Consider the parametric curve given by the equations x(t)=t^2+8t+17 y(t)=t^2+8t3

Question

Consider the parametric curve given by the equations x(t)=t^2+8t+17 y(t)=t^2+8t39 How many units of distance are covered by the point P(t)=(x(t),y(t)) between t=0 and t=9 Consider the parametric curve given by the equations x(t)=t^2+8t+17 y(t)=t^2+8t39 How many units of distance are covered by the point P(t)=(x(t),y(t)) between t=0 and t=9 Consider the parametric curve given by the equations x(t)=t^2+8t+17 y(t)=t^2+8t39 How many units of distance are covered by the point P(t)=(x(t),y(t)) between t=0 and t=9

Explanation / Answer

to get a distance between points we use the distance formula but first we need the points themselves.
Point 1 is found by subbing t=0 in for t in x(t) and y(t)
Point 2 is found by subbing t=9 in for t
in x(t) and y(t)
x(t) = (0)^2 +8(0)+17= 17
y(t) = (0)^2 +8(0) -39 = -39
so point 1 is (17,-39)

x(t) = (9)^2 +8(9)+17= 170
y(t) = (9)^2 +8(9) -39 = 114
so point 2 is (170,114)

distance d=sqrt((114+39)^2+(170-17)^2)

=216.4

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