Let c represent the weight of cashews and p the weight of pecans.
Then c + 10 = total weight of the nut mixture.
An equation for the value of the mixture follows:
$1.50(10 lb) + $0.75c = (c+10)($1.00)
Solve this equation for c: 15 + .75c = c + 10. Subtract .75c from both sides:
15 = 1c - 0.75c + 10. Then 5=0.25c, and c = 5/0.25, or 20.
Need 20 lb of cashews.
Check: the pecans weigh 10 lb and are worth $1.50 per lb, so the total value of the pecans is $15. The total value of the cashews is (20 lb)($0.75/lb), or $15. Does (20 lb + 10 lb)($1/lb) = $15 + $15? Yes. So c= 20 lb is correct.
We need to use Law of sine.
sin A/a = sin C/c
sin A/|CB| = sin C/|AB|
sin A/14 = sin(118⁰)/ 20
sin A = (14*sin(118⁰))/ 20
A=arcsin((14*sin(118⁰))/ 20) ≈ 38⁰
The answer is A, yes his answer is reasonable because 6 times 0.74 is 44.4
f(x) = 3 - 2sin(x)
0 = 3 - 2sin(x)
- 3 - 3
-3 = -2sin(x)
-2 -2
1¹/₂ = sin(x)
sin⁻¹(1¹/₂) = sin⁻¹[sin(x)]
sin⁻¹(1¹/₂) = x
