3 years ago

Choose a number between 67 and 113 that is a multiple of 3, 9, and 12

Mathematics

1 answer:

Anestetic [448]3 years ago

3 0

72 is multiples of 3,9, and 12

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$\dfrac{\sqrt2}2=C_1\cos\left(\dfrac\pi4\right)+C_2\sin\left(\dfrac\pi4\right)$

$\implies\dfrac1{\sqrt2} = \dfrac{C_1}{\sqrt2}+\dfrac{C_2}{\sqrt2}$

$\implies C_1+C_2=1$

Similarly, given that x' (p/4) = 0, you have

$0=-C_1\sin\left(\dfrac\pi4\right)+C_2\cos\left(\dfrac\pi4\right)$

$\implies 0=-\dfrac{C_1}{\sqrt2}+\dfrac{C_2}{\sqrt2}$

$\implies C_1=C_2$

From this result, it follows that

$C_1+C_2=2C_1=1 \implies C_1=C_2=\dfrac12$

So the particular solution to the DE that satisfies the given conditions is

$\boxed{x=\dfrac12\cos(t)+\dfrac12\sin(t)}$

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3 years ago