Chapter 1.9, Problem 58E

Solution

a.

To Sketch: The given equations in the graphing calculator.

Given:

The equations are,

  $y=7.51x^2-16.4x+35.0$

  $y=100$

Graph:

The graph of the equations $y=7.51x^2-16.4x+35.0$ and $y=100$ is shown below.

  

b.

To Sketch: The given equations in the graphing calculator according to the given scaling.

Given:

The equations are,

  $y=7.51x^2-16.4x+35.0$

  $y=100$

The scaling are $0\le x\le 9$ and $0\le y\le 300$

Graph:

The graph of the equations $y=7.51x^2-16.4x+35.0$ and $y=100$ for the scaling $0\le x\le 9$ and $0\le y\le 300$ is:

  

c.

To Determine: The point where the graphs are intersecting each other by using the intersect feature.

The point where the graphs are intersecting each other is $\left(4.2,102.5\right)$ .

Given:

The equations are,

  $y=7.51x^2-16.4x+35.0$

  $y=100$

Graph:

Find the intersecting points of the two graphs of the functions $y=7.51x^2-16.4x+35.0$ and $y=100$

are as follows:

  

Interpretation:

From, the above graph it can be seen that the graph of the equations $y=7.51x^2-16.4x+35.0$ and $y=100$ intersecting each other at the point $\left(4.2,102.5\right)$ .

d.

To Determine: The years in which the number of competing teams greater than $100$ .

The years in which the number of competing teams greater than $100$ is after $4$ years.

Given:

The equations are,

  $y=7.51x^2-16.4x+35.0$

  $y=100$

Graph:

Find the years in which the number of competing teams greater than $100$:

  

Interpretation:

Here $x-$ axis denoted the years and $y-$ axes denoted the number of competing teams. So, the curve reaches above $100$ when $x-$ axis is $4.2$ which is approximately $4.$ Hence, after $4$ years the number of competing teams greater than $100$ .