Question

The table below shows the distance that a baseball travels after being hit at various angles.Angle (degrees)Distance (feet)10115.615157.220189.224220.830253.834269.240284.845285.048277.450269.258244.260231.464180.4(a) Use a graphing calculator or spreadsheet program to find a quadratic model that best fits this data, using the angle as t and distance as Pt. Round each coefficient to two decimal places.Pt = (b) Based on this model, what distance is expected for a ball hit at 55 degrees? Round your answer to the nearest tenth of a foot. feet(c) What distance is expected for a ball hit at 75 degrees? Round your answer to the nearest tenth of a foot. feet(d) Which of the two previous predictions is likely to be more reliable?75 degrees55 degrees(e) What is the smallest angle that you expect to yield a distance of 200 feet? Round your answer to the nearest tenth of a degree. degrees

Answer 1

using a quadratic regression calculator

Please wait a minute to calculate the model

we have

Pt=A+Bt+Ct^2

A=-21.90

B=14.52

C=-0.17

therefore

Part a

Pt=-0.17t^2+14.52t-21.90

Part b

Based on this model, what distance is expected for a ball hit at 55 degrees? Round your answer to the nearest tenth of a foot

For t=55 degrees

Pt=-0.17(55)^2+14.52(55)-21.90

Pt=262.5 ft

Part c

What distance is expected for a ball hit at 75 degrees? Round your answer to the nearest tenth of a foot

For t=75 degrees

Pt=-0.17(75)^2+14.52(75)-21.90

Pt=110.9 ft

Part d

Which of the two previous predictions is likely to be more reliable?

the answer is 55 degrees

Part e

What is the smallest angle that you expect to yield a distance of 200 feet? Round your answer to the nearest tenth of a degree

we have

For Pt=200 ft

200=-0.17t^2+14.52t-21.90

-0.17t^2+14.52t-221.90=0

solve the quadratic equation

the solutions are

t=19.9 degrees and t=65.5 degrees

the smallest angle is 19.9 degrees