Question

Please Check My Work?!?!
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 y^2 + x^2 = 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’ path if the ship's original trajectory is y = x.

Answer 1

lol they really stretch for these "word problems" don't they?

Answer 2

So, what i did is used substitution and plugged x in for y: so i got x^2 + x^2 = 40,000
2x^2 = 40,000
so, i divided by 2 to get
x^2 = 20,000
square root each side..
then i got
x = 141.42
y= 141.42

Answer 3

and lol yes they do :D

Answer 4

i think you are being asked to solve where the line \(y=x\) crosses the circle \(x^2+y^2=40,000\)

Answer 5

you have a mistake i think
it is \(x^2+y^2\) not \(x^2+x^2\)

Answer 6

yeah... and this is Systems of Equations, by the way...

Answer 7

ooh i see, \(y=x\) you are right, i am wrong

Answer 8

ok :D

Answer 9

sorry, you are completely correct
\[2x^2=40,000\\
x^2=20,000\\
x=\pm\sqrt{20,000}\]

Answer 10

don't forget the \(\pm\) there, there are two places where the line crosses the circle

Answer 11

Thank you soo sooo much... :D

Answer 12

yw
you did all the work

Answer 13

:D you checked it for me though :D