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nikdorinn [45]
3 years ago
5

The height of a cone is increasing at a rate of 10 cm/sec and its radius is decreasing so that its volume remains constant. How

fast is the radius changing when the radius is 4 cm and the height is 10 cm?
Physics
1 answer:
ki77a [65]3 years ago
6 0

Answer:

dr/dt = -2 cm/s.

Explanation:

The volume of a cone is given by:

V=\frac{1}{3} \pi r^{2}h (1)

  • r is the radius
  • h is the height

Let's take the derivative with respect to time in each side of (1).

\frac{dV}{dt}=\frac{1}{3} \pi \frac{d}{dt}(r^{2}h)=\frac{1}{3} \pi \left(2r\frac{dr}{dt}h+r^{2}\frac{dh}{dt} \right) (2)

We know that:

  • dh/dt = 10 cm / s (rate increasing of height)
  • dV/dt = 0 (constant volume means no variation with respect of time)
  • r = 4 cm
  • h = 10 cm

We can calculate how fast is the radius changing using the above information.

0=\frac{1}{3} \pi \left( 2\cdot 4\cdot \frac{dr}{dt} \cdot 10 + 4^{2}\cdot 10)\right  

Therefore dr/dt will be:

\frac{dr}{dt}=-\frac{160}{80}=-2 cm/s

The minus signs means that r is decreasing.

I hope it helps you!

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STALIN [3.7K]

The car traverses a distance x after time t according to

x=\dfrac12at^2

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5 is pretty close to 4, so we can approximate the square root of 5 by 2. Then the car's velocity v after 2 s of travel is given by

v=\left(10\dfrac{\rm m}{\mathrm s^2}\right)(2\,\mathrm s)\approx20\dfrac{\rm m}{\rm s}

which makes C the most likely answer.

3 0
3 years ago
A light bulb dissipates 100 Watts of power when it is supplied a voltage of 220 volts.
ycow [4]

Given Information:

Power = P = 100 Watts

Voltage = V = 220 Volts

Required Information:

a) Current = I = ?

b) Resistance = R = ?

Answer:

a) Current = I = 0.4545 A

b) Resistance = R = 484 Ω

Explanation:

According to the Ohm’s law, the power dissipated in the light bulb is given by

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Where V is the voltage across the light bulb, I is the current flowing through the light bulb and P is the power dissipated in the light bulb.

Re-arranging the above equation for current I yields,

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Therefore, 0.4545 A current is flowing through the light bulb.

According to the Ohm’s law, the voltage across the light bulb is given by

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Where V is the voltage across the light bulb, I is the current flowing through the light bulb and R is the resistance of the light bulb.

Re-arranging the above equation for resistance R yields,

R = \frac{V}{I} \\\\R = \frac{220}{0.4545} \\\\R = 484 \: \Omega

Therefore, the resistance of the bulb is 484 Ω

3 0
3 years ago
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Acar accelerates from 4 meters/second to 16 meters/second in 4 seconds. The car's acceleration is
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To understand this question, you need to understand the concept of acceleration first. Have you ever been in a car and noticed that it was getting faster and faster? That "speeding up" of the car is known as acceleration! Acceleration is essentially the rate at which you speed up.

Okay, so we now know what acceleration is. What are its units? The unit of acceleration is the change in velocity over a period of time: \frac{∆v}{t}

If you haven't learned about velocity yet, just think about it as speed for now. The funny-looking triangle, ∆, is a symbol for "the change of." For example, if I started walking at 3 \frac{feet}{second} then sped up to 5 \frac{feet}{second}, then the change in my speed would be 2 \frac{feet}{second}, because I started walking 2 \frac{feet}{second} faster!

Okay, enough with all the explanations. Hopefully, you understand the units now. Let's take a look at the question. A car accelerates from 4 \frac{meters}{second} to 16 \frac{meters}{second}  in 4 seconds. What would the acceleration be? Let's set up an equation:

a = \frac{∆v}{t}

a is the acceleration, ∆v is the change in velocity, and t is the time elapsed.

Now, let's plug in our values! ∆v is the change in velocity, and to find that we simply have to subtract 16 \frac{meters}{second} by 4 \frac{meters}{second}. That makes sense, right? Back to the equation.

a = \frac{∆v}{t}
a = \frac{16-4}{4}

(16 - 4 is the change in velocity, and 4 is the number of seconds the car was accelerating)

a = \frac{12}{4}

a = 3 (\frac{meters}{second^{2}})

We have our answer! The car's acceleration is 3 meters per second^{2}.

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Let me know if you need clarification on anything I explained here!
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iVinArrow [24]

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5 0
3 years ago
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Sati [7]

Answer:

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or

R = 1.549 m

Thus, the radius of the red circle is 1.549 m

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3 years ago
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