Consider the region bounded by the curves y=x2 and y=9. Find the volume of the solid formed when this region is rotated around the x-axis.

Answers

Answer 1

Answer:

V  = 36Π cubic Centimetres

Step-by-step explanation:

Step(i):-

Volume of the solid

The Volume of the solid formed by revolving the region bounded by the curve y = f(x) and rotated around  the x-axis defined by

                [tex]V = \pi \int\limits^a_b {[f(x)]^{2} } \, d x[/tex]

Step(ii):-

Given two curves are y = x²  and y = 9

The point of intersection of two curves

                                y = x²...(i)

                        and y = 9 ...(ii)

Equating both equations , we get

                       x² - 9 =0

                 ⇒  x² - 3² =0

                 ⇒ (x+3)(x-3) =0

                 ⇒ x+3=0  and x-3=0

                 x = 3 ⇒ y = 9

                x = -3 ⇒y = 9

The point of intersection ( -3,9) and (3,9)

Step(iii):-

                 [tex]V = \pi \int\limits^a_b {[(f(x)]^{2} } \, -[g(x)]^{2})d x[/tex]

The limits x- varies from -3 to 3

                   [tex]V =\pi (\int\limits^3_3 {x^{2} } \, dx +\int\limits^3_3{9} \, dx[/tex]

                   [tex]V =\pi (\frac{x^{3} }{3} -9 x)^{3} _{-3}[/tex]

                 [tex]V= \pi ( \frac{27}{3} - 9(3) - (\frac{-27}{3} -9(-3))[/tex]

                V = π ( |-36| = 36Π cubic Centimetres

Final answer:-

The volume of the solid

  V = π ( |-36| = 36Π cubic Centimetres


Related Questions

Find the midpoint of the segment with the following endpoints.
(5,9) and (0,3)

Answers

Answer:

(5/2, 6)

Step-by-step explanation:

(x, y)=[(5+0)/2, (9+3)/2]

(x, y)=[5/2, 12/2]

(x, y)=(5/2, 6)

The Midpoint of the Line Segment that has the endpoints (5,9) and (0,3) is (5/2,6).

What is the line segment?

In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.

Now it is given that,

The endpoints of line segment is (5,9) and (0,3)

So, x₁ = 5

y₁ = 9

x₂ = 0

y₂ = 3

Let (x,y) be the midpoint of segment .

∴To find the midpoint of segment we have,

(x,y) =  {[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}

Put the values, we get

(x,y) = (5+0)/2 , (9+3)/2

solving them,

(x,y) = {(5/2) ,(12/2)}

or,

(x,y) = (5/2,6)

which is the required midpoint of the line segment.

Hence,the Midpoint of the Line Segment that has the endpoints (5,9) and (0,3) is (5/2,6).

To learn more about midpoint of line segment :

brainly.com/question/12774890

#SPJ2

An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?

Answers

Answer:

Step-by-step explanation:

The givens form a right triangle. The operational definition is The opposite over the hypotenuse, where the hypotenuse is the unknown.

sin(x) = 21000/hypotenuse

sin(55) = 21000 / hypotenuse

hypotenuse * sin(55) = 21000

hypotenuse = 21000/sin(55)

hypotenuse = 25636 feet.= 26000 feet rounded.

The answer does make sense. The hypotenuse is larger than the given height.

Temp went from -16 to 7.What was the change in temperature

Answers

Answer:

Change in temperature is +23 degrees.

Answer:

23 Degrees

Step-by-step explanation:

To solve this, we set up an equation:

T = 7 - -16

This can be rewritten as:

T = 7 + 16

T = 23

___________________________________________________I AM ALWAYS HAPPY TO HELP :)

Point U is located at (1,-4) on the coordinate plane. Point U is reflected on

-axis to create point U'. What ordered pair describes the location of U'?

Answers

Given :

A point U located at (1,-4) on the coordinate plane.

To Find :

The reflection of point U on x-axis.

Solution :

Reflection of any point ( h , k ) on x-axis is ( h , - k ) .

So , the reflection of point U i.e ( 1 , -4 ) is ( 1 , 4 ) .

Therefore , the ordered pair describes the location of U' is ( 1 , 4 ).

Hence , this is the required solution .


Use the map to find the distance between Brookline and Davenport to the nearest tenth

Answers

Answer:

8.5

Step-by-step explanation:

The distance between Brookline(8, 2) and Davenport(5, 10) can be calculated using the distance formula given as [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y1)^2} [/tex].

