MATHS P-2 AND P-3

[Sweet_angel]

Can any1 plzzzzz help me out in solving dis ques. as i m nt getting hw to solve it.....




1. An orchestra tunes to a frequency of 440 , which sounds the A above middle C . Each octave higher doubles the frequency , and each of the 12 semitones in the octave increases the frequency in the same ratio.
(a) What is this ratio ? Ans : 1.059
(b) Find the frequency of middle C. Ans : 262
(c) Where on the scale is a note with a frequency of 600 ? Ans : between D and D#

(P-2 or P-3 chap.3 Ex.3A 2nd ques)







2. A cup of coffee at 85 degree celsius is placed in a freezer at 0 degree celsius . The temperature of the coffee decreases exponentially , so that after 5 minutes it is 30 degree celsius .
(a) What is its temperature after 3 minutes ? Ans : 45.5 degree celsius
(b) Find , by trial , how long it will take for the temperature to drop to 5 degree celsius . Ans : 13.6 minutes

(P-2 or P-3 chap.3 Ex.3A 3rd ques)

 

[CaptainDanger]

I dont get it either as its A level quesion I guess... Someone help....

 

[usman]

I'll try the problem 2 1st:-
The temp/deg C after t min shud be T(t = t min) = T(t = 0 min) * exp[(rate of change of T) * t)]
= 85*exp(r*t)
where; r = rate of change of T, t = time t
Applying this to the given condition i.e., T = 30 deg C @ t = 5min
30 = 85*exp(r*5)
--> r = 0.2*ln(6/17)

Using this value of r to calculate T @ t = 3 min,
T = 85*exp(r*3)
----> T ~ 45.5 deg C

Similarly, looking @ part (b),
5 = 85*exp(r*t)
------> t ~ 13.6 min