Question: Plot the pair of parametric equations as t ranges from -10 to 10. Label the x-axis time and the y-axis temperature x = t + 2 Sin t, y = t + 2 Cos 5t.
a. Find the exact roots of f(x) = 3x4 - 15x3 + 18x2
b. Find the decimal values of these roots, listing the roots in table form.
Solution:
x[t_] := t + 2Sin[t]
y[t_] := t + 2 Cos[t]
ParametricPlot[{x[t], y[t]}, {t, -10,10}, AxesLabel-> {"Time", "Temperature"}, PlotStyle-> {Hue[.5], Thickness[.005]}];
SHIFT + ENTER
Part (a):
Solve[3x^4-15x^3+18x^2==0]
SHIFT + ENTER
{{x -> 0}, {x -> 0}, {x -> 2}, {x -> 3}}
Part (b):
b = NSolve[3x^4-15x^3+18x^2==0];
PaddedForm[TableForm[b],{8,3}]
SHIFT + ENTER
X -> 3.000
X -> 2.000
X -> 0.000
X -> 0.000