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-Dominant- [34]
3 years ago
15

Suppose you are drinking root beer from a conical paper cup. The cup has a diameter of 10 centimeters and a depth of 13 centimet

ers. As you suck on the straw, root beer leaves the cup at the rate of 4 cm3/sec. At what rate is the level of the root beer in the cup changing when the root beer is 10 centimeters deep?
Physics
1 answer:
sveta [45]3 years ago
3 0

Answer:

The level of the root beer is dropping at a rate of 0.08603 cm/s.

Explanation:

The volume of the cone is :

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

Where, V is the volume of the cone

r is the radius of the cone

h is the height of the cone

The ratio of the radius and the height remains constant in overall the cone.

Thus, given that, r = d / 2 = 10 / 2 cm = 5 cm

h = 13 cm

r / h = 5 / 13

r = {5 / 13} h

V=\frac {1}{3}\times \frac {22}{7}\times ({{{\frac {5}{13}\times h}}})^2\times h

V=\frac {550}{3549}\times h^3

Also differentiating the expression of volume w.r.t. time as:

\frac {dV}{dt}=\frac {550}{3549}\times 3\times h^2\times \frac {dh}{dt}

Given: \frac {dV}{dt} = -4 cm³/sec (negative sign to show leaving)

h = 10 cm

So,

-4=\frac{550}{3549}\times 3\times {10}^2\times \frac {dh}{dt}

\frac{55000}{1183}\times \frac {dh}{dt}=-4

\frac {dh}{dt}=-0.08603\ cm/s

<u>The level of the root beer is dropping at a rate of 0.08603 cm/s.</u>

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Church organs have a set of pipes with different lengths. With those different pipes organs can produce sounds over a wide range
Paraphin [41]

Answer: The shortest possible wavelength of sound the organ can produce is 0.224 m

Explanation:

To calculate the wavelength of light, we use the equation:

\lambda=\frac{c}{\nu}

where,

\lambda = wavelength of the light

c = speed of light = 331m/s

As wavelength and frequency follows inverse relation, shortest wavelength is produced by highest frequency.

\nu = highest frequency of light = 1.48kHz=1.48\times 10^3Hz=1.48\times 10^3s^{-1}       1Hz=1s^{-1}

\lambda=\frac{331m/s}{1.48\times 10^3s^{-1}}=0.224m

Thus the shortest possible wavelength of sound the organ can produce is 0.224 m

8 0
4 years ago
What is the highest-frequency sound to which this machine can be adjusted without exceeding the prescribed limit
Tresset [83]

The highest frequency sound to which the machine can be adjusted is :

  • 4179.33 Hz

<u>Given data :</u>

Pressure = 10 Pa

Speed of sound = 344 m/s

Displacement altitude = 10⁻⁶ m

<h3>Determine the highest frequency sound ( f ) </h3>

applying the formula below

Pmax = B(\frac{2\pi f}{v}) A --- ( 1 )

Therefore :

f = ( Pmax * V ) / 2\pi \beta A

 = ( 10 * 344 ) / 2\pi * 1.31 * 10⁵ * 10⁻⁶

 = 4179.33 Hz

Hence we can conclude that The highest frequency sound to which the machine can be adjusted is : 4179.33 Hz .

Learn more about Frequency : brainly.com/question/25650657

<u><em>Attached below is the missing part of the question </em></u>

<em>A loud factory machine produces sound having a displacement amplitude in air of 1.00 μm, but the frequency of this sound can be adjusted. In order to prevent ear damage to the workers, the maximum pressure amplitude of the sound waves is limited to 10.0 Pa. Under the conditions of this factory, the bulk modulus of air is 1.31×105 Pa. The speed of sound in air is 344 m/s. What is the highest-frequency sound to which this machine can be adjusted without exceeding the prescribed limit?</em>

4 0
2 years ago
Ian walks 2 km to his best friend’s house, then walks 0.5 km to the library. He then makes a 2.5 km walk home. The entire walk t
Sonbull [250]

Average speed = (total distance covered) / (time to cover the distance)

Ian's total distance = (2km + 0.5km + 2.5km) = 5 km

Ian's total time = 3 hours

Average speed = (5km) / (3 hours)

Average speed = 1.66 km/hr

4 0
3 years ago
The specialized capillary bed responsible for the pressure that drives filtration is the
Evgen [1.6K]

Answer: GLOMERULUS

Explanation:

The specialized capillary bed responsible for the pressure that drives filtration is the

GLOMERULUS.

The kidney is an organ responsible for the excretion of nitrogenous wastes from the human body and osmoregulation of the blood and body fluids. The structure which is responsible for formation of urine is the nephron( kidney tubule). The GLOMERULUS are found within the Bowman's capsule of the nephrons. It is made up of specialised bundle of capillary beds which are the only capillary beds that are not surrounded by interstitial fluid in the body. In the glomerulus, blood pressure is high because an arteriole enters and exists the capillary beds which is responsible for the pressure that drives filtration.

3 0
4 years ago
Which of the following corn pests causes galls to develop on the plant?
Vlad1618 [11]

Answer:

The answer is Smut.

Explanation:

5 0
3 years ago
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