Answer:
Rate at which water is being pumped into the tank, ![R_{in} = 429933.33 cm^3/min](https://tex.z-dn.net/?f=R_%7Bin%7D%20%3D%20429933.33%20cm%5E3%2Fmin)
Explanation:
Rate at which water is leaking out, ![R_{out} = 11, 0000 cm^3/min](https://tex.z-dn.net/?f=R_%7Bout%7D%20%3D%2011%2C%200000%20cm%5E3%2Fmin)
Height of the tank, h = 12 m
The top diameter of the tank, d = 8 m = 800 cm
The top radius of the tank, r = d/2 = 800/2 = 400 cm
The rate of change of water height, dh/dt = 30 cm/min
Height of water = 2 m
By carefully observing the diagram contained in the file attached to this solution, using the property of similar triangle:
h/r = 12/4
r = h/3
Since the tank is conical, volume of the water at time, t will be:
![V = \frac{1}{3} \pi r^{2} h\\\\V = \frac{1}{3} \pi (\frac{h}{3} )^{2} h\\\\V = \frac{1}{27} \pi h^{3} \\](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E%7B2%7D%20h%5C%5C%5C%5CV%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%28%5Cfrac%7Bh%7D%7B3%7D%20%29%5E%7B2%7D%20h%5C%5C%5C%5CV%20%3D%20%5Cfrac%7B1%7D%7B27%7D%20%5Cpi%20h%5E%7B3%7D%20%5C%5C)
Finding the derivative of the above with respect to t to get the rate of change in the volume of water.
![\frac{dV}{dt} = \frac{1}{9} \pi h^{2} \frac{dh}{dt} \\\\\frac{dV}{dt} = R_{in} - R_{out} \\\\\frac{1}{9} \pi h^{2} \frac{dh}{dt} = R_{in} - R_{out}\\\\\frac{1}{9} \pi * 200^{2}* 30 = R_{in} - 11000\\\\ R_{in} = 429933.33 cm^3/min](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D%20%5Cpi%20h%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%5C%5C%5C%5C%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20R_%7Bin%7D%20-%20R_%7Bout%7D%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B9%7D%20%5Cpi%20h%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20R_%7Bin%7D%20-%20R_%7Bout%7D%5C%5C%5C%5C%5Cfrac%7B1%7D%7B9%7D%20%5Cpi%20%2A%20200%5E%7B2%7D%2A%2030%20%3D%20R_%7Bin%7D%20-%2011000%5C%5C%5C%5C%20R_%7Bin%7D%20%3D%20429933.33%20cm%5E3%2Fmin)
Answer:
None.
Explanation:
The weight of the astronaut is equal to the force of gravity the astronaut feels that depends on the mass of the planet.
Because the mass of the Earth is different than that of Jupiter, Saturn and Mars, the astronaut's weight will change when he/she travels to either planets.
Answer:
D) a Battery
Explanation:
The best real-life example of direct current is a battery. Batteries have positive and negative terminals on a battery, the electrons in the wires will begin to flow to produce a current.
Answer: The mass of the sculpture is 11.8kg
Explanation:
Using the equation of fundamental frequency of a taut string.
f = (1/2L)*√(T/μ) .... (Eqn1)
Where
f= frequency in Hertz =80Hz
T = Tension in the string = Mg
M represent the mass of the substance (sculpture) =?
g= 9.8m/s^2
L= Length of the string=90cm=0.9m
μ= mass density = mass of string /Length of string
mass of string =5g=0.005kg
L=0.9m
μ=0.005/0.9 = 0.0056kg/m
Using (Eqn1)
80= 1/(2*0.9) √(T/0.0056)
144= √(T/0.0056)
Square both sides
20736= T/0.0056
T= 116.12N
Recall that T =Mg
116.12= M * 9.8
M=116.12/9.8
M= 11.8kg
Therefore the mass of the sculpture is 11.8kg