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s344n2d4d5 [400]
3 years ago
11

the graph shows tracys earnings from babysitting. does the graph show a proportional relationship? if so, what is the constant o

f proportionality and what does it represent? explain your answers.

Mathematics
1 answer:
Flura [38]3 years ago
3 0

Answer:

The constant of proportionality is 7 and this represents the amount she charges per hour.

Step-by-step explanation:

We can find this total by using the direct proportion or direct variation equation along with any of the points.

y = kx

14 = k(2)

7 = k

Which shows our constant.

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Answer:

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Step-by-step explanation:

1 cm above central position means D = 1, so we plug in 1 into D(t) and find the time and which this occurs.

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This is the time at which this occurs.

To find instantaneous rate of change, we differentiate D(t) and plug in this t we found. Remembering that d/dt (Sin t) = Cos t

D(t)=2Sin (4\pi(t+18))\\D(t)=2Sin(4\pi t + 72\pi)\\D'(t)=2Cos(4\pi t + 72\pi)(4\pi)

Now putting t:

D'(t)=2Cos(4\pi t + 72\pi)(4\pi)\\D'(\frac{\frac{\pi}{6}-72\pi}{4\pi})=2Cos(4\pi (\frac{\frac{\pi}{6}-72\pi}{4\pi}) + 72\pi)(4\pi)\\=8\pi Cos(\frac{\pi}{6})\\=21.75

Thus, the instantaneous rate would be around 21.75 cm/s

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