Answer:
Step-by-step explanation:
Use the half angle identity for cosine:
cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)
I'm going to figure out the sign part first for cos(x/2)...
so x is in third quadrant which puts x between 180 and 270
if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)
cosine is negative in the second quadrant
so we know that
cos(x/2)=-sqrt(1+cos(x))/sqrt(2)
Now we need cos(x)... since we are in the third quadrant cos(x) is negative...
If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.
So let's plug it in:
cos(x/2)=-sqrt(1+4/5)/sqrt(2)
No one likes compound fractions (mini-fractions inside bigger fractions)
Multiply top and bottom inside the square roots by 5.
cos(x/2)=-sqrt(5+4)/sqrt(10)
cos(x/2)=-sqrt(9)/sqrt(10)
cos(x/2)=-3/sqrt(10)
Rationalize the denominator
cos(x/2)=-3sqrt(10)/10
Answer:
Brook is faster.
Step-by-step explanation:
1 hour=60 minutes
2 hours=2*60=120 minutes
-------------
7 miles in 30 minutes vs 25 miles in 120 minutes
7/30=0.233...mile per minute
25/120=0.20833...mile per minute
Answer:
Options A and C and F are correct.
Step-by-step explanation:
5(2+4)
5*2+5*4
5*6
Have a great day! :)
and can I please have brainliest?
Thanks!
Answer:
3/10 of the aquarium are yellow tangs.
Step-by-step explanation:
Given that in an aquarium 2/5 of the fish or surgeonfish and of these, 3/4 are yellow tangs, to determine what fraction of all fish in the aquarium are yellow tangs the following calculation must be performed:
2/5 = 0.40
0.40 x 3/4 = X
1.20 / 4 = X
0.30 = X
0.30 = 3/10
Therefore 3/10 of the aquarium are yellow tangs.
|x| < 7
means x < 7 and x > -7
answer is -7 < x < 7
