Domain: (-infinity,infinity)
Range: (0, infinity)
The asymptote is at 0
Answer:
y = x -2
Step-by-step explanation:
Slope is 1, y-intercept is (0,-2)
<u>35.12 miles </u><u>is the total number of minutes that it took krissy to run these three miles.</u>
What is a simple definition of time?
The measured or measurable period during which an action, process, or condition exists or continues : duration. b : a nonspatial continuum that is measured in terms of events which succeed one another from past through present to future.
Krissy ran three miles one morning she ran the first mile in time 1 = 11.74
Krissy ran three miles one morning she ran the first mile in time 2 = 11.26
Krissy ran three miles one morning she ran the first mile in time 3 = 12.12
To get total time , we have to add all the time 1,2,3
Total time = Time1 + Time2 + Time3
= 11.74 + 11.26 + 12.12
Total Time = 35.12 <u>miles</u>
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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> :
