Answer:
Part 4) The number of meters by which each dimension must be increased is [tex]2\ m[/tex]
Part 5) The ball hit the ground at [tex]t=9\ sec[/tex]
Step-by-step explanation:
Part 4) we know that
The area of the original Joe's garden is equal to
[tex]A=6*4=24\ m^{2}[/tex]
Increasing the length and the width with the same amount to double the area
we have
Let
x------> the number of meters by which each dimension must be increased
[tex]24*2=(x+6)(x+4)\\48=x^{2}+4x+6x+24\\x^{2}+10x-24=0[/tex]
Using a graphing tool solve the quadratic equation
see the attached figure
The solution is [tex]x=2\ m[/tex]
Part 5) we have
[tex]h=-144t-16t^{2}[/tex]
we know that
To calculate after how many seconds will the ball hit the ground, find the t-intercept of the function
Remember that
The t-intercept of the function h(t) is the value of t when the value of h(t) is equal to zero
so
equate h(t) to zero
[tex]-144t-16t^{2}=0[/tex]
Using a graphing tool
Find the t-intercept
see the attached figure
The solution is [tex]t=9\ sec[/tex]
