A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation f(t)=3+5t−16t^2 f(t)=3+5t-16t^2 , where t t is measured in seconds since the ball was thrown. Find the solutions to the equation 0=3+5t−16t^2 0=3+5t-16t^2 using the quadratic formula. Show your work! What do the solutions tell us about the tennis ball?

t = -0.304 and 0.62 secs

the ball was thrown 0.62 secs later

Step-by-step explanation:

Given the quadratic equation

0=3+5t−16t^2

We are to factorize it using the formula;

The formula is expressed as

t = -b±√b²-4ac/2a

From the given expression

a = -16 b = 5 c = 3

Substitute

t = -5 ±√5²-4(-16)(3)/2(-16)

t = -5 ±√25+192/-32

t=  -5 ±√217/-32

t= -5 ±14.73/-32

t = -5+14.73/-32 and t = -5-14.73/-32

t = -9.73/32 and -19.73/-32

t = -0.304 and 0.62 secs

Hence the ball was thrown 0.62 secs later

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b