Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
The time taken by the rock to reach the lake below is 5.123 sec
t= 5.123 sec
What is quadratic equation?
A quadratic equation is an algebraic expression of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2} +bx+c=0[/tex] where a, b are the coefficients, x is the variable, and c is the constant term.
It is given that,
H= [tex]-16t^{2} +32t+256[/tex], which represent the height of the rock
Also, we have given that the height of the cliff is 256 feet.
Now to find the time taken by the rock, take H=0
[tex]-16t^{2} +32t+256[/tex]=0
[tex]-16(t^{2} -2t-16) = 0[/tex]
[tex]t^{2} -2t-16 = 0[/tex]
- Solve the above quadratic equation using Discriminant Method
[tex]t= \frac{-(b)\pm\sqrt{(b)^{2}- 4 *a*c } )}{2*a}[/tex]
From above equation, a=1, b=-2, c=-16
So,
[tex]t= \frac{-(-2)\pm\sqrt{(-2)^{2}- 4 *1*(-16) } )}{2*1}[/tex]
[tex]t= \frac{2\pm\sqrt{(4+64 } )}{2}[/tex]
[tex]t= \frac{2\pm\sqrt{(68 } )}{2}[/tex]
There will be two value one with positive [tex]t= -2+\sqrt{(68 } )[/tex] and another with negative [tex]t= -2-\sqrt{(68 } )[/tex]
We will neglect negative value because time can't be negative.
[tex]t= \frac{2+\sqrt{(68 } )}{2}[/tex]
[tex]t= \frac{2+8.246}{2}[/tex]
[tex]t= \frac{10.246}{2}[/tex]
t= 5.123 sec
The time taken by the rock to reach the lake below is t= 5.123 sec
Learn more about quadratic Equation here:
https://brainly.com/question/2263981
#SPJ1
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.