Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
7/8 and 3/4
Both need to have same denominator so it would be 32, in this case because 8*4 is 32.
7/32+3/32=10/32 simplified to 5/16
90/300
To make it simpler, make it,out of 100 by dividing it all by 3. This will make it:
30/100
Therefore it is 30%
There is no solution. Here is the explanation with both of the methods :)
Answer:
a) 
b) 334,858 bacteria
c) 4.67 hours
d) 2 hours
Step-by-step explanation:
a) Initial number of bacteria is the coefficient, that is, 250. And the growth rate is the coefficient besides “t”: 0.15. It’s rate of growth because of its positive sign; when it’s negative, it’s taken as rate of decay.
Another way to see that is the following:
Initial number of bacteria is N(0), which implies 
. And 
. The process is:
b) After 2 days means 
. So, we just replace and operate:
c) 
d) 
