Givens
sin(2x) = 2 * sin(x) * cos(x)
Equation
sin(x)*sin2(X) = 2sin(x) * 2sin(x)*cos(x) = 1
4*sin^2(x)* cos(x) = 1
sin^2(x) = 1 - cos^2(x)
4(1 - cos^2(x) ) * cos(x) = 1 Divide by 4
(1 - cos(x) ) *cos(x) = 1/4
cos(x) - cos^3(x) = 1/4
Let y = cos(x)
y - y^3 = 1/4
This is a cubic. I have to use a calculator's built in formula to solve it.
a = -1
b = 0
c = 1
d = - 1/4
Solution
y1 = - 1.107. Extraneous cos(x) can't be less than 1.
y2 = 0.8376
y3 = 0.2696
but cos(x) = y
cos-1(0.8376) = 33.11 degrees.
cos-1(0.2696) = 74.36 degrees.
The cosine is also plus in quad 4.
x = 360 - 33.11 = 326.89
x = 360 - 74.36 = 285.64
The graph of the cubic is below. It pretty much confirms what I found.
80/100 or 8/10 It's not mixed but that's what I got
Answer: x = -9
Step-by-step explanation:
18/x = -2
18x = -2x
x = -18/2 = -9
9514 1404 393
Answer:
- $9,000 at 15%
- $4,000 at 10%
Step-by-step explanation:
Let x represent the amount borrowed at 15%. Then the amount borrowed at 10% is (13000-x). The interest at the end of the year is ...
0.15(x) + 0.10(13000 -x) = 1750
0.05x = 1750 -1300 . . . . . . . . . . . . simplify, subtract 1300
x = 450(20) = 9000 . . . . . . . . . . multiply by 20
$9,000 was borrowed at 15%; $4,000 was borrowed at 10%.
Answer:
positive and negative or d1