Functions

[Gretta99]

Word Problem:
An observation balloon is released at a point 10 miles from the station that receives its signal and rises vertically. Express the distance D between the balloon and the receiving station as a function of the altitude H of the balloon.
I'm not sure how to do this. Would I tie the pythagorean theorem into this? Or what equation should I use. The image on the example is a right triangle.
So would it be 10^2+ h^2=d(x)^2 or what?

Michelle

 

[Deleted member 4993]

Word Problem:
An observation balloon is released at a point 10 miles from the station (horizontal distance?)that receives its signal and rises vertically. Express the distance D between the balloon and the receiving station as a function of the altitude H of the balloon.
I'm not sure how to do this. Would I tie the pythagorean theorem into this? Or what equation should I use. The image on the example is a right triangle.
So would it be 10^2+ h^2=d(x)^2 or what?

Michelle

Define your ' h', 'd' and your 'x' - I think you should use 'H' & 'D' as suggested by the problem.

 

[tkhunny]

You seem to have it, but the notation needs a little work.

"express ... as a function of" requires an explicit definition.

h = height of baloon in miles
d(h) = distance as a function of balloon's height

You must solve for 'd' and get rid of the 'x' that doesn't mean anything.

\(\displaystyle d(h) = \sqrt{10^{2}+h^{2}}\)