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3 years ago

James and Tom both go for a drive and return home.

Mathematics

1 answer:

yawa3891 [41]3 years ago

8 0

Distance is the number of units between two points.

Tom's distance was 15 km shorter than James's

<h3>How to interpret the graphs</h3>

From Tom's graph, the highest distance from home is 10 km
From Jame's graph, the highest distance from home is 25 km

Calculate the difference between these distances

$d = 25km -10km$

Evaluate the differences

$d = 15km$

Hence, Tom's distance was 15 km shorter than James's

Read more about distance and graphs at:

brainly.com/question/4931057

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Answer:

14. D=70°

e=110°(straight line angles)

15. R=42°(vertically opposite angles)

S=68°(sum of interior angles of a triangle)

16.x=50°(angles on a straight line)

y=70°(sum of interior angles of a triangle)

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3 years ago

Help me with this problem...

IgorLugansk [536]

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3 years ago

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

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Kruka [31]

Answer:

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3 years ago