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Schach [20]
2 years ago
14

Find the area of the surface generated when the given curve is rotated about the x-axis. y = 4 squareroot x on [60, 77] The area

of the surface generated by revolving the curve about the x-axis is square units. (Type an exact answer, using it as needed.)

Mathematics
1 answer:
In-s [12.5K]2 years ago
8 0

Answer:

A≅562.45π u²

Step-by-step explanation:

Knowing that the volume the a solid is V=πR²h, then A=πR², therefore

A=π(4√x),  integrating on both sides ∫A=4π∫√xdx ⇒ ∫√xdx = \frac{2}{3}x^{3/2}

evaluated (60,77), then

A=\frac{8\pi }{3}(77^{3/2}-60^{3/2})\\A=\frac{8\pi }{3}(675.67-161.75})\\A=562.45\pi

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Consider a propeller driven aircraft in forward flight at a speed of 150 mph: The propeller is set up with an advance ratio such
meriva

a)  The thrust of the propeller is  23,834 lbf

b)  The induced velocity is 8.44 mph

c)  The velocity in the downstream far field away from the propeller disc     is 161.56 mph

d) The power absorbed by the fluid is  42.7 hp

e)  the propeller power (thrust flight speed) is  4,844.08 hp

f)  The propeller efficiency is 113.6%

a)The thrust of the propeller can be calculated using the equation,

Thrust = 2πρR^2V^2, where ρ is the air density, R is the propeller radius, and V is the average velocity of the propeller disc. For sea level at a speed of 150 mph, the air density is about 0.002377 slugs/ft^3.

the thrust of the propeller can be calculated as: Thrust = 2π x 0.002377 x (6 ft)^2 x (170 mph)^2 = 23,834 lbf

b)The induced velocity can be calculated using the equation v_ind = (1/2) V ∞ [1–(V_∞/V_tip)^2]^(1/2), where V_∞ is the free stream velocity and V_tip is the tip velocity of the propeller. For the given problem, the induced velocity can be calculated as: v_ind = (1/2) x 150 mph x [1–(150 mph/170 mph)^2]^(1/2) = 8.44 mph

c) The velocity in the downstream far field can be calculated using the equation V_∞ = V_tip – v_ind, where V_tip is the tip velocity of the propeller and v_ind is the induced velocity. For the given problem, the velocity in the downstream far field can be calculated as: V_∞ = 170 mph – 8.44 mph = 161.56 mph

d)The power absorbed by the fluid can be calculated using the equation P_fluid = (1/2) ρ V_ind^3 A_disc, where ρ is the air density, V_ind is the induced velocity, and A_disc is the area of the propeller disc. For the given problem, the power absorbed by the fluid can be calculated as P_fluid = (1/2) x 0.002377 x (8.44 mph)^3 x (π x (6 ft)^2) = 42.7 hp

e)The power absorbed by the propeller can be calculated using the equation P_prop = T x V, where T is the thrust of the propeller and V is the flight speed of the aircraft. For the given problem, the power absorbed by the propeller can be calculated as: P_prop = 23,834 lbf x 150 mph = 3,575,500 ft-lbf/s = 4,844.08 hp

f)The efficiency of the propeller can be calculated using the equation η = P_prop/P_fluid, where P_prop is the power absorbed by the propeller and P_fluid is the power absorbed by the fluid. For the given problem, the efficiency of the propeller can be calculated as: η = 4,844.08 hp/42.7 hp = 113.6%

To know  more  about induced velocity refer to the link brainly.com/question/15280442

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8 0
1 year ago
How many ways can 6 people sit on a bench if 3 of them have to sit side by side
pickupchik [31]

Answer:

144 ways

Step-by-step explanation:

Let's think of the 3 persons sitting together as "one". So essentially we have 3 + "1" = "4" persons to arrange.

THey can be arranged in 4! ways, which is:

4! = 4 * 3 * 2 * 1 = 24 ways

Now, the 3 persons themselves can be arranged in 3! ways, which is:

3! = 3 * 2 * 1 = 6 ways

Total ways = 4! * 3! = 24 * 6 = 144 ways

4 0
3 years ago
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mamaluj [8]
Simplify both to 1/2 because both numerators are half of their denominators. Then multiply straight across to 1/4.
4 0
2 years ago
If the logan family can drive 23 1/8 miles on 1 gallon of gas how far can they drive 17 gallons
puteri [66]
1/8 = 0.125
23.125 x 17 gallons = 393.125 
393.125 = 393 1/8 miles 
4 0
3 years ago
Read 2 more answers
3 1/2 + 1 4/8 = to what?
zlopas [31]

It's 5.

1/2 can also be written as 4/8.

So, it's 3 and 4/8 plus 1 and 4/8.

7 0
2 years ago
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