First: the homogeneous solutions: the characteristic equation is4r^2 - 4r - 3 = 0which has roots r = 3/2, -1/2 hence the homogeneous solution isy = c1.exp(-x/2) + c2.exp(3x/2)
next you need the general form for the guess for yp and that isyp = A1cos(2x) + A2sin(2x)
Now substitute that into the equation and solve for A1, A2.
assuming the maximum is the most common occurred, the answer is 32
assuming the minimum is the smallest number, it is 8
Step-by-step explanation:
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<em>Answer:</em>
<em>A proportion can be used to find the distance on the map that represents 50 miles, you can calculate this using the following steps:
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<em>200 miles ... 5 inches
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<em>50 miles ... x inch = ?
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<em>200 * x = 5 * 50
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<em>x = 5 * 50 / 200
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<em>x = 1.25 inch
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<em>The correct result would be x = 5 * 50 / 200.</em>
Answer:
Yes, each x-value has a unique y-value.
Step-by-step explanation:
This is a function because each x-value has its own y-value. If this is not the case then it is not a function, because then, two points with the same x-value and different y-values would fail the VLT.
Your graph does not have overlaps and each x-value has a unique y-value
VLT
The vertical line test (VLT) is a <u>simple method that mathematicians made because</u><u> they were lazy</u><u> to make a table of values and find duplicates. </u>
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- Passing the VLT means that if you drew a vertical line anywhere on the graph, it would only go through one point.
- Failing the VLT would mean that the vertical line
A quick way to check if it is a function is by looking for duplicates of x-values and check that the duplicates have the same y-value.
-Chetan K
Images/Examples