Let,

[tex] Brookline(8, 2) = (x_1, y_1) [/tex]

[tex] Davenport(5, 10) = (x_2, y_2) [/tex]

[tex] d = \sqrt{(5 - 8)^2 + (10 - 2)^2} [/tex]

[tex] d = \sqrt{(-3)^2 + (8)^2} [/tex]

[tex] d = \sqrt{9 + 64} = \sqrt{73} [/tex]

[tex] d = 8.5 [/tex] (nearest tenth)

Which expression is equivalent to 1/2 x + (-70) - 2 1/4 x - (-2) *

Answers

Answer:

-7/4x-68

Step-by-step explanation:

A survey of 500 farmers showed that of the​ farmers, 121 grew only​ wheat, 108 grew only​ corn, 92 grew only​ oats, 195 grew​ wheat, 59 grew wheat and​ corn, 48 grew wheat and​ oats, and 176 grew corn. Determine the number of farmers who ​a) grew at least one of the​ three, ​b) grew all​ three, ​c) did not grow any of the​ three, and ​d) grew exactly two of the three.

Answers

Answer:

The farmers in regions II, IV, and VI had exactly two of the three Summing the numbers in these regions 25 + 15 + 10 we find the that 50 farmers grew exactly two of the three.

0.01 is...........0.01

Answers

Answer:

=

Step-by-step explanation:

0.01 is = to 0.01

historians label an event as a turning point when it​

Answers

Answer:

F

Step-by-step explanation:

Answer:

Historians label an event as a turning point when it​ marks the beginning of a distant historical period

Step-by-step explanation:

Items 2-4. Points P, Q, and Sare
collinear.
(3x - 5)
0
(x + 1)
s
2. What is the value of x?
3. What is m ZPQR?
will
11. M
4. If a ray QT bisects ZRQS, what
will be the measure of one of the
resulting angles?
m
of
5. Points L, M, and N are collinear.
You are given LM = 5 and LN = 17.
What is a possible value of MN?
Flb
6. Ray BD bisects ZABC so that
mZDBC = x + 6 and
mZABD = 2x - 12. What is x?

Answers

Answer:

See below

Step-by-step explanation:

2......................

∠PQR and ∠RQS are supplementary, which add up 180°

∠PQR = 3x - 5∠RQS = x + 1

Sum:

3x - 5 + x + 1 = 1804x - 4 = 1804x = 184x = 46°

3......................

∠PQR = 3x - 5 = 3*46° - 5° = 138° - 5° = 133°

4......................

From the picture and the value of x we got above:

∠RQS = x + 1 = 46 + 1= 47°

QT bisects ∠RQS and we get two equal angles

Each will measure:

47°/2 = 23.5°

5......................

LM = 5, LN = 17, MN = ?

If L is between M and N, then

MN = LM + LN = 5 + 17 = 22

M is between L and N, then

MN = LN - LM = 17 - 5 = 12

5......................

Ray BD bisects ∠ABC, then formed angles are equal:

m∠DBC = x + 6 m∠ABD = 2x - 12

m∠DBC = m∠ABD

x + 6 = 2x - 122x - x =6 + 12x = 18°

Alternate Interior Angles Theorem a. b. c. Corresponding Angles Flow Proof a. b. c. d. e. Proof Diagram a. b. c.

Answers

Answer:

Step-by-step explanation:

(1). m∠5 = 40° → (a) Given

m∠2 = 140° → (b) Given

∠5 and ∠2 are supplementary angles → (c) Interior angles on the same side of the transversal.

∠5 and ∠2 are the same side interior angles → (d) Both angles are supplementary

a║b → (e) By interior angles theorem of the parallel lines.

(2).            Statements                 Reasons

   1.     l║n                               1. Given

   2.    ∠2 ≅ ∠6                      2. Corresponding angles  

   3.    ∠4 ≅ ∠2                      3. Vertical angles

   4.    ∠6 ≅ ∠4                      4. Transitive property of equality

(3).         Statements                Reasons

     1.       ∠1 ≅ ∠5                   1. Given

    2.       ∠4 ≅ ∠1                  2. Vertical angles

    3.       ∠4 ≅ ∠5                 3. Alternate interior angles

    4.       p║r                         4. Definition of parallel lines

write the sentence as a equation
b is 380 more than the quality y times 268​

Answers

A: b = 268y + 380
is : =

A rectangle is 5 times as long as it is wide. If the area is 45 square feet, find its perimeter.

Answers

Answer:

225 sq ft

Step-by-step explanation:

If the rectangle is 5 times as long as it is wide and the area is 45 sq ft then that would make it 225 sq ft. Happy to help!

Simplify the given expression below:
(-5 + 3i) times(1 - 2i)

Answers

Answer:

Step-by-step explanation:

Hello,

[tex](-5+3i)\times(1-2i)=-5(1-2i)+3i(1-2i)\\\\=-5+10i+3i-6i^2\\\\=-5+13i+6\\\\\boxed{=1+13i}[/tex]

Thanks

Answer:

Same answer as the other person, it is 1 + 13i

Step-by-step explanation:

They were first and is right so I don't think I have to put down a explanation! ^^

Please 5 stars and thank me if I'm right! -w-

please answer thank you!

