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Pluto's distance P(t)P(t)P, left parenthesis, t, right parenthesis (in billions of kilometers) from the sun as a function of tim

Xelga [282]

Answer: P(t) = 1.25.sin( $\frac{\pi}{3}$ .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 = $\frac{2.\pi}{B}$

C is the phase shift or horizontal shift: $\frac{C}{B}$

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.

Amplitude:

a = $\frac{largest - smallest}{2}$

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 = $\frac{6.9-4.4}{2}$

a = 1.25

b

A time period for Pluto is T=66 years:

66 = $\frac{2.\pi}{b}$

b = $\frac{\pi}{33}$

Vertical Shift

It can be calculated as:

d = $\frac{largest+smallest}{2}$

d = $\frac{6.9+4.4}{2}$

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( $\frac{\pi}{3}$ .t) + 5.65

The Pluto's distance from the sun as a function of time is

P(t) = 1.25.sin( $\frac{\pi}{3}$ .t) + 5.65

8 0

3 years ago

All fractions equivalent to 27/81

Strike441 [17]

There is more than a trillion of equivalent fractions to 27/81, you just need to divide of multiply that number to any other numbers, but not 1 and 0, it can be negative number also
Ex: 1/3, 3/9, 54/12, 81/243, etc...

3 0

4 years ago

The ratio of football players to soccer players in the room was 5 to 7. If the football and soccer players in the room totaled 4

Anika [276]

There were 20 football players in the room. Because the ratio of football players to soccer players was 5 to 7, that meant that, should the ratio represent the actual number of football players in the room, there would be 12 football players in the room. However, the ratio has to be set equal to accomodate the 48 football players, therfore the 12 hypothetical players in the room would have to be multiplied by 4 to equalize. But that also means that everything else in the ratio will have to be multiplied by 4 to truly balance the ratio. Since there were 5 out of 12 football players, and there are actually 48 football players, and 12 times 4 equals 48, then 5 times 4 should give us our actual number of football players. Finally, some basic math will tell you that because 5 times 4 equals 20, and we can say that there are actually 20 football players in the room.

8 0

3 years ago

Read 2 more answers

A painting is 16 inches wide. it is placed inside a frame with a border that is x inches wide. The total width of the painting a

zloy xaker [14]

16 + 2x = 20
2x = 20 - 16 = 4
x = 4/2 = 2 inches

4 0

3 years ago

9. Answer the questions about the graph showing Bobby's pedi-cab rides.

Aleksandr [31]

Answer/Step-by-step explanation:

a. The order pair are:

(1, 6) => when x (distance) = 1, y (price) = 6

(3, 8) => when x (distance) = 3, y (price) = 8

(5, 10) => when x (distance) = 5, y (price) = 10

(7, 12) => when x (distance) = 7, y (price) = 12

{(1, 6) (3, 8), (5, 10), (7, 12)}

b. The graph represents a function because every domain value (x-value) has only one range value (y-value) that is related to each.

7 0

3 years ago