when the temperature stays the same, the volume of the gas is inversely proportional to the pressure of the gas. If a balloon is filled with 87 cubic inches of a gas at a pressure of 14 pounds per square inch. Find the new pressure of the gas if the volume is decreased to 29 cubic inches.

find the vertical asymptotes, if any, of the graph of the rational function

f(x)=x/x(2)+8

When the temperature stays the same, the volume of a gas is inversely proportional to the pressure of the gas. If a balloon is filled with 87 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 29 cubic inches.

Pressure times Volume is constant in a costant-temperature situation. Let the new pressure be P.

P * 29 = 14 * 87
P = (87/29)*14

Do the calculation.

f(x)=x/x(2)+8

I am going to guess you mean

f(x)=x/(x^2+8)

( the ^ sign is the standard way to indicate an exponent)

Vertical asymptotes result when a division close to zero takes place, so
you are looking at the x2 + 8 part.
but this cannot have a real solution.
since we would have to solve x^2 = -8

so your function has no vertical asymptotes.

56

To solve this problem, we can use the principle of Boyle's Law, which states that when the temperature of a gas remains constant, the volume of the gas is inversely proportional to the pressure of the gas.

Boyle's Law can be mathematically expressed as:

P₁V₁ = P₂V₂

Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure
V₂ = final volume

Let's plug in the given values into the equation:

P₁ = 14 pounds per square inch
V₁ = 87 cubic inches
V₂ = 29 cubic inches

P₁V₁ = P₂V₂

14 * 87 = P₂ * 29

Now, we can solve for P₂:

1218 = 29P₂

Divide both sides of the equation by 29:

P₂ = 1218 / 29

P₂ ≈ 42 pounds per square inch

Therefore, the new pressure of the gas is approximately 42 pounds per square inch.