A science geek brews tea at 195195 °F, and observes that the temperature T(t)T(t) of the tea after tt minutes is changing at the rate of T'(t)=−4.5e−0.07tT′(t)=−4.5e−0.07t °F/min. What is the average temperature of the tea during the first 55 minutes after being brewed? Round your answer to the nearest hundredth of a degree.

Step-by-step explanation:

See enclosed file for answer.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

7 is the median   7.875 is the mean

step-by-step explanation:

3,4,5,6,8,11,13,13