The graph of the function f(x) is shown. Which graph represents the function f(2x)

Mathematics

1 answer:

slava [35]3 years ago

8 0

Answer:

It should be the top left graph where there is point (1,1) and (-1, -1) y = 1/x

Step-by-step explanation:

from the original graph, I see:

f(x) = 2/x because f(2) = 1 = 2/2

f(1/4)= 2/(1/4) = 2

...

so then f(2x) compresses f(x) horizontally by a factor of 2

so f(2x) = 2/(2x) = 1/x

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MAXImum [283]

Pythagoras
28^2-19^2= 423
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Answer = 20.5669638

4 0

2 years ago

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of pi (no approximations)

Kisachek [45]

Answer:

40π in^2

Step-by-step explanation:

360°/72°=5

so, each of the two shaded regions are 1/5 of the circle.

the formula for finding the area of a circle is πr^2, so:

area for one of the shaded regions:

1/5πr^2

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this means that the area for one of the shaded regions is 20π. however, since there are two of them:

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2 years ago

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and t

WINSTONCH [101]

Answer:

Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.

How long will it take for this population to grow to a hundred rodents? To a thousand rodents?

Step-by-step explanation:

Use the initial condition when dp/dt = 1, p = 10 to get k;

$\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}$

Seperate the differential equation and solve for the constant C.

$\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}$