Answer:
Step-by-step explanation:
tan x/2=-√3/3
sec²x/2-tan²x/2=1
sec²x/2-3/9=1
sec² x/2=1+1/3=4/3
cos² x/2=3/4
2cos² x/2=3/2
1+cos x=3/2
cos x=3/2-1=1/2=cos π/3,cos (2π-π/3)
x=π/3,5π/3
or
cos x=(1-tan²x/2)/(1+tan²x/2)=(1-1/3)(1+1/3)=(2/3)/(4/3)=1/2=cos π/3,cos (2π-π/3)
or x=π/3,5π/3
x=π/3
x/2=π/6
tan x/2=tan π/6=√3/3
so x=π/3 is an extraneous value.
x=5π/3 is the solution.
or
tan x/2=-√3/3=-1/√3=(-1/2)/(√3/2) [by dividing numerator and denominator by 2]
=-tan π/6=tan (π-π/6),tan (2π-π/6)
x/2=5π/6,11π/6
x=5π/3,11π/3,
now 11π/3 >2π
so x=5π/3
12 divuded by3=4, 12 dibed by 4=3, 12 divided by 6=2, 12dibided by 2=6, 12 divided by1=12, 12 divided by 12=1
Answer:
- 150 short-sleeved shirts
- 100 long-sleeved shirts
Step-by-step explanation:
Let S and L represent the numbers of short- and long-sleeved shirts ordered.
The expected earnings were ...
5S +10L = 1750
The number sold was ...
(1/3)S + (1/2)L = 100
We can multiply the first equation by 1/5 and the second equation by 6 to put the equations into standard form:
Subtracting the second equation from twice the first gives ...
2(S +2L) -(2S +3L) = 2(350) -(600)
L = 100 . . . . . . simplify
2S +3(100) = 600
S = 150
150 short-sleeved and 100 long-sleeved shirts were ordered.
Answer:
f(x) is an even function for all even values of m.
Step-by-step explanation:
I believe the correct answer from the choices listed above is option. The reason of that is because no matter what m is, assuming it is an integer 2m will always be an even number. Hope this answers the question.
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