the volume v of a gas at a constant temperature varies inversely with the pressure p. when the volume is 100 cubic inches the pressure is 25 pounds per square inch. What is the pressure when the volume is 125 cubic inches?
30••
20
25
40
The length of a violin string varies inversely as the frequency of its vibrations. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 8-inch string.
409.6
512
640••
612
1. (100/125 ) * 25 =
2. 10/8 * 512 = 640 cps.
1. B 50
2. C 20
3. B 25
4. B 20 pounds per square inch
5. C 640 cycles per second
1st one needs work
p v = k ... as volume goes up , pressure goes ?
Okay so I believe that the first one is 30 pounds per square inches I did my work and I got 31.25
And
2 . 409.6 cycles per second
Let me know if I’m correct
idek is correct!
To solve the first question, we need to use the formula for inverse variation:
Variation formula: V = k/p
Where V is the volume, p is the pressure, and k is a constant.
Given that the volume is 100 cubic inches when the pressure is 25 pounds per square inch, we can substitute these values into the equation:
100 = k/25
To solve for k, we can cross multiply:
100 * 25 = k
k = 2500
Now we can use the value of k to find the pressure when the volume is 125 cubic inches:
125 = 2500/p
To solve for p, we can cross multiply again:
125 * p = 2500
p = 2500/125
p = 20
So the pressure when the volume is 125 cubic inches is 20 pounds per square inch.
For the second question, we use the same concept of inverse variation:
Length = k/frequency
Given that the length is 10 inches when the frequency is 512 cycles per second, we can substitute these values into the equation:
10 = k/512
To solve for k, we can cross multiply:
10 * 512 = k
k = 5120
Now we can use the value of k to find the frequency when the length is 8 inches:
8 = 5120/frequency
To solve for the frequency, we can cross multiply:
8 * frequency = 5120
frequency = 5120/8
frequency = 640
So the frequency of an 8-inch string is 640 cycles per second.