14. Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P of the gas is inversely proportional to the volume V of the gas. Suppose that at a certain temperature the volume is 728 cm!, the pressure is 182 kPa, and the pressure is decreasing at a rate of 25 kPa/min. At what rate is the volume increasing at this instant?

dV/dt = 100 cm³/min

Step-by-step explanation:

Given

V = 728 cm³

P = 182 kPa

dP/dt = - 25 kPa/min

dV/dt = ?

If we apply the ideal gas equation

P*V = n*R*T

where n*R*T is constant

we have

d(P*V)/dt = d(n*R*T)/dt

⇒ d(P*V)/dt = 0

⇒ V*(dP/dt) + P*(dV/dt) = 0

⇒ dV/dt = - (V/P)*(dP/dt)

Plugging the known values we obtain

⇒ dV/dt = - (728 cm³/182 kPa)*(- 25 kPa/min)

⇒ dV/dt = 100 cm³/min

the aswere is the one with all 8's and the second one is with the 10,8 and 6

step-by-step explanation:

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have