A ball is thrown from an initial height of 5 feet with an initial upward velocity of 23/fts. The ball's height h (in feet) after tseconds is given by the following. h=5+23t - 16t2Find all values of t for which the ball's height is 13 feet.

x₂ = 0,59 sec

x₁  = 0,8475 sec

Step-by-step explanation:

h(t) = -16*t² + 23*t + 5

h(t) is the trajectory of the ball, the curve is a parable opens downwards

if we force h(t) = 13 feet, we get;

h(t) =  13

13 =  -16*t² + 23*t + 5   ⇒  -16*t² + 23*t - 8 = 0

or    16*t² - 23*t + 8 = 0

The above expression is a second degree equation, we proceed to solve it for t

x =  [ 23  ±  √529 - 512 ] /32

x = [ 23 ± √17 ] /32

x₁ =  [ 23 + 4,12 ]/32    ⇒  x₁  = 27,12/32    ⇒   x₁  = 0,8475 sec

x₂ =   [ 23 - 4,12 ]/32   ⇒  x₂ = 18,88 /32   ⇒   x₂ = 0,59 sec

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

answer:  

step-by-step explanation:

odd numbers are only divisible by 1 and itself.

even numbers are divisible by more than 1 and itself.

for example 6 is even because it is divisible by more than 1 and its self. 1 x 6= 6 ; 2 x 3= 6

and 7 is odd because only 7 x 1 equals seveb