A ball is launched into the air from a platform 14 feet off the ground with an initial velocity, v0, of 64 feet per second. The height H(t) of the ball at any time, t can be modeled by the formulae H(t)=-16t^2+v0t+h0 When will the ball hit the ground rounded to the nearest hundredth?At what time will the ball have a height of 62 feet during the descent?

a) After 4.21 seconds

b) t=1 or t=2 seconds

Step-by-step explanation:

The height of the ball at anytime t, is modeled  by:

, where feet per second and feet.

We substitute the initial velocity and the initial height to obtain:

When the ball hit the ground, then the heigth becomes zero.

We equate the function to zero to obtain:

We use the quadratic formula to obtain:

where a=-16, b=64 and c=14.

We substitute to obtain:

This simplifies to:

or

We discard the negatively, value to get t=-4.21 seconds.

The ball will hit the ground after 4.21 seconds.

To find the  time  that the ball have a height of 62 feet during the descent, we set H(t)=62 and solve for t.

Divide through by 16 to get:

There the ball will first have a height of 62 at t=1 seconds and the second time is t=3 seconds

3x^3-x^2+6x-9

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: