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:
60 square units
Step-by-step explanation:
You can get there a couple of ways.
One way is to consider the enclosing rectangle, which is 9 units by 11 units, so has an area of 99 square units. From that will be subtracted two triangles having height 2 and width 6, and two triangles having height 3 and width 9. Thus the net area in rectangle DEFG is ...
99 - 2·6 - 3·9 = 60 . . . square units
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Another way is to find the lengths of each of the sides and multiply those.
Short side = √(2²+6²) = 2√10
Long side = √(3²+9²) = 3√10
area = short side × long side = (2√10)(3√10) = 6·10 = 60 . . . square units
Answer:
81,250 people live there after 10 years.
Step-by-step explanation:
first 10 x 8%
second 80% x 65,000
=81,250
Answer:
x=15
Step-by-step explanation:
x+165degrees=180degrees
x=180-165
x=15
