<span>Think of arcsin (-1/3) as an angle, and call it "theta." The the original problem becomes "find sec [ 2 theta ]"
1 1
which is the same as "find ------------------ " or --------------------------------------
cos[2 theta] (cos theta)^2 - (sin theta)^2
Recall that theta = the angle whose sine is -1/3. Thus, sin theta = -1/3 and cos theta = 2sqrt(2) / 3.
So we now have:
1
-------------------------------------------
2 sqrt(2) -1
[------------------- ]^ 2 - [ ------- ]^2
3 3
which boils down to:
1 1
----------------- = ---------------- = 9/7 (answer)
8 1 7/9
------ - --------
9 9
</span>
Answer:
see below
m = males = 50
e = females = 25
a = adults = 7
Step-by-step explanation:
Givens
Let the adults = a
let the males students = m
lef the female students = e
Equations
a + m + e = 82
m = 7*a + 1
e = 1/2 * (7a + 1)
Solution
a + 7a + 1 + 1/2(7a + 1) = 82 Remove the brackets on the left.
a + 7a + 1 + 3.5*a + 1/2 = 82 Combine the like terms on the left.
11.5a + 1.5 = 82 Subtract 1.5 from both sides.
11.5a + 1.5 - 1.5 = 82 - 1.5 Combine
11.5a = 80.5 Divide by 11.5
a = 80.5/11.5
a = 7
The number of adults = 7
===============================
m = 7a + 1
m = 7*7 + 1
m = 50
===============================
e = 1/2 m
e = 1/2 * 50
e = 25
Answer:
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Answer:
D)
Step-by-step explanation:
=>
Multiplying and dividing by conjugate
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=>
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=> 3 +