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3 years ago

Find the area of the circle. Round your answer to the nearest hundredth.

Mathematics

2 answers:

soldi70 [24.7K]3 years ago

6 0

Answer:

50.27

Step-by-step explanation:

area of a circle: pi X r^2

r= radius

olga2289 [7]3 years ago

5 0

Answer:

50.27 square inches

Step-by-step explanation:

The formula for finding the area of a circle is πr², and the radius is 4, so first you do 4², which is 16, and then you multiply 16 by π, which is 50.2654824574, or rounded to the nearest hundredth, 50.27. Hope this helps.

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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

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

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3 years ago

The numbers are {0, 1, 2, 3, 4, ...}. whole rational natural real integer

Brilliant_brown [7]

Answer:

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Step-by-step explanation:

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