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3 years ago

Tom throws a Frisbee into the air from a height of 4 feet with

Mathematics

1 answer:

siniylev [52]3 years ago

5 0

Answer:

68 feet

Step-by-step explanation:

Vertical motion model:

h = -16t² + vt + s

Given v = 64 and s = 4:

h = -16t² + 64t + 4

This is a parabola. The maximum of a parabola is at the vertex.

For y = ax² + bx + c, the vertex is at x = -b/(2a).

Therefore, the time to reach the maximum height is:

t = -64 / (2 × -16)

t = 2

And the maximum height is:

h = -16(2)² + 64(2) + 4

h = 68

So the Frisbee reaches a maximum height of 68 feet.

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2 years ago

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Recall that

sin(a + b) = sin(a) cos(b) + cos(a) sin(b)

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2 years ago

A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

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Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

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The number of bacteria after 1 hour would approximate be 27,569 bacteria

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

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After about 103 minutes, there will be 50,000 bacteria

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