Value of 't' for which height of the given quadratic equation is 14 feet is equals to t = 0.64seconds or t = 1.17seconds.
What is quadratic equation?
" Quadratic equation is defined as algebraic expression shows the relation between the variables with highest exponent equals to 2."
Formula used
For Quadratic equation
[tex]ax^{2} + bx + c= 0[/tex]
Roots are =[tex]\frac{-b \± \sqrt{D} }{2a}[/tex]
[tex]D = b^{2} -4ac[/tex]
D > 0 roots are real and distinct.
According to the question,
't' represents the time in seconds
'h' represents the height in feet = 14feet
Given quadratic equation is,
[tex]h = 2+ 29t -16t^{2}[/tex]
Substitute the value of 'h' in the given quadratic equation we get,
[tex]14 = 2+ 29t -16t^{2}\\\\\implies 16t^{2} -29t +12 =0[/tex]
Substitute the value in the discriminant formula we get,
[tex]D = (-29)^{2} - 4(16)(12)\\ \\\implies D = 73 > 0[/tex]
Quadratic equation has real and distinct roots.
Substitute the value in the formula to get the value of 't' ,
[tex]t = \frac{-(-29) \±\sqrt{73} }{2(16)} \\\\\implies t = \frac{29 \±8.54}{32} \\\\\implies t = 0.639 or 1.173[/tex]
t= 0.64 seconds or t = 1.17 seconds ( nearest hundredth)
Hence, value of 't' for which height of the given quadratic equation is 14 feet is equals to t = 0.64seconds or t = 1.17seconds.
Learn more about quadratic equation here
https://brainly.com/question/2263981
#SPJ3
