The value of x is 8.5.
Solution:
U is the mid-point of TV.
TU = 6
UV = 2x - 11
TU = UV
6 = 2x - 11
Add 11 on both sides.
6 + 11 = 2x - 11 + 11
17 = 2x
Divide by 2 on both sides.
8.5 = x
Switch the sides.
x = 8.5
Option B is the correct answer.
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2 answers:
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9514 1404 393
Answer:
- maximum: (x, y) = (12.4n+3.2, 186.322)
- minimum: (x, y) = (12.4n+9.4, 163.498)
Step-by-step explanation:
You know that cos(α) is a maximum at α=0, 2π, 4π, and all even multiples of π. You know cos(α) is a minimum for α=π, 3π, 5π, and all odd multiples of π.
You can find your value of x at which y will be a maximum by setting the argument of the cosine function equal to zero (and/or 2nπ). If we use α=2nπ, then we have ...
α = (5π/31)(x -3.2) = 2nπ
(x -3.2) = (31/5)(2n) = 12.4n
Tidal maxima will occur at ...
x = 12.4n +3.2 . . . . . for integer values of n
Without bothering to go through the solution for α being odd multiples of π, we can see from this that the period is 12.4 hours. We know the tidal minimum will be half a period later, or 6.2 hours later than this.
Tidal minima will occur at ...
x = 12.4n +9.4 . . . . for integers n
__
Of course, cos(α) has extremes of ±1, so your tidal maximum will be ...
y = 11.412 +174.91 = 186.322
and your tidal minimum will be ...
y = -11.412 +174.91 = 163.498
