12 boys share water even the amongst 12 canteens how much water would each boy get in their canteen

Mathematics

1 answer:

miss Akunina [59]3 years ago

4 0

Answer: 1 canteen

Step by step: 12 boys divided by 12 canteens 1, so each boy gets 1 canteen

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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

3 years ago

Help me out with this problem please!!and (please tell me how you got the answer.)

Sati [7]

The answers are that the number can equal -4 or 1.

You can find this by setting the number equal to x.

x^2 (The square of a number) + 3x (three times a number) = 4

x^2 + 3x = 4 ---> subtract 4 from each side
x^2 + 3x - 4 = 0

Then you can factor this to find the answers

(x - 4)(x + 1) = 0

Set both equal to 0 and solve.

5 0

4 years ago

Please helpp!!!!!!!!

Otrada [13]

Step-by-step explanation:

the answer is in picture