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
barxatty [35]
2 years ago
9

Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis

.
y= -x +4
Mathematics
1 answer:
guapka [62]2 years ago
8 0

Answer: V = \frac{64}{3}\pi

Step-by-step explanation: A solid formed by revolving the region about the x-axis can be considered to have a thin vertical strip with thickness Δx and height y = f(x). The strip creates a circular disk with volume:

V = \pi. y^{2}.Δx

Using the <u>Disc</u> <u>Method</u>, it is possible to calculate all the volume of these strips, giving the volume of the revolved solid:

V = \int\limits^a_b {\pi. y^{2} } \, dx

Then, for the region generated by  y = - x + 4:

V = \int\limits^4_0 {\pi.(-x+4)^{2} } \, dx

V = \pi.\int\limits^4_0 {(x^{2}-8x+16)} \, dx

V = \pi.(\frac{x^{3}}{3}-4x^{2}+16x )

V = \pi.(\frac{4^{3}}{3}-4.4^{2}+16.4 - 0 )

V = \frac{64}{3}.\pi

The volume of the revolved region is V = \frac{64}{3}.\pi

You might be interested in
Which of the following options is a root of the function? f(x) = (3x + 5) (x2 - 6x + 9)2
Alika [10]

Answer:

The roots of the function are x = -5/3 and 3. Select these.

Step-by-step explanation:

The roots of the function are the solutions to the function. They are also called the x-intercepts or zeros. To find them, factor the function completely and solve using the zero product property.

f(x) = (3x+5)(x2-6x+9)2 becomes f(x) = (3x+5)(x-3)^2

Set each factor equal to 0 and solve for x.

(3x+5)=0

3x = -5

x = -5/3

(x-3)^2 = 0

x - 3=0

x = 3

3 0
3 years ago
Dale has three dollars more than twice the amount of money that Leo has.
KATRIN_1 [288]
2+3+4+5+y+7+8+9+10c11+12+13+14+15
8 0
3 years ago
Read 2 more answers
Please help me idk this
Natali [406]

Answer:9000

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
When y = 35,x = 2.5. If the value of y varies directly with x what is the value of y when the value of xis 3.25
leonid [27]

Answer:

The value of y would be 45.5

Step-by-step explanation:

To solve this problem, start with the base form of direct variation.

y = kx

Now we can use our original values to model the equation and find k.

35 = k(2.5)

14 = k

Now we can model the equation as:

y = 14x

Now to find y, when x = 3.25, simply put 3.25 into the equation.

y = 14(3.25)

y = 45.5

8 0
3 years ago
What’s 8x8 <br> This is to test how the app works not serious
lisov135 [29]

Answer:

64

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • I need help can someone help me
    14·1 answer
  • When a certain polynomial is divide by binomial x-3, the result is 4x-5+6/x-3. What is the polynomial
    9·1 answer
  • About how many times larger is 6.14 x 10-3 than 1.98 x 10-4?
    10·2 answers
  • The five interior angles in a  pentagon are in the ratio 2:3:4:5:6. What is the measure of the pentagon's largest angle?
    15·1 answer
  • Find all complex solutions of 3x^2+2x+5=0 . (If there is more than one solution, separate them with commas.)
    6·1 answer
  • 21 − 3 ) ÷ 32 =<br> 72 × ( 6 ÷ 3 ) =<br> 17 + 15 ÷ 3 − 24 =<br> ( 8 + 56 )÷ 4 − 32 =
    14·1 answer
  • How can you tell if an ordered pair is a solution of a system of linear equations by examining the graphs of the equations?
    13·1 answer
  • Keisha, Boris, and Jose sent a total of 126 text messages over their cell phones during the weekend. Boris sent 4 times as many
    5·1 answer
  • How can the graph of f(x) = 1/(- x) - 9 be obtained from the graph of y = 1/x
    14·1 answer
  • Hey I’ve got the answer for the first question but I’m stuck on this one 5^-3 X 2^-1
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!