SOLUTION: The temperature, T, in degrees Fahrenheit, in a car's radiator during the first 4 minutes of driving is a function of time, t. The temperature can be found by the formula T=5.8t^2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The temperature, T, in degrees Fahrenheit, in a car's radiator during the first 4 minutes of driving is a function of time, t. The temperature can be found by the formula T=5.8t^2      Log On


   

Question 134509: The temperature, T, in degrees Fahrenheit, in a car's radiator during the first 4 minutes of driving is a function of time, t. The temperature can be found by the formula T=5.8t^2+13t+32, 0 less than or equal to t less than or equal to 4.
a) What is the car's radiator's temperature at the instant the car is turned on?
b) What is the car's radiator's temperature after the car has been driven for 3 minutes?
c) How long after the car has begun operating will the car's radiator temperature reach 90 degrees Fahrenheit?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Given: T=5.8t%5E2%2B13t%2B32
a) What is the car's radiator's temperature at the instant the car is turned on? What is the time when the car is turned on? time = 0
So replace t with 0 in the function and solve
T=5.8%2A0%5E2%2B13%2A0%2B32
T+=+32
b) What is the car's radiator's temperature after the car has been driven for 3 minutes?
What value should yo use for t now? t = 3
T=5.8%2A3%5E2%2B13%2A3%2B32
T+=+5.8%2A9+%2B+13%2A3+%2B+32
T+=+123.2
c) How long after the car has begun operating will the car's radiator temperature reach 90 degrees Fahrenheit?
This time you are given a tempurature (T) and asked to find the time.
90=5.8t%5E2%2B13t%2B32
0+=+5.8t%5E2+%2B+13t+-+58
Use the quadratic equation to find values for t. Then pick the value that 'makes sense"
0 = at^2 + bt + c, so a = 5.8, b = 13 and c = -58
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
I get t = 2.24
Check your answer by replacing t with 2.23
T+=+5.8%2A+2.24%5E2+%2B+13+%2A+2.24+%2B+32
T+=+29.01+%2B+29.12+%2B+32+ ~ 90