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8090 [49]
3 years ago
10

I WILL GIVE BRAINLIEST TO WHOEVER IS CORRECT.

Mathematics
1 answer:
faust18 [17]3 years ago
4 0

the domain is the numbers you can use for x


x is how many papers you can buy

you can't buy negative papers

but the store only has 5 papers so the answer is all inegers from 1 to 5 including 1 and 5

integes are like -3,-2,-1,0,,2,3,4, but since we have 1 to 5 we have 1,2,3,4,5

it isn't all real numbers from 1 to 5 because you can't buy 3.141592 reams of paper

answer is first one

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1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26
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Step-by-step explanation:

<u>Part A</u>

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

<u>Part B</u>

The graph's function would be in the form of y=acos(bx+c)+d where a is the amplitude, \frac{2\pi}{b} is the period, -\frac{c}{b} is the phase/horizontal shift, and d is the average/midline.

We already know our amplitude of a=3 from part A.

Since our period is given to us as 26 seconds, then we can use the equation \frac{2\pi}{b}=26 to find b, which happens to be b=\frac{\pi}{13}.

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity sin(x)=cos(x-\frac{\pi}{2}) which shifts the cosine graph \frac{\pi}{2} units to the right. This means that c=-\frac{\pi}{2}, making our phase shift -\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5, or 6.5 feet to the right

Our average/midline would be d=12 as given as the average height by the problem.

Therefore, the function is f(x)=3cos(\frac{\pi}{13}x-\frac{\pi}{2})+12

<u>Part C</u>

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

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