Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 2.1, Problem 65E

To determine

To graph:The path of th football.

Expert Solution

Explanation of Solution

Given:

The equation of the path of football is $y=−162025x2+95x+32$

Formula/ concept used:

The graph is drawn using graphing calculator.

Graph:

The graph for function (trajectory) is shown in Figure-1 here.

Precalculus with Limits: A Graphing Approach, Chapter 2.1, Problem 65E

Interpretation of Graph:

The graph of path of football is a parabola with vertex $(113.906,104.016)$ .

To determine

The height of the football when it is punted.

Expert Solution

Answer to Problem 65E

The height of football when it is punted is $1.5$ feet.

Explanation of Solution

Given:

The equation of path of football is $y=−162025x2+95x+32$ .

Concept used:

The initial height when football is punted is obtained when $x=0$ .

Calculations:

The equation of path of football is $y(x)=−162025x2+95x+32$ where x and y (in feet) are the horizontal and vertical position of the football respectively.

Therefore, the initial vertical position or the height of football when it is punted is $y(0)=−162025(0)2+95(0)+32=1.5$ feet.

Conclusion:

The height of football when it is punted is $1.5$ feet.

To determine

The maximum height of the football.

Expert Solution

Answer to Problem 65E

The maximum height of the football is $104.016$ feet.

Explanation of Solution

Given:

The equation of path of football in part (a)

Conceptused:

When the parabola opens downward its maxima occurs at the vertex and if $(h,k)$ be the vertex of the parabola $y(x)=−ax2+bx+c$ then vertex is $(h,ymax.)$ , i.e. $ymax.=k$ .

Calculations:

From the graph in part (a), the vertex of the parabola represented by the equation of the path of football $y(x)=−162025x2+95x+32$ is $(113.906,104.016)=(h,ymax.)$ .

Thus, $ymax.=104.016$ .

The maximum height of the football is $104.016$ feet.

Conclusion:

The maximum height of the football is $104.016$ feet.

To determine

The horizontal distance the football strike the ground

Expert Solution

Answer to Problem 65E

The football strikes the ground at horizontal distance $x=228.643$ feet from the initial point.

Explanation of Solution

Given:

The equation of path of football in part (a).

Formula used:

The football strikes the ground when its vertical height is zero.

Calculations:

The equation of path of footballis $y(x)=−162025x2+95x+32$ .

The football will on the ground when $y(x)=0$ .

From the graph in part (a) we see that $y(x)=0$ when $x=228.643$

Thus,the football strikes the ground at horizontal distance $x=228.643$ feet from the initial point.

Conclusion:

The football strikes the ground at horizontal distance $x=228.643$ feet from the initial point.

To determine

To compare: The results from parts (b), (c), and (d).

Expert Solution

Answer to Problem 65E

The results obtained parts (b), (c), and (d) are identical.

Explanation of Solution

Given:

The results obtained in parts (b), (c), and (d).

Explanations:

In parts (b), (c), and (d) we find that the area $Amax.=2500$ sq. ft. when $x=25$ and $y=50$ ft.

Thus, the results obtained parts (b), (c), and (d) are identical.

