The rocket exceed the height of 500 ft in 1.46 seconds or 8.43 seconds.
Standard form of the quadratic equation in the variable x is an equation of the form a[tex]x^{2}[/tex] + bx + c = 0, where a, b, c are real numbers and a ≠ 0. Any equation of the form P(x) = 0, Where P(x) is a polynomial of degree 2, is a quadratic equation.
Given equation of height is:
h(t)= -[tex]16t^{2} +160t+300[/tex]
Now, the exceeded to 500 feet.
So,
-[tex]16t^{2} +160t+300[/tex]=500
16[tex]t^{2}[/tex] -160 t +200=0
Now, solve for t: a=16, b= -160, c= 200
D= [tex]\sqrt{b^{2}-4ac }[/tex]
= [tex]\sqrt{(-160)^{2}-4*16*200 }[/tex]
= [tex]\sqrt{12800 }[/tex]
= 80√2
As D>0 then,
x= [tex]\frac{-b\pm \sqrt{b^{2}-4ac }}{2a}[/tex]
x= (160 ±80√2)/32
x= (160 +80√2)/32 or x= (160 -80√2)/32
So, x= 8.43 and x=1.46
Learn more about quadratic equation here:
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