Question

PLEASEE HELP!!


How long would it take a ball to reach the ground if the height was modeled by
h(t) = -4t2 + 12t + 100, where t is the time in seconds?
A) about 6.7 seconds
B) about 7.6 seconds
C) about 3.7 seconds
D) about 5.2 seconds

Answer 1

Answer:

A)t=6.7

Step-by-step explanation:

to understand this

you need to know about:

• quadratic equation
• quadratic equation word problems
• solving quadratic

given:

h(t) = -4t² + 12t + 100

to solve:

t

tips and formulas:

• the Ball will hit the ground when the height is 0
• solving quadratics using quadratic formula
• PEMDAS

let's solve:

$step - 1 : \: define$

$- 4 {t}^{2} + 12t + 100 = 0$

$step - 2 : \\ divide \: both \: sides \: by \: - 4$

${t}^{2} - 3t - 25 = 0$

$step - 3 : \\ solve \: the \: quadratic$

$formula : \\ x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a}$

$define \: a ,b \: and \: c \\ which \: are \: 1, - 3 \: and \: - 25 \: respectively$

$t = \frac{ - ( - 3)± \sqrt{ {( - 3)}^{2} - 4.1. - 25 } }{2.1}$

$t = \frac{ 3± \sqrt{ 9 + 100} }{2}$

$t = \frac{3 + \sqrt{ 109 } }{2}$

$t = \frac{3 - \sqrt{ 109 } }{2}$

$t = 6.7 \\ t = - 3.7$

$as \: we \: know \: time \: cannot \: be \: negative$

$\huge \therefore \: t = 6.7$