Pluto's maximum distance from the sun (aphelion) is 7.47.47, point, 4 billion kilometers. Its minimum distance from the sun (perihelion) is 4.44.44, point, 4 billion kilometers. Pluto last reached its perihelion in the year 198919891989, and will next reach its perihelion in 22372237

Step-by-step explanation:

Assume a sine/cosine wave.

the period (min to max) is 2237–1989 = 248 years

so the first trial is D = M sin ((2πt/248) + k)

where k is the phase and M is the amplitude.

D = M sin (2π(t–1989)/248)

D = M sin ((2πt/248) – (2π1989/248))

at t = 1989, we have sin(0) = 0

at t = 2237, we have sin(56.67534–50.39216) = sin 2π = 0

but we want a min at those points, equivalent to sin 270º or 3π/2, or –π/2, so we have to add in additional phase shift.

D = M sin ((2πt/248) – (2π1989/248) – (π/2))

D = M sin (0.0253354t – 50.39216 – 1.570796)

D = M sin (0.0253354t – 51.96296)

at t = 1989,

D = M sin (50.39216 – 51.96296) = M sin 1.5708 = –1 ok

min to max distance is 7.4 – 4.4 = 3

so the equation is

D = 5.9 + 1.5sin (0.02534t – 51.96) (billions km)

in 2000

D = 5.9 + 1.5 sin (0.02534×2000 – 51.96) (billions km)

D = 5.9 + 1.5 sin (-1.28)

D = 5.9 – 1.5 × 0.02234

d = 5.87 billions km

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

d. vertex

step-by-step explanation: