Write parametric equations for each of the following curves. (a) The straight line segment traced from...

Write parametric equations for each of the following curves.

(a) The straight line segment traced from (3,2) to (5,8) as t goes from 0 to 1.

(b) A circle centered at (3,2), of radius 4, traced out two times, counterclockwise, as t goes from 0 to 2pi.

Expert Solution

milcah answered 1 year ago

Consider the equations for the following straight-line supply curves. In each case, p is the price...

Consider the equations for the following straight-line supply curves. In each case, p is the price (measured in dollars per unit) and QS is the quantity supplied of the product (measured in thousands of units per month). Supply A: pQSA, and Supply B: pQSB a. Plot each supply curve on a scale diagram. In each case, plot point 1, which corresponds to price equal to $20, and point 2, which corresponds to price equal to $40. 1.) For each supply...

Find parametric equations for the tangent line to the curve with the given parametric equations at...

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$(b): Find the unit tangent vector $\mathbf{T}$, the principal unit normal $\mathbf{N}$, and the curvature $\kappa$ for the space curve,$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$

Consider the curve traced out by the parametric equations: { x = 1 + cos(t) y...

Consider the curve traced out by the parametric equations: { x = 1 + cos(t) y = t + sin(t) for 0 ≤ t ≤ 4π. 1. Show that that dy dx = − 1 + cos(t)/sin(t) = − csc(t) − cot(t). 2. Make a Sign Diagram for dy dx to find the intervals of t over which C is increasing or decreasing. • C is increasing on: • C is decreasing on: 3. Show that d2y/dx2 = − csc2...

Cycloid is the curve traced by a point P on the circumference of a circle of radius a rolling along a straight line in a plane. See the figure. The parametric equation of the cycloid is

Cycloid is the curve traced by a point P on the circumference of a circle of radius a rolling along a straight line in a plane. See the figure. The parametric equation of the cycloid is (a) Find the tangent to the cycloid at the point where \theta=\pi / 3(b) At what points is the tangent horizontal? When is it vertical?(c) Find the length and area under one arch of the cycloid.

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Write parametric equations for each of the following curves. (a) The straight line segment traced from...

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