Question

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 Upper T equals 5.8 t squared plus 14 t plus 32​, 0less than or equalstless than or equals4. ​a) What is the car​ radiator's temperature at the instant the car is turned​ on? ​b) What is the car​ radiator's temperature after the car has been driven for 2 minutes​? ​c) How long after the car has begun operating will the car​ radiator's temperature reach 80degrees​F?

Answer 1

Explanation:

T = 5.8t² + 14t + 32 ( 0 ≤ t ≤4 )

a ) when t = 0 ( when car is turned on )

T = 32 ° F .

b ) When t = 2

T = 5.8t² + 14t + 32

= 5.8 x 2² + 14 x 2 + 32

= 23.2 + 28 + 32

= 83.2 ° F

c )

T = 80 ; to find t = ?

80 = 5.8t² + 14t + 32

5.8t² + 14 t - 48 = 0

t =
`(-14+/-(14^2-4* 5.8* -48)^(1)/(2) )/(2* 5.8)`

t = 1.9 minutes . approx .