Answers

Answer:

C

Step-by-step explanation:

C is the answer because -2+16=14 and 9x+x=10x

forget this ever happened at all

Answers

Answer:

i- isnt it 2-

Step-by-step explanation:

1 + 1 is 2

i hope this helped?

Find the area of the parallelogram shown below.60 squ

Answers

Answer:

A

Step-by-step explanation:

The area for a parallelogram is given by the formula:

[tex]A=bh[/tex]

Where b is the base length and h is the vertical height.

The base length is 6 and the height is 10 (if you flip the figure 90 degrees). So:

[tex]A=6(10)[/tex]

Multiply:

[tex]A=60\text{ units}^2[/tex]

Our answer is A.

And we're done!

Help me please i dont understand :(

Answers

h(x)=0 means that you replace the x in the problemwith the number given. 4(0)+4= 4

Write a story that includes both integers -10 and 12.

Answers

Answer:

In Alaska, it was -10 degrees in the morning and rose by 12 degrees.

Step-by-step explanation:

Frank needs 3.6 meters of ribbon to wrap gifts for friends this year. If each spool contains 90 cm of ribbon,how many spools will Frank need to purchase?

Answers

Answer:a lot

Step-by-step explanation:

9 and 26 find the LCM

Answers

Answer:

The answer is 234

Step-by-step explanation:

Answer:234..............

Another college precalculas question, please and thank you!

Answers

Answer:

B) (-∞,∞)

Step-by-step explanation:

The domain is the x-values, so it’s all real numbers in this graph.  

I would use interval notation and choose B) (-∞,∞)

The range is the y-values, so it’s (2,-1), if that’s the next question.

What is the y in the equation? 15-y-3y=17

Answers

Answer: -1/2 or .5
-14y=17-15
-4y=2
Y=1/2

given the following functions f(x) and g(x), evaluate (gºf)(-2). Enter answer.
f(x)=2x^2+2x-5
g(x)=-1/-4x+6​

Answers

Answer:

the composition results in [tex]\frac{23}{4}[/tex]

Step-by-step explanation:

Assuming that what you typed for function g is correct (looks a bit peculiar, but we will use it as typed):

[tex]g(x)=-\frac{1}{-4x} +6[/tex]

gof(-2) can be understood as: g(f(-2)), so what we need to do is to find the value for f(-2) using its given expression, and using then the obtained value as input for g(x):

[tex]f(x)=2x^2+2x-5\\f(-2)=2\,(-2)^2+2\,(-2)-5\\f(-2)= 8-4-5\\f(-2)= -1[/tex]

So, we now evaluate g(-1):

[tex]g(x)=-\frac{1}{-4x} +6\\g(-1)= -\frac{1}{-4(-1)} +6\\g(-1)= -\frac{1}{4} +6\\g(-1)=\frac{23}{4}[/tex]

Precalc Help me Please

Answers

We just need to solve for y when x = -2

Solution:

y = 2|-2 + 1|

y = 2|-1|

y = 2(1)

y = 2

Therefore, the answer is Option 3

Best of Luck!

Please answer the question. Thank you.

Answers

your answer will be D
Answer: not sure if B or A is first but one of them and than it goes C and D

2/7+3/8= Please I don’t know what to do so can you help me

Answers

37/56 is the answer

you can cross multiply

Answer:

37/56

Step-by-step explanation:

Find the least common multiple of the denominators (56).

7x8=56

8x7=56

2x8=16

3x7=21

16+21=37

37/56

(10x^4+5x^3+4x^2-9)(x-1)​

Answers

Answer:

10x3 - 5x2 + 9x - 9

Step-by-step explanation:

                           10x4 + 5x3 + 4x2 - 9

Simplify   ————————————————————

                                        x + 1        

Answer:

10x^5 - 5x^4 - x^3 - 4x^2 - 9x + 9

Step-by-step explanation:

(10x^4+5x^3+4x^2-9) × (x-1)​

10^5 - 10x^4 + 5x^4 -5x^3 +4x^3 - 4x^2 -9x + 9

Collect Like terms

10^5 - 10x^4 + 5x^4 -5x^3 +4x^3 - 4x^2 -9x + 9

10^5 - 5x^4 -x^3 - 4x^2 -9x + 9

Final Answer

10x^5 - 5x^4 - x^3 - 4x^2 - 9x + 9

Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the larger angle?

Answers

Answer:

C

Step-by-step explanation:

4x-5+x=180. Add 5 to both sides

5x=185. Divide by 6

X=37

180-37=143

143

what is the mathematical symbol for 0 is an integer

Answers

Answer:

0

Step-by-step explanation:

there is no symbol for 0

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