Question

Need help with question 3. 27 points

Answer 1

Answer:

3 seconds

Step-by-step explanation:

Our function is

h(t) = -16t²+24t+72

To find how long it takes the roll to hit the ground, we must find the roots of this equation.  We first set the function equal to 0:

0 = -16t²+24t+72

Next we factor out the GCF.  The GCF of -16, 24 and 72 is 8:

0 = 8(-2t²+3t+9)

To factor the remaining trinomial, we find factors of -2(9) = -18 that sum to 3:

-18 = -1(18) or 1(-18); these do not sum to 3.

-18 = -2(9) or 2(-9); these do not sum to 3.

-18 = -3(6) or 3(-6); -3 and 6 sum to 3.  We will split 3t into -3t and 6t:

0 = 8(-2t²-3t+6t+9)

Group together the first two terms and the second two terms:

0 = 8((-2t²-3t)+(6t+9))

Factor out the GCF of each group.  The GCF of the first group is -t:

0 = 8(-t(2t+3)+(6t+9))

The GCF of the second group is 3:

0 = 8(-t(2t+3)+3(2t+3))

The common factor is now 2t+3:

0 = 8(2t+3)(-t+3)

Using the zero product property, either 2t+3 = 0 or -t+3 = 0:

2t+3 = 0

Subtract 3 from each side:

2t+3-3 = 0-3

2t = -3

Divide both sides by 2:

2t/2 = -3/2

t = -1.5

-t+3 = 0

Subtract 3 from each side:

-t+3-3 = 0-3

-t = -3

Divide both sides by -1:-

-t/-1 = -3/-1

t = 3

This means the roots are at t = -1.5 and t = 3.

This means the toilet paper hits the ground at -1.5 seconds and 3 seconds.  Since we do not have negative time, the correct answer is 3 seconds.

Answer 2

Answer:

your answer would be -10.25

Step-by-step explanation:

You just divide the two numbers and boom there's your answer

I hope this helps

-Scorpion