Answer:
Step-by-step explanation:
1/3 of 12, because 1/3 has three parts, on the other hand 1/4 has four parts, which make each 1 of the 4 parts smaller than the 1/3
Answer:
Step-by-step explanation:
10-8=2
10+8=18
sum of two sides greater than the third.
difference of two sides is less than the third.
so 2<x<18
For , on the left we have , and on the right,
(where we use the double angle identity: )
Suppose the relation holds for :
Then for , the left side is
So we want to show that
On the left side, we can combine the fractions:
Recall that
so that we can write
(another double angle identity: )
Then recall that
which lets us consolidate the numerator to get what we wanted:
and the identity is established.
Answer:
120
Step-by-step explanation:
20% of 600
= 120 girls
If x terminates in the fourth quadrant, then we know that sin(x) < 0 and cos(x) > 0. Given that sec(x) = 8, we immediately have
cos(x) = 1/sec(x) = 1/8
Recall the Pythagorean identity,
cos²(x) + sin²(x) = 1
Then it follows that
sin(x) = -√(1 - cos²(x)) = -3√7/8
Now recall the double angle identities,
sin(2x) = 2 sin(x) cos(x)
cos(2x) = cos²(x) - sin²(x)
Then
sin(2x) = 2 (-3√7/8) (1/8) = -6√7/64 = -3√7/32
cos(2x) = (1/8)² - (-3√7/8)² = -62/64 = -31/32
By definition of tangent,
tan(x) = sin(x)/cos(x)
Then
tan(2x) = sin(2x)/cos(2x) = (=3√7/32) / (-31/32) = 3√7/31