Mathematics: Afountain shoots a water arc that can be modeled by the graph of the equation y=-0.006x^2+1.2x+10, where x is the horizontal distance (in feet) from the river s north shore and y is the height (in feet) above the river. does the water arc reach a height of 50 feet? if so, about how far from the north shore is the water arc 50 feet above the water?

It would take 41 min for 14 people to paint 14 walls...

Afountain shoots a water arc that can be modeled

dragongacha777

14.01.2022

ANSWER

The water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.

EXPLANATION

The water arc is modeled by the function:

$y = - 0.006 {x}^{2} + 1.2x + 10$

We write this function in vertex form:

$y = - 0.006 ({x}^{2} - 200x )+ 10$

$y = - 0.006 ({x}^{2} - 200x + ( - 100)^{2} ) - - 0.006( - 100)^{2} + 10$

$y = - 0.006 ( x- 100)^{2} ) + 60+ 10$

$y = - 0.006 ( x- 100)^{2} ) +70$

The vertex of this function is at

(100,70).

This means that the water arc reached a height of 50ft.

We put y=50 and solve for x.

$- 0.006 ( x- 100)^{2}+70 = 50$

$- 0.006 ( x- 100)^{2} = - 20$

$( x- 100)^{2} = \frac{10000}{3}$

$x = 100 \pm \frac{100 \sqrt{3} }{3}$

x=42.3 or x=157.7

Hence the water arc is 50 ft above the water approximately 42ft and 158ft from the north shore.

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