1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Svetradugi [14.3K]
2 years ago
9

use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines abo

ut the y-axis. y=8-x^2,y=x^2,x=0
Mathematics
1 answer:
sukhopar [10]2 years ago
7 0

Answer:

16π square units.

Step-by-step explanation:

Please refer to the graph below.

So, if we draw a representative rectangle, the width of the rectangle will be (x), and the height of the rectangle at each (x) will be given by f(x) - g(x).

By the shell method:

\displaystyle V=2\pi\int_a^bp(x)h(x)\,dx

We are integrating from x = 0 to x = 2. p(x) is x and h(x) is f(x) - g(x):

\displaystyle V=2\pi\int_0^2(x)((8-x^2)-(x^2))\,dx

Evaluate. Simplify:

\displaystyle V=2\pi \int_0^2(8x-2x^3)\,dx

Hence:

\displaystyle V=2\pi\Big(4x^2-\frac{1}{2}x^4\Big|_{0}^{2}\Big)

Evaluate:

\displaystyle \begin{aligned} V &= 2 \pi \Big[(4(2)^2-\frac{1}{2}(2)^4)-(4(0)^2-\frac{1}{2}(0)^4)\Big]\\ &=2\pi(8) \\&=16\pi\text{ square units} \end{aligned}

You might be interested in
Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f
vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

f(x)=ax^3+bx^2+cx+d

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

y = x^3 - x

Equate y to 0

x^3 - x = 0

Expand

x(x^2 - 1) = 0

Express x^2 - 1 as difference of two squares

x(x - 1)(x +1 ) = 0

<em>x = 0 or 1 or -1</em>

For 2 x intercepts

y = x^3 - x

y  =(x-5)^2)(x+7)

Equate y to 0

(x-5)^2(x+7) = 0

Expand

(x-5)(x-5)(x+7) = 0

<em>x= 5 or x = -7</em>

For 1 x intercept

y = x^3

Equate y to 0

x^3 = 0

Take cube roots of both sides

x = 0

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

y = x^2 + x + 17

<em>The above function has no x intercept.</em>

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

y = x^2- 6x + 9

Equate y to 0

x^2- 6x + 9 = 0

Expand

x^2 - 3x - 3x + 9 = 0

(x - 3)(x-3) = 0

x = 3

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0
2 years ago
Find the area of each circle in terms of PI, the circles diameter is 2cm, what do i do know?
choli [55]
Given diameter 2cm
Find the area of a circle 
the formula for area of a circle 
A = pi r^2
the diameter is the radius times two 
so to find the radius given the diameter 2/2 = 1
radius is 1cm
pi is ~3.14
A = (3.14) * (1)^2
A = (3.14) * 1
A = 3.14

Hope this helps :)
7 0
3 years ago
HI GUYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYS
Viefleur [7K]

Answer:

Step-by-step explanation:

HEY

6 0
2 years ago
.......... is the slope zero
Eddi Din [679]

Answer:


Step-by-step explanation:

OK... You have to use this formula: <u>Y2 - Y1</u>

                                                          X2 - X1

  • -2 represents X1
  • 7 represents Y1
  • 2 represents X2
  • -5 represents Y2    

<u>Y2 - Y1</u>

X2 - X1

<u>-5 - 7</u>

2 - - 2

<u>-12</u>

-2

Simplify by dividing both -12 & -2 by 2: <u>-6</u>

                                                                 -1

It's either <u>-6</u> or it's just -6 by itself... Really sorry if I'm wrong...

                -1  




4 0
3 years ago
Read 2 more answers
Help me with this question please
mojhsa [17]

Step-by-step explanation:

so, he will not wear any pants ? socks ? not to mention underwear ?

anyway, we have to deduct the $35 for the shoes, as he is seemingly buying them in any case.

so, we are left with 100 - 35 = $65 for shirts.

as one shirt costs $15, we need to see how often 15 fits into 65, as that is the answer how many shirts he can buy for this money.

65 / 15 = 4.333333333...

since he cannot buy a part shirt, we can only rely on the integer part of the calculation.

so, he can buy 4 shirts and will have $5 left.

8 0
2 years ago
Other questions:
  • The ratio of employee wages and benefits to all other operational costs of a business is 2:3. If a business operates expeses are
    10·1 answer
  • A student bought 1 box of crayons and five reams of paper for $54 she bought five boxes of crayons and three 3 reams of paper fo
    14·1 answer
  • Charlie reads quickly. He reads 1 and 3 seventh pages every 2 third minutes. Charlie reads at a constant rate. How many pages do
    12·1 answer
  • What is the value of the expression?<br><br> −4.2(0.35−3.5)
    7·1 answer
  • 52<br> 5v2.<br> Find the value of x. Write your answer in simplest form.
    9·1 answer
  • What is the slope of y=-4
    10·2 answers
  • Parker and his family are going on a trip to see Mount Rushmore. They will travel 55 miles per
    8·1 answer
  • Is this a linear equation
    15·2 answers
  • This question is 87 points. this is a lot of points. use it wisely. respect the point.
    12·2 answers
  • The second of three numbers is 8 more than the first,
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!