Help please :c
Having survived the meteor impact, thanks to some last minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path. y=2x+1

Question

Help please :c
Having survived the meteor impact, thanks to some last minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y2 + x2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path. y=2x+1

anonymous · Answer

@mathmale

anonymous · Answer

@hartnn

anonymous · Answer

@ganeshie8

anonymous · Answer

So far I got 4x^4+4x+1=40,000

ganeshie8 · Answer

so you want to solve below equations to knw where the both trajectories intersect is it ?

$ y^2 + x^2 = 40,000$

$y=2x+1$

anonymous · Answer

correct!

anonymous · Answer

which I put y into the equation and squared it getting 4x^2+4x+1+x^2=40,000

ganeshie8 · Answer

looks good^

ganeshie8 · Answer

get it into standard quadratic form,
then apply quadratic formula

anonymous · Answer

so I have to set one side equal to zero?

anonymous · Answer

I'm sorry, I'm terrible at math.

ganeshie8 · Answer

$4x^2+4x+1+x^2=40,000$

combine like terms 

$5x^2+4x+1=40,000$

subtract 40,000 both sides 

$5x^2+4x - 39,999= 0 $

ganeshie8 · Answer

use quadratic formula and use ur calculator

anonymous · Answer

You're going to hate me for saying this but I have no clue where to start

ganeshie8 · Answer

lol no, below is the quadratic formula :

$$\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$

anonymous · Answer

okay let me solve it, one second (:

ganeshie8 · Answer

your equation :
$5x^2+4x - 39,999= 0$

a = 5
b = 4
c = -39,999

ganeshie8 · Answer

plug them in the formula and USE UR CALCULATOR. u cannot solve it by hand

anonymous · Answer

Too much work by hand lol

ganeshie8 · Answer

it gives u two solutions, u take whichever u want..

ganeshie8 · Answer

or both... depending on which direction the ship/satellite are going

anonymous · Answer

i got $$-4\sqrt{-799980}\25$$

ganeshie8 · Answer

$$\dfrac{-4 \pm \sqrt{4^2-4(5)(-39,999)}}{2(5)}$$

$$\dfrac{-4 \pm \sqrt{4^2+799980}}{10}$$

ganeshie8 · Answer

simplify further

ganeshie8 · Answer

$$\dfrac{-4 \pm \sqrt{4^2-4(5)(-39,999)}}{2(5)}$$

$$\dfrac{-4 \pm \sqrt{4^2+799980}}{10}$$

$$\dfrac{-4 \pm 894.4}{10}$$

anonymous · Answer

Okay, that wouldn't be the intersecting point though, right?

ganeshie8 · Answer

http://www.wolframalpha.com/input/?i=solve+5x%5E2%2B4x+-+39%2C999%3D+0

anonymous · Answer

Thank you so much!!

ganeshie8 · Answer

attachment

ganeshie8 · Answer

^^there ur both intersecting points A and B
graphing is the best method to solve these equations i think

anonymous · Answer

Which one would I use though? point a or b?

anonymous · Answer

Or would I include both?

ganeshie8 · Answer

$A = (-89.84, -178.68)$
$B = (89.04, 179.08)$

ganeshie8 · Answer

I think you only want the point B

anonymous · Answer

You're a life saver man!

anonymous · Answer

Thanks again

ganeshie8 · Answer

u wlc :)