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).

sine

step-by-step explanation:

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.