The contents of the fuel tank of a car can be modeled by the function g(x)= -0.04x + 10, where x is in miles driven and g(x) rep
1 answer:
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Answer:
When the volume of a gas in a container varies inversely with the pressure on the gas and a container of nitrogen has a volume of 29.5 litres with 2000 psi. So, if the tank has a 14.7 psi pressure, then the volume of the tank would be 4013.6 litres.
Step-by-step explanation:
- The volume of a gas in a container varies inversely with the pressure on the gas. If a container of nitrogen has a volume of litres with psi, what is the volume if the tank has a psi pressure.
- Calculate the volume to the nearest whole number.
- Use the given values and calculate the proportionality constant as well as required solution.
Step 1 of 2
Write the inversely proportionality relation between the volume and pressure of a gas in container.
Where volume is represented by v and pressure is represented by p.
Remove the proportionality and place a constant say k.
Substitute the given values of nitrogen that v=29.5 and
p=2000 and calculate the value of k from above equation.
Step 2 of 2
Substitute the value p=14.7 and above calculated k value in the equation
You know 1 is not a root because the sum of the coeffcients of the equation is 14, not zero.
It is fairly easy to try 3 by synthetic division (see attachment), which tells you that 3 is a root and the remaining quadratic factor is x²-3x-5. The quadratic formula tells you the roots of that factor are
... x = (-b±√(b²-4ac))/(2a) = (3±√29)/2
The appropriate choices are
... C. (3-√29)/2
... D. (3+√29)/2
... F. 3
_____
The quadratic formula tells you the solution to
... ax²+bx+c=0
is x = (-b±√(b²-4ac))/(2a)
We have a=1, b=-3, c=-5.
