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3 years ago

6

A golf ball is hit from the ground, and its height in feet above the ground is modeled by the function h(t) = -16t^2 + 180t, whe

re t represents the time in seconds after the ball is hit. How long is the ball in the air

2 answers:

Scilla [17]3 years ago

6 0

Answer:

the answer is 342 for plato. trust me i got it right

Step-by-step explanation:

Aloiza [94]3 years ago

4 0

The time that the ball is in the air is 2x the time that it takes to reach the maximum value.

In order to find the time at the max value you use the equation -b/2a where b is the value attached to the t and a is the value attached to t^2.

therefore, the time at the max value is -180/(2)(-16)=5.625 seconds

Total time= (5.625)(2)=11.25

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1. S(–4, –4), P(4, –2), A(6, 6) and Z(–2, 4) a) Apply the distance formula for each side to determine whether SPAZ is equilatera

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a) SPAZ is equilateral.

b) Diagonals SA and PZ are perpendicular to each other.

c) Diagonals SA and PZ bisect each other.

Step-by-step explanation:

At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.

a) If figure is equilateral, then SP = PA = AZ = ZS:

$SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}$

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$PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}$

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$AZ \approx 8.246$

$ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}$

$ZS \approx 8.246$

Therefore, SPAZ is equilateral.

b) We use the slope formula to determine the inclination of diagonals SA and PZ:

$m_{SA} = \frac{6-(-4)}{6-(-4)}$

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Since $m_{SA}\cdot m_{PZ} = -1$ , diagonals SA and PZ are perpendicular to each other.

c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:

$M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)$

$M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)$

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$M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)$

$M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)$

$M_{PZ} = (2,-1)+(-1,2)$

$M_{PZ} = (1,1)$

Then, the diagonals SA and PZ bisect each other.

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