a baseball team manager is trying to determine how the angle at which a ball leaves a players bat impacts…

a baseball team manager is trying to determine how the angle at which a ball leaves a players bat impacts the distance the ball travels. the table shows the average distance a baseball travels based on the launch angle of the ball. the quadratic function ( y = - 0.32x^{2}+20.61x + 5 ) models this data. use the function to estimate the distance a baseball would travel if it were hit at a ( 55^{circ} ) angle. round your answer to the nearest whole number. feet

a baseball team manager is trying to determine how the angle at which a ball leaves a players bat impacts the distance the ball travels. the table shows the average distance a baseball travels based on the launch angle of the ball. the quadratic function ( y = - 0.32x^{2}+20.61x + 5 ) models this data. use the function to estimate the distance a baseball would travel if it were hit at a ( 55^{circ} ) angle. round your answer to the nearest whole number. feet

Answer

Explanation:

Step1: Substitute (x = 55) into the quadratic function

Given the quadratic function (y=-0.32x^{2}+20.61x + 5). When (x = 55), we substitute (x) into the function: [ \begin{align*} y&=-0.32\times(55)^{2}+20.61\times55 + 5\ \end{align*} ]

Step2: Calculate ((55)^{2})

((55)^{2}=55\times55 = 3025) [ \begin{align*} y&=-0.32\times3025+20.61\times55 + 5\ \end{align*} ]

Step3: Calculate (-0.32\times3025) and (20.61\times55)

(-0.32\times3025=- 968), (20.61\times55=(20 + 0.61)\times55=20\times55+0.61\times55=1100+33.55 = 1133.55) [ \begin{align*} y&=-968+1133.55 + 5\ \end{align*} ]

Step4: Calculate the sum

(y=-968+1133.55+5=170.55)

Step5: Round to the nearest whole number

Rounding (170.55) to the nearest whole number. Since the decimal part (0.55\geqslant0.5), we round up.

Answer:

(171)