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3 years ago

Does anybody know how to do this or at least part of it anything would really help!!

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

So the given equation is h= -5t^2+40t

the first question asks when it will be 75 meters above the ground. So plug in 75 for h and find t

75= -5t^2+40t

start by dividing everything by 5

15= -x^2 + 8x

then you can add x squared to both sides and subtract 8x

x^2 - 8x + 15 =0

then you can plug it into the quadratic formula, which is a pain to type so I did it on paper.

x = 5 or 3

so it will be 75 meters above the ground at 3 seconds and 5 seconds

Rewriting the equation

ok so I accidentally already factored it when I divided everything by 5...

I believe the answer here is x^2 - 8x + 15 =0

The meaning of the x intercepts is when h=0 or the object is 0 meters above the ground (basically when it starts and when it ends)

the maximum height is greater than 75 because it gets to 75 meters 3 seconds after it is thrown, and continues going higher before it comes back to 75 two seconds later.

The object is airborne for 8 seconds because the second x intercept is at (8,0)

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A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will

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3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

$\frac{dy}{dt} = ky(1-y)$

Solving the differential equation,

$y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}$

The total number of inhabitants of the town = 2000

The number of people that heard the rumor = 160

At 8 AM, let t = 0,

$y(0) = \frac{160}{2000}$

= 0.08

By noon, half of the town as heard the rumor.

Then,

$y(4) = \frac{1}{2}$

Therefore,

$\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}$

$\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}$

$0.08 + 0.92e^{-4k} = 0.16$

$0.92e^{-4k} = 0.16 - 0.08$

$0.92e^{-4k} = 0.08$

$e^{-4k} = \frac {0.08}{0.92}$

$k = - \frac{1}{4} In(\frac {0.08}{0.92})$

k ≈ 0.06106

Calculating time, t when y(t) = 90%

⇒ y(t) = 0.9

$\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9$

$0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}$

$0.08 + 0.92e^{-0.06106t} = 0.089$

$0.92e^{-0.06106t} = 0.089 - 0.08$

$0.92e^{-0.06106t} = 0.0089$

$t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})$

t = 7.59 hours

⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

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