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5. During a game of golf, Kayley hits her ball out of a sand trap. The height of the golf ball is modeled by the
equation h=-16r² + 20 - 4, where h is the height in feet and is the time in seconds since the ball was hit.
Find how long it takes Kayley's golf ball to hit the ground.
a. Write the equation that you are trying to solve.
b. Solve the equation by factoring.

Respuesta :

semsee45

Answer:

(a) [tex]\sf -16r^2+20r-4=0[/tex]

(b)  r = 1,  r = 1/4

Step-by-step explanation:

Given equation:   [tex]\sf h=-16r^2+20r-4[/tex]

where:

  • h = height (in feet)
  • t = time (in seconds)

Question (a)

The ball will hit the ground when h = 0

[tex]\sf \implies-16r^2+20r-4=0[/tex]

Question (b)

To factor [tex]\sf -16r^2+20r-4=0[/tex]

Divide both sides by 4:

[tex]\sf \implies-4r^2+5r-1=0[/tex]

Swap signs:

[tex]\sf \implies 4r^2-5r+1=0[/tex]

Split middle term:

[tex]\sf \implies 4r^2-4r-r+1=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\sf \implies 4r(r-1)-(r-1)=0[/tex]

Factor out common term (r - 1):

[tex]\sf \implies (4r-1)(r-1)=0[/tex]

Therefore:

[tex]\sf \implies (4r-1)=0 \implies r=\dfrac14[/tex]

[tex]\sf \implies (r-1)=0 \implies r=1[/tex]

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