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2 years ago

What are the rules for setting up an integral of rotation?

1 answer:

3 0

Setting up an integral of rotation is used as a method of of calculating the volume of a 3D object formed by a rotated area of a 2D space. Finding the volume is similar to finding the area, but there is one additional component of rotating the area around a line of symmetry.

<span>First the solid of revolution should be defined. The general function is y=f(x), on an interval [a,b].</span>

Then the curve is rotated about a given axis to get the surface of the solid of revolution. That is the integral of the function.

<span>It all depends of the function f(x), which must be known in order to calculate the integral.</span>

You might be interested in

What is the name of the small early planets, which formed through gravitational attraction reaching sizes of a few miles to even

Svetradugi [14.3K]

Answer:

Planetesimals (Ex, Mercury, Venus , Mars & Earth)

Explanation:

They are known as Planetesimals , They are small in size and have rocky surface. The examples of Planetesimals are Mercury, Venus Mars and Earth.

They are small early planets , which also has gravitational attraction.

Thanks

6 0

3 years ago

A boat sails south with the help of a wind blowing in the direction S36°E with magnitude 300 lb. Find the work done by the wind

goldfiish [28.3K]

Answer:

The work done by the wind as the boat moves 130 ft is (rounded) W= 31,550 ft-lb.

Explanation:

F= 300 lb < -54º

Fsouth= 300 lb * cos(36º)

Fsouth= 242.7 lb

d= 130 ft

W= F*d

W= 31551 ft-lb

6 0

2 years ago

A woman living in a third-story apartment is moving out. Rather than carrying everything down the stairs, she decides to pack he

Flura [38]

Answer:

T = 480.2N

Explanation:

In order to find the required force, you take into account that the sum of forces must be equal to zero if the object has a constant speed.

The forces on the boxes are:

$T-Mg=0$ (1)

T: tension of the rope

M: mass of the boxes 0= 49kg

g: gravitational acceleration = 9.8m/s^2

The pulley is frictionless, then, you can assume that the tension of the rope T, is equal to the force that the woman makes.

By using the equation (1) you obtain:

$T=Mg=(49kg)(9.8m/s^2)=480.2N$

The woman needs to pull the rope at 480.2N

8 0

3 years ago

A 26.4 g silver ring (cp = 234 J/kg·°C) is heated to a temperature of 66.2°C and then placed in a calorimeter containing 4.94 ✕

Slav-nsk [51]

Answer:

The final temperature of the mixture = 64.834 °C.

Explanation:

Heat lost by the silver ring = heat gained by the water + heat transferred to the surrounding.

c₁m₁(t₁-t₃) = c₂m₂(t₃-t₂) + Q..............Equation 1

Where c₁ = specific heat capacity of the silver copper, m₁ = mass of the silver copper, t₁ = initial temperature of the silver copper, t₃ = final temperature of the mixture. c₂ = specific heat capacity of water, t₂ = initial temperature of water, m₂ = mass of water, Q = energy transferred to the surrounding.

making t₃ the subject of the equation,

t₃ = [c₁m₁t₁+c₂m₂t₂-Q]/(c₁m₁+c₂m₂)........................ Equation 2

Given: c₁ = 234 J/kg.°C, m₁ = 26.4 g, t₁ = 66.2 °C, c₂ = 4200 J/K.°C, m₂ = 4.92×10⁻² kg, t₂ = 24.0 °C, Q = 0.136 J.

Substituting into equation 2

t₃ = [(234×26.4×66.2)+(4200×0.0492×24)-0.136]/[(234×26.4)+(4200×0.0492)]

t₃ = (408957.12+4959.36-0.136)/(6177.6+206.64)

t₃ = (413916.48-0.136)/6384.24

t₃ = 413916.34/6384.24

Thus the final temperature of the mixture = 64.834 °C.

6 0

3 years ago

A good train took 7 hours to complete its journey. For the first 3 hours, it travelled an average speed of 186km/h. What was the

Sliva [168]

I really hope this helps

4 0

2 years ago