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1

Manipulate[ PolarPlot[{1, a + Sin[3 θ]}, {θ, 0, 2 π}, PlotRange -> {{-3.5, 3.5}, {-4, 3.2}}], {a, -3, 3}]


1

Using Piecewise is a good choice. gradePoint[grade_] := With[{g = Ceiling[grade]}, Piecewise[{{4., g >= 80}, {3.75, g >= 75}, {3.5, g >= 70}, {3.25, g >= 65}, {3., g >= 60}, {2.75, g >= 55}, {2.5, g >= 50}, {2.25, g >= 45}, {2., g >= 40}}, 0]]; You may check whether the function works perfectly. ...


1

You can use TableForm to set up the table. row1 = {"GP", 0, 2., 2.25, 2.5, 2.75, 3.0, 3.25, 3.75, 4.}; row2 = {"Marks", "0-39", "40-44", "45-49", "50-54", "55-59", "60-64", "65-69", "70-74", "75-79", "80-100"}; {row2, row1} // TableForm It wasn't clear to me what you want to do with this data, but you can get the mean of the GPs with ...


1

Using memoization f[n_Integer] := f[n] = (2 n - 1) f[n - 1] f[1] = 1; f /@ Range[3] {1, 3, 15}


0

f[n_] := -1 + 2 Range@n // Apply@Times Range[30] // Map@f // Timing (* ...


3

Use the n!! function: Table[Factorial2[2 n - 1], {n, 1, 3}] {1, 3, 15}



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