What is the remainder in the synthetic division problem below?
1 answer:
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Answer: P(t) = 1.25.sin(.t) + 5.65
Step-by-step explanation: A motion repeating itself in a fixed time period is a periodic motion and can be modeled by the functions:
y = A.sin(B.t - C) + D or y = Acos(B.t - C) + D
where:
A is amplitude A=|A|
B is related to the period by: T =
C is the phase shift or horizontal shift:
D is the vertical shift
In this question, the motion of Pluto is modeled by a sine function and doesn't have phase shift, C = 0.
<u>Amplitude</u>:
a =
At t=0, Pluto is the farthest from the sun, a distance 6.9 billions km away. At t=66, it is closest to the star, P(66) = 4.4 billions km. Then:
a =
a = 1.25
<u>b</u>
A time period for Pluto is T=66 years:
66 =
b =
<u>Vertical</u> <u>Shift</u>
It can be calculated as:
d =
d =
d = 5.65
Knowing a, b and d, substitute in the equivalent positions and find P(t).
P(t) = a.sin(b.t) + d
P(t) = 1.25.sin(.t) + 5.65
The Pluto's distance from the sun as a function of time is
P(t) = 1.25.sin(.t) + 5.65
Answer:
Step-by-step explanation:
The volume V of the fountain is equal to:
V = L*W*h
Where L is the lenght of the fountain, W is the width of the fountain and h is the high of the fountain
We already know that h is equal to x. On the other hand, if we cut a square with side of length x, L and W are calculated as:
L = 18 - 2x
W = 12 - 2x
So, replacing L, W and h on the equation of the volume, we get:
V = (18-2x)*(12-2x)*x
Finally, simplifying the function we get: