I'll write "x" instead theta.
sin x + 1 = cos(2x)
formula: cos(2x) = 1 - 2sin²x
sin x + 1 = 1 - 2sin²x
2sin²x + sin x = 0
sin x (2sin x + 1) = 0
sin x = 0 or sin x = -1/2
x1 = πk and x2 = -π/6 + 2πk and
x3 = 5π/6 + 2πk
for domain 0≤x<2π :
x1 = 0 (for k=0 in x1)
x2 = π (for k=1 in x1
x3 = 11π/6 (for k=1 in x2)
x4 = 5π/6 (for k=0 in x3).
k is an integral.
In order they are
1.1 * 10^12, 9.5 * 10^11 and 5*10^8
Using linear functions, the inequality that represents when Gilberta has more wallpaper left in her room than María has in hers is: t < 5.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
For this problem, we consider:
- The initial amount as the y-intercept.
Hence the amounts Gilberta and Maria have left after t hours are given by:
Gilberta has more papers when:
G(t) > M(t).
Hence:
35 - 4.3t > 30.5 - 3.4t
-0.9t < -4.5
Multiplying by -1:
0.9t < 4.5
t < 4.5/0.9
t < 5.
Hence the inequality is:
t < 5.
More can be learned about linear functions at brainly.com/question/24808124
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Answer:
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Step-by-step explanation:
