The skaters collide when their y-values are the same, which implies that their x-values must also be the same. Hence, we equate the two equations and solve for x:
-3x + 72 = -3x^2 + 30x
This simplifies to:
3x^2 - 33x + 72 = 0
From factoring or using the quadratic formula, we get two solutions for x:
x = 12, x = 2
Substituting these solutions back into the equations for y, we get the corresponding y-values:
For x = 12:
For the linear equation, y = -3*12 + 72 = 36.
For the quadratic equation, y = -3*(12)^2 + 30*12 = 36.
For x = 2:
For the linear equation, y = -3*2 + 72 = 66.
For the quadratic equation, y = -3*(2)^2 + 30*2 = 66.
Hence, the two skaters might collide at the points (12, 36) and (2, 66).
Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows the path y=-3x+72, while the other skater follows the curve y=-3x^2+30x .Find all the points where they might collide if they are not careful.
1 answer
1 answer