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Fiesta28 [93]
3 years ago
5

Please help. no links

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
7 0

Answer:

144

Step-by-step explanation:

20×12=240

add 4 to 20 and 12

makes a new rectangle 24×16

24×16=384

384-240=144

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Read 2 more answers
2. When Joey dives off a diving board, the equation of his pathway can be modeled by h = -16- + 15 + 12.
Sergeu [11.5K]

Answer:

a) The maximum height is approx 15.5 unit.

b) The time it will take for Joey to reach the water is 1.45 hour.

Step-by-step explanation:

Given : When Joey dives off a diving board, the equation of his pathway can be modeled by h(t)= -16t^2+15t + 12

To find : a) Find Joey's maximum height.

b) Find the time it will take for Joey to reach the water.

Solution :

Modeled  h(t)= -16t^2+15t + 12 ....(1)

a) To find maximum height

Derivate (1) w.r.t. t,

h'= -32t+15

For critical point put h'=0,

-32t+15=0

t=\frac{15}{32}

t=0.46875

Derivate again w.r.t. t,

h''= -32

It is maximum at t=0.46875.

Substitute t in equation (1),

h(0.46875)= -16(0.46875)^2+15(0.46875)+12

h(0.46875)= -3.515625+7.03125+12

h(0.46875)= 15.515625

The maximum height is approx 15.5 unit.

b) To find the time it will take for Joey to reach the water.

Put h=0 in equation (1),

-16t^2+15t + 12=0

Apply quadratic formula, x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Here, a=-16 , b=15, c=12

t=\frac{-15\pm\sqrt{(15)^2-4(-16)(12)}}{2(-16)}

t=\frac{-15\pm\sqrt{225+768}}{-32}

t=\frac{-15\pm\sqrt{993}}{-32}

t=\frac{-15+\sqrt{993}}{-32},\frac{-15-\sqrt{993}}{-32}

t=−0.515,1.453

Reject negative value.

The time is t=1.45.

The time it will take for Joey to reach the water is 1.45 hour.

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