Please help me with this. (show work.)

Mathematics

1 answer:

BlackZzzverrR [31]2 years ago

5 0

GCF: greatest common factor of any two (or more) numbers

Top left:

GCF of 24 and 60: 12

Top right:

GCF of 12 and 18: 6

Bottom left:

GCF of 18 and 42: 6

Right left:

GCF of 30 and 72: 6

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W(t)W, left parenthesis, t, right parenthesis models the daily water level (in \text{cm}cmstart text, c, m, end text) at a pond

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Answer:

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Step-by-step explanation:

W(t)models the daily water level at a pond in Arizona, t days after the hottest day of the year. (t is entered in radian)

$W(t) = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43$

We want to determine the first time,t at which the water level is 30cm.

When W(t)=30

$30 = 15\cos\left(\dfrac{2\pi}{365}t\right) + 43\\30-43=15\cos\left(\dfrac{2\pi}{365}t\right)\\-13=15\cos\left(\dfrac{2\pi}{365}t\right)\\-\dfrac{13}{15} =\cos\left(\dfrac{2\pi}{365}t\right)\\cos^{-1}(-\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)\\cos^{-1}(\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)$

$cos^{-1}(\dfrac{13}{15})=\dfrac{2\pi}{365}t\right)\\t=\dfrac{365}{2\pi}\cdot cos^{-1}(\dfrac{13}{15})\\t=152.16\\\approx 152 days \text{ (to the nearest whole day)}$

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