle here:

brainly.com/question/11833983

#SPJ5

Answer:

A:)

Step-by-step explanation:

See attached!

Henri has $24,000 invested in stocks and bonds. The amount in stocks is $6,000 more than three times the amount in​ bonds

Answers

Answer:

s + b = $24,000

And,

s = 3b + $6,000

Step-by-step explanation:

Let us assume the stock be s

And, the bonds be b

So according to the question

It is given that

s + b = $24,000

And,

s = 3b + $6,000

The answers are

s + b = $24,000

And,

s = 3b + $6,000

The same would be considered

8) Determine the surface area of the figure. ​

Answers

Answer:

all you do is add all the numbers of the fac es together boom

Step-by-step explanation:

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