Simplify. please help 2+x8x3+xx
1 answer:
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We need to convert the mixed fractions into improper fractions.
1*8 = 8
8+7 = 15
15/8
2*3 = 6
6+1 = 7
7/3
Now we can finish and multiply
15*7 = 105
8*3 = 24
Simplify 105/24
105/24
24*4 = 96
105 - 96 = 9
4 is the whole number, and 9 is the numerator.
4 9/24
Simplify that,
9/3 = 3
24/3 = 8
4 3/8
Answer:
1*8 = 8
8+7 = 15
15/8
2*3 = 6
6+1 = 7
7/3
Now we can finish and multiply
15*7 = 105
8*3 = 24
Simplify 105/24
105/24
24*4 = 96
105 - 96 = 9
4 is the whole number, and 9 is the numerator.
4 9/24
Simplify that,
9/3 = 3
24/3 = 8
4 3/8
Answer:
Answer:
0.20 and 0.36
Step-by-step explanation:
y(t) = 2 sin (4π t) + 5 cos (4π t)
We wish to convert this to:
y = A sin(ωt + φ)
We know that ω = 4π. We also know the following:
5 = A sin φ
2 = A cos φ
Divide the first equation by the second equation:
5/2 = tan φ
φ = tan⁻¹(5/2)
Now, square the two equations and add them together.
5² + 2² = (A sin φ)² + (A cos φ)²
29 = A²
A = √29
The equation of the wave is therefore:
y = √29 sin(4π t + tan⁻¹(5/2))
The maximum negative position is -√29. And half of that is -½√29.
-½√29 = √29 sin(4π t + tan⁻¹(5/2))
-½ = sin(4π t + tan⁻¹(5/2))
7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)
7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π
t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24
Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.
t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24
t ≈ 0.20 or 0.36
