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3 years ago

The function (t) = 300,000t represents the distance (in kilometers) that light travels in t seconds

Mathematics

1 answer:

Anika [276]3 years ago

4 0

Answer:

The answer is: 4,500,000 kilometers or in scientific notation: 4.5 x 10^6 kilometers.

Step-by-step explanation:

Multiply to get the answer:

300,000 * 15 =

4,500,000 km

In scientific notation: 4.5 x 10^6

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D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

2 years ago

Explain whether the example is proportional or non-proportional.

kifflom [539]

Answer:

Porpotional

Step-by-step explanation:

because it is non proportional

5 0

3 years ago

Read 2 more answers

Four members from a 50 person committee are to be randomly selected to serve as chairperson, vicechairperson, secretary, and tre

alexdok [17]

Answer:

So, exists 5527200 different leadership structures.

Step-by-step explanation:

We know that four members from a 50 person committee are to be randomly selected to serve as chairperson, vicechairperson, secretary, and treasurer. The first perosn to be selected is the chairperson, the second to be selected as vice chairperson, the third is secretary, and the fourth is treasurer.

Since the order of the people is important to us, we have the following:

50·49·48·47=5527200

So, exists 5527200 different leadership structures.

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3 years ago

Fre-e points 915 9482 0043 Gm1fgZ join

Minchanka [31]

Answer:

Thanks, but join what?

Step-by-step explanation:

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2 years ago