Answer:
2, 4, 6, and 8, respectively
Step-by-step explanation:
The rule says that 2 times the x value, which we are given, equals to y, which we must find. So all we hve to do is multiply each of the given x values by two to get the y value.
The answer: The absolute value
The probability of selecting a vowel from the English alphabet is 5/26 (≈19.2%) if you include only A, E, I, O, and U as vowels
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I believe your answer is:
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Here’s why:
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Hope this helps you. I apologize if it’s incorrect.
The differential equation
has characteristic equation
<em>r</em> ⁴ - <em>n </em>² <em>r</em> ² = <em>r</em> ² (<em>r</em> ² - <em>n </em>²) = <em>r</em> ² (<em>r</em> - <em>n</em>) (<em>r</em> + <em>n</em>) = 0
with roots <em>r</em> = 0 (multiplicity 2), <em>r</em> = -1, and <em>r</em> = 1, so the characteristic solution is
For the non-homogeneous equation, reduce the order by substituting <em>u(x)</em> = <em>y''(x)</em>, so that <em>u''(x)</em> is the 4th derivative of <em>y</em>, and
Solve for <em>u</em> by using the method of variation of parameters. Note that the characteristic equation now only admits the two exponential solutions found earlier; I denote them by <em>u₁ </em>and <em>u₂</em>. Now we look for a particular solution of the form
where
where <em>W</em> (<em>u₁</em>, <em>u₂</em>) is the Wronskian of <em>u₁ </em>and <em>u₂</em>. We have
and so
So we have
and hence
Finally, integrate both sides twice to solve for <em>y</em> :