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Phantasy [73]
3 years ago
11

Water is leaking out of an inverted conical tank at a rate of 1.5 cm3 /min at the same time that water is being pumped into the

tank at a constant rate. The tank has height 10 cm and the diameter at the top is 6 cm. If the water level is rising at a rate of 1.0 cm/min when the height of the water is 2 cm, find the rate at which water is being pumped into the tank. (a) Draw a picture of the situation for any time t. (b) What quantities are given in the problem

Physics
1 answer:
iris [78.8K]3 years ago
5 0

Answer:

a) Check Explanation

b) Check Explanation

c) The rate at which water is being pumped into the tank = 2.631 cm³/min

Explanation:

Let the rate of flow of water into the tank be k cm³/min

a) The image of the conical tank is presented in the attached image

Note, the radius and height of a cone are related through the similar triangles principle.

As shown in the attached image, it is evident that

r/h = 3/10

r = 3h/10 = 0.3 h

b) The quantities given in the problem.

- Shape of the tank, conical tank, Hence volume of the tank = πr²h/3

- total height of the tank, H = 10 cm

- Radius of the tank at the top, R = D/2 = 6/2 = 3 cm

- rate at which water is leaking from the tank = 1.5 cm³/min

- water is being pumped into the tank at constant rate of k cm³/min

- As at height of water, h = 2 cm, the rate of rise in water level = 1 cm/min

c) volume of the tank at any time = πr²h/3

Rate of change in the volume of water in the tank = (rate of flow into the tank) - (Rate of water flow out of the tank)

dV/dt = k - 1.5

V = πr²h/3 and r = 0.3 h, r² = 0.09 h²

V = 0.03πh³

dV/dt = (dV/dh) × (dh/dt)

dV/dh = 0.09π h²

dV/dt = 0.09π h² (dh/dt)

dV/dt = k - 1.5

0.09π h² (dh/dt) = k - 1.5

But at h = 2 cm, (dh/dt) = 1.0 cm/min

0.09π h² (dh/dt) = k - 1.5

0.09π 2² (1) = k - 1.5

k - 1.5 = 1.131

k = 1.5 + 1.131 = 2.631 cm³/min

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Answer:

hi zzayn i will solve this later

Explanation:

Let's establish that x= number of polio vaccinations and y=number of measles vaccinations.

Since Dr. P gave a total of 60 VACCINATIONS, we know that x+y=60. (This is equation #1)

We also know that Dr. P gave a total of 184 DOSES of the vaccinations and that the polio vaccine has 4 doses, while the measles vaccine has 2 doses. This means that our second equation is 4x+2y=184. (This is equation #2)

You can get either variable (x or y) by itself from equation #1. I always choose x.

x+y=60

-y.     -y

x=60-y

Now we can plug our x value into equation #2.

4x+2y=184

4(60-y)+2y=184

240-4y+2y=184

240-2y=184

-240    -240

-2y=-56

/-2 /-2

y=28 measles vaccines

So we know that Dr. P administered 28 measles vaccines. We need to plug our y value back into equation #1 (or, to make it easier, our switched around equation) to find the number of polio vaccines.

x=60-y

x=60-28

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A pulley system has an efficiency of 74.2%. If you perform 200 J of work, how
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Answer:

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