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Norma-Jean [14]
3 years ago
9

In Shadow Bay in July, high tide is at 1:30 pm. The water level is 4 feet at high tide and 0 feet at low tide. Assuming the next

high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Shadow Bay's water level in July as a function of time (t).
f(t) = 2 cos pi over 6 t + 1
f(t) = 2 cos pi over 6 t + 2
f(t) = 4 cos pi over 2 t + 1
f(t) = 4 cos pi over 2 t + 2
Mathematics
1 answer:
dimaraw [331]3 years ago
7 0
<span>In Shadow Bay in July, high tide is at 1:30 pm. The water level is 4 feet at high tide and 0 feet at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Shadow Bay's water level in July as a function of time (t).
</span>
2cos pi/6 t + +2
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I suppose you just have to simplify this expression.

(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)

Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :

… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)

Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have

… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)

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Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :

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… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)

… = (-4<em>y</em>) / (-2<em>y</em>)

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