The volume of gas in a container at a constant temperature varies inversely as the pressure. If the volume is 32 cubic centimeters at a
pressure of 8 pounds, find the pressure when the volume is 60 cubic centimeters.
The pressure is
pounds

The new pressure is 4.27 pounds

Step-by-step explanation:

In this question, we have the volume varying inversely as the pressure;

Firstly, let's say the volume is V and the pressure is P

Mathematically;

V ∝ 1/P

Let us insert a constant of proportionality K

⇒ VP = K

Let's calculate the value of K

K = 32 × 8 = 256

Now in the second scenario, pressure is unknown but we know the volume to be 60

Recalling;  VP = K

P = K/V = 256 /60 = 4.27 pounds

4.2667 pounds.

Step-by-step explanation:

To solve this problem, as the measures are inversely proportional, we can use an inverse rule of three (that is, we multiply the lines instead of dividing). So, for the volume of 32 cm3, we have a pressure of 8 pounds, so for a volume of 60 cm3, we have that:

32 cm3 -> 8 pounds

60 cm3 -> x pounds

32 * 8 = 60 * x

x = 32 * 8 / 60 = 4.2667 pounds.

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)