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3 years ago

What can be concluded about a line that passes through the points (1-2) and (4-2) Check all that apply.

Mathematics

1 answer:

Thepotemich [5.8K]3 years ago

3 0

The equation of the line is y-2

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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

QveST [7]

Answer:

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

7 0

3 years ago

the volume of a sphere is 950 cubic inches. Use the formula for the volume of a sphere to find the radius to the nearest tenth o

pashok25 [27]

Volume of a sphere=(4/3)πr³ ⇒r=∛(3v/4π)
volume of a sphere=950 in³
Therefore:
r=∛(3*950 in³/4π)=6.09834... in≈6.1 in

answer: radius=6.1 in

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3 years ago

Plz help.........................

Salsk061 [2.6K]

The second one the are both perfect squares

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3 years ago

Given the parent function of f(x) = x^4, what change will occur when the function is changed to -f(1/2x) ?

Studentka2010 [4]

We are given with a function equal to f(x) = x^4. When the function is changed to -f(1/2x), the function changes to -f(1/2x) = (1/2 x)^4 equal to (-1/16 x^4). The graph of the function should be opening the opposite way and has a narrower plot. answer is C

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4 years ago

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What is the average rate of change of f(x) over the interval [6, 8]?

worty [1.4K]

[ 6 , 8 ]

X = 6 Y = 8 f(x) stands for y. so, i think the answer is 8.

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3 years ago