Answer:
3.63 * 10^19
Step-by-step explanation:
Given that :
Number of choices to select = 12
Category available :
Blues - 14
Country - 25
Disco - 21
To select an equal number of song for each category ; then 4 songs will be selected from each :
Using combination :
(14C4 * 25C4 * 21C4)
Since the order matters for the 12 selected songs ; it thus requires 12 permutation
Thus ;
(14C4 * 25C4 * 21C4) * 12!
nCr = n! / (n-r)!r!
Using calculator;
14C4 = 1001 ;
25C4 = 12650
21C4 = 5985
12! = 479001600
Hence,
(1001 * 12650 * 5985) * 479001600
= 36301596217286400000
=3.63 * 10^19
Answer: b=13, t=29
Step-by-step explanation:
Substituting the first equation into the second,

Take the derivative with respect to t

the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero

divide by w

we add sin(wt) to both sides

divide both sides by cos(wt)

OR

(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

since 2npi is just the period of cos

substituting our second soultion we get

since 2npi is the period

so the maximum value =

minimum value =
Answer:
d, 700
Step-by-step explanation:
it's the only one that makes sense