Chapter 2.1, Problem 64E

Chapter 2.1, Problem 66E

Chapter 2 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45E Ch. 2.6 - Prob. 46E Ch. 2.6 - Prob. 47E Ch. 2.6 - Prob. 48E Ch. 2.6 - Prob. 49E Ch. 2.6 - Prob. 50E Ch. 2.6 - Prob. 51E Ch. 2.6 - Prob. 52E Ch. 2.6 - Prob. 53E Ch. 2.6 - Prob. 54E Ch. 2.6 - Prob. 55E Ch. 2.6 - Prob. 56E Ch. 2.6 - Prob. 57E Ch. 2.6 - Prob. 58E Ch. 2.6 - Prob. 59E Ch. 2.6 - Prob. 60E Ch. 2.6 - Prob. 61E Ch. 2.6 - Prob. 62E Ch. 2.6 - Prob. 63E Ch. 2.6 - Prob. 64E Ch. 2.7 - Prob. 1E Ch. 2.7 - Prob. 2E Ch. 2.7 - Prob. 3E Ch. 2.7 - Prob. 4E Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Prob. 81E Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Prob. 87E Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2.7 - Prob. 91E Ch. 2.7 - Prob. 92E Ch. 2.7 - Prob. 93E Ch. 2.7 - Prob. 94E Ch. 2.7 - Prob. 95E Ch. 2.7 - Prob. 96E Ch. 2.7 - Prob. 97E Ch. 2.7 - Prob. 98E Ch. 2.7 - Prob. 99E Ch. 2.7 - Prob. 100E Ch. 2.7 - Prob. 101E Ch. 2.7 - Prob. 102E Ch. 2.7 - Prob. 103E Ch. 2.7 - Prob. 104E Ch. 2.7 - Prob. 105E Ch. 2.7 - Prob. 106E Ch. 2.7 - Prob. 107E Ch. 2.8 - Prob. 1E Ch. 2.8 - Prob. 2E Ch. 2.8 - Prob. 3E Ch. 2.8 - Prob. 4E Ch. 2.8 - Prob. 5E Ch. 2.8 - Prob. 6E Ch. 2.8 - Prob. 7E Ch. 2.8 - Prob. 8E Ch. 2.8 - Prob. 9E Ch. 2.8 - Prob. 10E Ch. 2.8 - Prob. 11E Ch. 2.8 - Prob. 12E Ch. 2.8 - Prob. 13E Ch. 2.8 - Prob. 14E Ch. 2.8 - Prob. 15E Ch. 2.8 - Prob. 16E Ch. 2.8 - Prob. 17E Ch. 2.8 - Prob. 18E Ch. 2.8 - Prob. 19E Ch. 2.8 - Prob. 20E Ch. 2.8 - Prob. 21E Ch. 2.8 - Prob. 22E Ch. 2.8 - Prob. 23E Ch. 2.8 - Prob. 24E Ch. 2.8 - Prob. 25E Ch. 2.8 - Prob. 26E Ch. 2.8 - Prob. 27E Ch. 2.8 - Prob. 28E Ch. 2.8 - Prob. 29E Ch. 2.8 - Prob. 30E Ch. 2.8 - Prob. 31E Ch. 2.8 - Prob. 32E Ch. 2.8 - Prob. 33E Ch. 2.8 - Prob. 34E Ch. 2.8 - Prob. 35E Ch. 2.8 - Prob. 36E Ch. 2.8 - Prob. 37E Ch. 2.8 - Prob. 38E Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 71RE Ch. 2 - Prob. 72RE Ch. 2 - Prob. 73RE Ch. 2 - Prob. 74RE Ch. 2 - Prob. 75RE Ch. 2 - Prob. 76RE Ch. 2 - Prob. 77RE Ch. 2 - Prob. 78RE Ch. 2 - Prob. 79RE Ch. 2 - Prob. 80RE Ch. 2 - Prob. 81RE Ch. 2 - Prob. 82RE Ch. 2 - Prob. 83RE Ch. 2 - Prob. 84RE Ch. 2 - Prob. 85RE Ch. 2 - Prob. 86RE Ch. 2 - Prob. 87RE Ch. 2 - Prob. 88RE Ch. 2 - Prob. 89RE Ch. 2 - Prob. 90RE Ch. 2 - Prob. 91RE Ch. 2 - Prob. 92RE Ch. 2 - Prob. 93RE Ch. 2 - Prob. 94RE Ch. 2 - Prob. 95RE Ch. 2 - Prob. 96RE Ch. 2 - Prob. 97RE Ch. 2 - Prob. 98RE Ch. 2 - Prob. 99RE Ch. 2 - Prob. 100RE Ch. 2 - Prob. 101RE Ch. 2 - Prob. 102RE Ch. 2 - Prob. 103RE Ch. 2 - Prob. 104RE Ch. 2 - Prob. 105RE Ch. 2 - Prob. 106RE Ch. 2 - Prob. 107RE Ch. 2 - Prob. 108RE Ch. 2 - Prob. 109RE Ch. 2 - Prob. 110RE Ch. 2 - Prob. 111RE Ch. 2 - Prob. 112RE Ch. 2 - Prob. 113RE Ch. 2 - Prob. 114RE Ch. 2 - Prob. 115RE Ch. 2 - Prob. 116RE Ch. 2 - Prob. 117RE Ch. 2 - Prob. 118RE Ch. 2 - Prob. 119RE Ch. 2 - Prob. 120RE Ch. 2 - Prob. 121RE Ch. 2 - Prob. 122RE Ch. 2 - Prob. 123RE Ch. 2 - Prob. 124RE Ch. 2 - Prob. 125RE Ch. 2 - Prob. 126RE Ch. 2 - Prob. 127RE Ch. 2 - Prob. 128RE Ch. 2 - Prob. 129RE Ch. 2 - Prob. 130RE Ch. 2 - Prob. 131RE Ch. 2 - Prob. 132RE Ch. 2 - Prob. 133RE Ch. 2 - Prob. 134RE Ch. 2 - Prob. 135RE Ch. 2 - Prob. 136RE Ch. 2 - Prob. 137RE Ch. 2 - Prob. 138RE Ch. 2 - Prob. 139RE Ch. 2 - Prob. 140RE Ch. 2 - Prob. 141RE Ch. 2 - Prob. 142RE Ch. 2 - Prob. 143RE Ch. 2 - Prob. 144RE Ch. 2 - Prob. 145RE Ch. 2 - Prob. 146RE Ch. 2 - Prob. 147RE Ch. 2 - Prob. 148RE Ch. 2 - Prob. 149RE Ch. 2 - Prob. 150RE Ch. 2 - Prob. 151RE Ch. 2 - Prob. 152RE Ch. 2 - Prob. 153RE Ch. 2 - Prob. 154RE Ch. 2 - Prob. 155RE Ch. 2 - Prob. 156RE Ch. 2 - Prob. 157RE Ch. 2 - Prob. 158RE Ch. 2 - Prob. 159RE Ch. 2 - Prob. 160RE Ch. 2 - Prob. 161RE Ch. 2 - Prob. 162RE Ch. 2 - Prob. 163RE Ch. 2 - Prob. 164RE Ch. 2 - Prob. 165RE Ch. 2 - Prob. 166RE Ch. 2 - Prob. 167RE Ch. 2 - Prob. 168RE Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 17CT Ch. 2 - Prob. 18CT Ch. 2 - Prob. 19CT Ch. 2 - Prob. 20CT Ch. 2 - Prob. 21CT Ch. 2 - Prob. 22CT Ch. 2 - Prob. 23CT

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