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A gymnast, who can stretch her arms up to reach 6 feet, jumps straight up on a trampoline. The height of
her feet above the trampoline can be modeled by the equation h =-16x2 + 12x, where x is the time in
seconds after her jump.
Do the gymnast's hands reach a height of 11 feet above the trampoline? Use the discriminant to explain.
(Hint: Since h = height of feet, you must use the difference between the heights of the hands and feet.)
The value of the discriminant is
The discriminant is a (select) number. So, there
(select) real solutions for this height. The gymnast hands (select) reach a height of 11 feet.

Answer :

Answer:

The discriminant of the equation is less than zero. The gymnast's hands do not reach a height of 11 feet

Step-by-step explanation:

The gymnast's hands does not reach a height of 11 feet above the trampoline.

What is Quadratic Equation?

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is a[tex]x^{2}[/tex] + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

It is given that ,

h= [tex]-16x^{2} +12x[/tex]

11-6= [tex]-16x^{2} +12x[/tex]

5 = [tex]-16x^{2} +12x[/tex]

[tex]-16x^{2} +12x[/tex] -5=0

Comparing the above equation with the standard form of quadratic equation [tex]ax^{2} +bx+c=0\\[/tex]

we get ; a=-16, b=12, c=-5

Using Discriminant method

D= [tex]\sqrt[]{b^{2} - 4*a*c}[/tex]

  = [tex]\sqrt[]{(12)^{2} - 4* (-16)*(-5)}[/tex]

  = [tex]\sqrt[]{144-320}[/tex]

  = [tex]\sqrt[]{-176}[/tex]

Hence D<0, which means there is no real value.

So, the gymnast's hands does not reach a height of 11 feet above the trampoline.

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