+143 the circular path of cars on a farris wheel can be modeled with the equation. the circular path of cars on a ferris wheel can be modeled with the equation x^2-14+y^2-150y=-49 measured in feet what is the maximum hight above ground of the riders.
a. 48 feet
b. 75 feet
c. 150 feet
d. 300 feet
+33616 We can rewrite the equation as
y2 - 150y + 35 = -x2
(y - 75)2 - 5625 + 35 = -x2
(y - 75)2 - 5590 = -x2
(y - 75)2 = 5590 - x2
Now the right-hand side has a maximum value of 5590, because as x moves away from zero, in either the positive or negative direction, x2 is positive and subtracts from 5590. Therefore the maximum value of y is obtained when x is zero:
(y - 75)2 = 5590
y = 75 + √5590 ≈ 150
So c. gives the maximum height.
.
+33616 We can rewrite the equation as
y2 - 150y + 35 = -x2
(y - 75)2 - 5625 + 35 = -x2
(y - 75)2 - 5590 = -x2
(y - 75)2 = 5590 - x2
Now the right-hand side has a maximum value of 5590, because as x moves away from zero, in either the positive or negative direction, x2 is positive and subtracts from 5590. Therefore the maximum value of y is obtained when x is zero:
(y - 75)2 = 5590
y = 75 + √5590 ≈ 150
So c. gives the maximum height.
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