Write the slope intercept form of a line that passes through the given two points (-5,-11) (-2,1)
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Answer:
See below for answers and explanations (along with a graph attached)
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 where
is the amplitude,
is the period,
is the phase/horizontal shift, and
is the average/midline.
We already know our amplitude of from part A.
Since our period is given to us as 26 seconds, then we can use the equation to find
, which happens to be
.
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 which shifts the cosine graph
units to the right. This means that
, making our phase shift
, or 6.5 feet to the right
Our average/midline would be as given as the average height by the problem.
Therefore, the function is
<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).
