Question

URGENT!
Another plan to secure the roller coaster involves using a cable and strut. Using the center of the half-circle as the origin, the concrete strut can be modeled by the equation and the mathematical model for the cable is . The cable and the strut will intersect. The equation of the coaster is y = √(900 - x^2). Algebraically find the point where the strut and cable intersect. Thank you!

Answer 1

Do you have or can you draw a diagram?

Answer 2

Model #2

Answer 3

The equations are \[y=\sqrt{2x+8}\] for the strut, and the cable is \[y=x-8\]

Answer 4

when things are the same, they are equal, so when y=y is what we are looking for

x-8 = sqrt(2x+8)

solve for x is my thoughts

Answer 5

I don't have the software, thanks for the equation.
x - 8 = (2x + 8)^1/2 square both sides
x^2 - 16x + 64 = 2x + 8 simplify
x^2 -18x + 56 = 0 Add 25 to both sides
x^2 -18 + 81 = 25
(x -9)^2 + 25 sq root of bothsides
x - 9 = +5 and -5
x = 14
x = 4

Answer 6

not that i want to be railroading over radars response :) but the asker messaged for help is the only reason im responding as such

Answer 7

No problem, I feel that I may not be of much help without a picture in mine of the thing.

Answer 8

I really appreciate the help, thank you both so much! :)

Answer 9

when we square as a result of the process, i believe we introduce a chance for extrenuous solutions

Answer 10

if x=4

-4 = sqrt(16)

is not technically correct since the range of sqrt(x) is 0 and up

Answer 11

We do, and I think the 4 may be extraneous, I was trying to use the completing the square method of solving.

Answer 12

you did fine :)

Answer 13

Radar. can you please help with 1 more problem?

Answer 14

I can only try, but you might be better to post it so others may pitch in.

Answer 15

ok!