The motion of a ship riding at anchor can be modeled by y=25-4 cos (pi/6)t, where y is the water depth in feet and t is the time
1 answer:
Answer: 29 feet (deepest) at 6 am
21 feet (shallowest) at Midnight & Noon
<u>Step-by-step explanation:</u>
y = -4 cos (π/6)t +25
Amplitude (A) = 4
-A means it is a reflection over the x-axis (starts at minimum)<em> </em>
Period = 2π/B → Period = 12
Phase shift = C/B → Phase Shift = 0
Midline (D) = 25
Midline (D) ± Amplitude (A) = Max & Min
Max: 25 + 4 = 29
Min: 25 - 4 = 21
Change the coordinates of y = cos (x) as follows:
- x-value: Add C then divide by B
- y-value: Multiply by A then add D
Note that the equation shows: A = -4, B = π/6, C = 0, D = 25
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Answer:
Y = 3x^x is a graph that has exponential growth while y = 3^-x has exponential decay.
Y = 3x^x (-∞, 0) and (∞, ∞).
Y = 3x^-x (-∞, ∞) and (∞, 0).
Step-by-step explanation:
The infinity symbols were being used to represent the x and y values of each graph. I will call y = 3^x "graph 1" and y = 3^-x "graph 2".
When graph 1 had positive ∞ for its x value, its y value was reaching towards positive ∞. When its x was reaching for negative ∞, its y was going for 0.
For graph 2, however, when its x was reaching for positive ∞, its x was reaching for 0. When its x was reaching for negative ∞, its y was going for positive ∞.
Here's an image of the graphs:
