Functions are used to represent equations and graphs
- The superhero will be able to leap over the building
- The support should be placed 48 feet from the edge
- Joe will not be able to stand up in the igloo
- Joe will be able to lay down in the igloo
Question 13: How to determine if the superhero will make it to the building
The function is given as:
[tex]f(x) = -16x^2 + 200x[/tex]
Differentiate the function
[tex]f'(x) = -32x + 200[/tex]
Set to 0
[tex]-32x + 200 =0[/tex]
So, we have:
[tex]-32x =-200[/tex]
Solve for x
[tex]x =6.25[/tex]
Calculate f(6.25)
[tex]f(x) = -16x^2 + 200x[/tex]
[tex]f(6.25) = -16 * 6.25^2 + 200 * 6.25[/tex]
[tex]f(6.25) = 625[/tex]
The above means that, the superhero reached a height of 625 feet.
625 is greater than 612.
Hence, the superhero will be able to leap over the building
Question 14: How to determine the distance from the edge
The function is given as:
[tex]f(x) = -0.03x^2 + 2.4x[/tex]
Differentiate
[tex]f'(x) = -0.06x + 2.4[/tex]
Set to 0
[tex]-0.06x + 2.4 = 0[/tex]
Subtract 2.4 from both sides
[tex]-0.06x = -2.4[/tex]
Solve for x
[tex]x = 40[/tex]
Calculate f(40)
[tex]f(x) = -0.03x^2 + 2.4x[/tex]
[tex]f(40) = -0.03*40^2 + 2.4*40[/tex]
[tex]f(40) = 48[/tex]
This means that, the support should be placed 48 feet from the edge
Question 15: Will Joe be able to stand up?
In (14), the maximum height is 48 feet.
Joe's height (70 feet) is greater than 48.
This means that, Joe will not be able to stand up in the igloo
Question 15: Will Joe be able to lay down?
In (14), the midpoint is 40 feet.
This means that the length of the igloo is 80 feet (i.e. 2 * 40 feet)
Joe's height (70 feet) is less than 80.
This means that, Joe will be able to lay down in the igloo
Read more about quadratic functions at:
https://brainly.com/question/8952707
