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
Ivahew [28]
3 years ago
7

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y

-axis.
y = 5x2, y = 30x − 10x2
Engineering
1 answer:
kow [346]3 years ago
3 0

Answer:

40π

Explanation:

First, find the limits (intersections).

5x² = 30x − 10x²

15x² − 30x = 0

x² − 2x = 0

x (x − 2) = 0

x = 0 or 2

Within this interval, 30x − 10x² is greater than 5x².

Dividing the volume into cylindrical shells, the volume of each shell is:

dV = 2π r h t

dV = 2π x (30x − 10x² − 5x²) dx

dV = 2π x (30x − 15x²) dx

dV = 30π (2x² − x³) dx

The total volume is the sum (integral):

V = ∫ dV

V = ∫₀² 30π (2x² − x³) dx

V = 30π ∫₀² (2x² − x³) dx

V = 30π (⅔ x³ − ¼ x⁴)|₀²

V = 30π (⅔ 8 − ¼ 16)

V = 30π (16/3 − 4)

V = 10π (16 − 12)

V = 40π

You might be interested in
What does pharmacist do in medical science?​
Kipish [7]
They are health care professionals that focus on the safe and effective use of medications
7 0
3 years ago
The hot combustion gases of a furnace are separated from the ambient air and its surroundings, which are at 25 oC, by a brick wa
yanalaym [24]

Answer:

T1 = 625.54 K

Explanation:

We are given;

T_α = Tsur = 25°C = 298K

h = 20 W/m².K,

L = 0.15 m

K = 1.2 W/m.K

ε = 0.8

Ts = T2 = 100°C = 373K

T1 = ?

Assumption:

-Steady- state condition

-One- dimensional conduction

-No uniform heat generation

-Constant properties

From Energy balance equation;

E°in - E°out = 0

Thus,

q"cond – q"conv – q"rad = 0

K[(T1 - T2)/L] - h(Ts-T_α) - εσ (Ts⁴ – Tsur⁴)

Where σ is Stephan-Boltzmann constant and has a value of 5.67 x 10^(-8)

Thus;

K[(T1 - T2)/L] - h(Ts-T_α) - εσ (Ts⁴ – Tsur⁴) = 1.2[(T1 - 373)/0.15] - 20(373 - 298] - 0.8x5.67x10^(-8)[373⁴ - 298⁴] = 0

This gives;

(8T1 - 2984) - (1500) - 520.31 = 0

8T1 = 2984 + 1500 + 520.31

8T1 = 5004.31

T1 = 5004.31/8

T1 = 625.54 K

7 0
3 years ago
Three natural materials that were used by early man as roof covering​
olga55 [171]

Explanation:

animal parts, wood, rock, and clay

8 0
2 years ago
Read 2 more answers
Write a class declaration named Circle with a private member variable named radius. Write set and get functions to access the ra
Leona [35]

Answer:

Explanation:

The following code is in C# Language

   public class Circle

   {

       private float radius;

       public float Radius

       {

           get { return radius; }

           set { radius = value; }

       }

       public void GetArea()

       {

           Console.WriteLine("The area of the circle is ", Math.PI* Radius  *Radius);

       }

 

8 0
3 years ago
When your car is broken down on the side of the road, you should make your vehicle as _____ as possible. A. visible B. comfortab
elena-14-01-66 [18.8K]

Answer:

A

Explanation:

If you're car brokebroke down and you may want people to see it so you can get help right away in case you are hurt.

5 0
2 years ago
Read 2 more answers
Other questions:
  • To be able to solve problems involving force, moment, velocity, and time by applying the principle of impulse and momentum to ri
    9·2 answers
  • 1) Pareto charts are used to: A) identify inspection points in a process. B) outline production schedules. C) organize errors, p
    6·1 answer
  • A parallel circuit with two branches and an 18 volt battery. Resistor #1 on the first branch has a value of 220 ohms and resisto
    7·1 answer
  • In your opinion, what is the external opportunity cost of a successful biking company in a community
    7·1 answer
  • or a metal pipe used to pump tomato paste, the overall heat- transfer coefficient based on internal area is 2 W/(m2 K). The insi
    14·1 answer
  • One of the most important parts about creating great photographs starts with choosing what to photograph
    6·1 answer
  • Which option identifies the step skipped in the following scenario?
    9·2 answers
  • For each of the resistors shown below, use Ohm's law to calculate the unknown quantity, Be sure to put your answer in proper eng
    8·1 answer
  • R-744 refrigerant is bad why
    6·1 answer
  • What do Engineering Systems achieve?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!