When you use a spray can and press the valve at the top, you decrease the pressure of the gas in the can. This decrease of pressure causes the volume of the gas in the can to increase. Because the gas needs more room than is provided in the can, it expands in spray form through the small hole near the valve. In general, if the temperature is constant, the pressure, P, of a gas in a container varies inversely as the volume, V, of the container. The pressure of a gas sample in a container whose volume is 8 cubic inches is 12 pounds per square inch. If the sample expands to a volume of 22 cubic inches, what is the new pressure of the gas?

Q: The variable s is proportional to t, and s = 15 when t = 105.Determine t when s = 40.

A: Given: The variable s is proportional to t. s = 15 when t = 105.

Q: If a 1600 foot bridge weighing 2100 tons supports 1400 tons, find the constant of proportionality k.…

A: Given:The weight a suspension bridge can support (B) = 2100 tonsBridge’s total length (l) = 1600…

Q: .  If y is inversely proportional to x, and if y = 16 when x = 5, find the constant of variation

A: Given: y is inversely proportional to x y=16 when x= To find the constant of variation

Q: The distance traveled by a bus varies directly with the weather. The bus traveled 240 km in 3 hours.…

A:

Q: The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure,…

A: Write the proportional equation for volume and then write both cases and eliminate the answer.

Q: ook a racecar driver 3 hours and 20 minutes to go 500 miles. What is the constant of proportionality…

A: Given that  It took a racecar driver 3 hours and 20 minutes to go 500 miles.  Number of miles (y) =…

Q: Assume that r varies directly as P. what is the constant of proportionality if R equals three when P…

A: Given r varies directly as p . we find the constantof proportionality if r ⊂ 3 and p=15

Q: z varies inversely with the product of x and y when x = 2, y = 4, and z = 0.5. Find z when x = 4 and…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.