The orbit of Pluto can be modeled by the equation {x^2}/{39.5^2} + {y^2}/{38.3^2 } = 1, where the units are astronomical units. Suppose a comet is following a path modeled by the equation x = y^{2} + 20. What are the points of intersection of the orbits of Pluto and the comet? (Not necessarily where they'll hit each other, just where the paths they take cross each other.)

9514 1404 393

  (39.24, -4.386), (39.24, 4.386)

Step-by-step explanation:

A graphing calculator solves this easily.

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For an algebraic solution, you can substitute for y^2. To avoid messing with large numbers, we define p=39.5^2 and q=38.3^2. Then after substitution for y^2, we have ...

  x^2/p +(x-20)/q = 1

Multiplying by pq gives ...

  qx^2 +px -20p = pq

  qx^2 +px -20p -pq = 0

  x = (-p +√(p^2 +4qp(p+q)))/(2q)

Putting the numbers back into this equation gives ...

  x ≈ 39.2401

  y = ±√(x -20) = ±4.38635

The crossing points are (39.2401, ±4.38635).

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5

answer: the center is the median and/or mean of the data. the spread is the range of the data. and, the shape describes the type of graph. the four ways to describe shape are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform. good luck

step-by-step explanation: