 # Parametric equations and a value for the parameter t are given x = (60 cos 30^{circ})t, y = 5 + (60 sin 30^{circ})t - 16t2, t = 2. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. slaggingV 2021-03-01 Answered
Parametric equations and a value for the parameter t are given $x=\left(60cos{30}^{\circ }\right)t,y=5+\left(60sin{30}^{\circ }\right)t-16t2,t=2$. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.
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Step 1 Given Parametric equations and a value for the parameter t $x=\left(60\mathrm{cos}{30}^{\circ }\right)t,y=5+\left(60\mathrm{sin}{30}^{\circ }\right)t-16{t}^{2}$ and $t=2$ We have to find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t. Step 2 Given parametric equation $x=\left(60\mathrm{cos}{30}^{\circ }\right)t,y=5+\left(60\mathrm{sin}{30}^{\circ }\right)t-16{t}^{2}$ As cos So, $x=\left(30\sqrt{3}\right)t,y=5+30t-16{t}^{2}$ (1) Now we have to find the coordinates of the point on the plane curve corresponding to the value $t=2$. On plugging in So, $\left(60\sqrt{3},1\right)$ is the point.