# Parametric equations, polar coordinates, and vector-v answers Recent questions in Parametric equations, polar coordinates, and vector-v
Parametric equations, polar coordinates, and vector-v
ANSWERED ### Find a parametric vector equation for the given plane: Parametric equations, polar coordinates, and vector-v
ANSWERED ### Using the point $$\displaystyle{P}_{{{0}}}={\left({1},{0},-{2}\right)}$$ and the vector $$v=(1,3,-1)$$ write a parametric vector equation for a line through $$\displaystyle{P}_{{{0}}}$$ in the direction of v

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Write the scalar equation for a plane through the point $$\displaystyle{P}_{{{0}}}={\left({1},{0},-{2}\right)}$$ with normal vector $$v=(1,3,-1)$$

Parametric equations, polar coordinates, and vector-v
ANSWERED ### $$x=t-\sin t$$ $$y=1-\cos t$$ to the curve given by the parametric equation $$\displaystyle{t}={\frac{{\pi}}{{{3}}}}$$ find teh equation of the line that is tangent at its point

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Consider the curve in the plane given in polar coordinates by $$\displaystyle{r}={4}{\sin{\theta}}$$. Find the cartesian equation for the curve and identify the curve

Parametric equations, polar coordinates, and vector-v
ANSWERED ### The position of an object in circular motion is modeled by the parametric equations $$\displaystyle{x}={3}{\sin{{2}}}{t}$$ $$\displaystyle{y}={3}{\cos{{2}}}{t}$$ where t is measured in seconds. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of motion (clockwise or counterclockwise), and the time t it takes to complete one revolution around the circle.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Parametric equations and a value for the parameter t are given $$\displaystyle{x}={\left({80}{\cos{{45}}}^{{o}}\right)}{t},{y}={6}+{\left({80}{\sin{{45}}}^{{o}}\right)}{t}-{16}{t}^{{2}}$$. t = 2. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Parametric equations and a value for the parameter t are given x = 3 - 5t, y = 4 + 2t. t = 1. Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Graph the sets of points whose polar coordinates satisfy the equations and inequalities $$\displaystyle{1}\le{r}\le{2}$$

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Given $$\displaystyle{u}=<{3},{5}>{\quad\text{and}\quad}{v}=<{6},{10}>$$, find the magnitude of the vector and find the dot product.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Graph the sets of points whose polar coordinates satisfy the equations and inequalities r = 2

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Give two pairs of parametric equations that generate a circle centered at the origin with radius 6.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Parametric equations and a value for the parameter t are given $$\displaystyle{x}={t}^{{2}}+{3},{y}={6}-{t}^{{3}}$$.t=2 Find the coordinates of the point on the plane curve described by the parametric equations corresponding to the given value of t.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Graph the sets pf points whose polar coordinates satisfy the equations and inequalities $$\displaystyle\theta=\frac{\pi}{{2}},{r}\ge{0}$$

Parametric equations, polar coordinates, and vector-v
ANSWERED ### A curve is given by the following parametric equations. $$\displaystyle{x}={20}{\cos{{t}}},{y}={10}{\sin{{t}}}$$. The parametric equations are used to represent the location of a car going around the racetrack. a) What is the cartesian equation that represents the race track the car is traveling on? b) What parametric equations would we use to make the car go 3 times faster on the same track? c) What parametric equations would we use to make the car go half as fast on the same track?

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Change from rectangular to cylindrical coordinates. (Let $$\displaystyle{r}\geq{0}$$ and $$\displaystyle{0}\leq\theta\leq{2}\pi$$.) a) $$\displaystyle{\left(-{2},{2},{2}\right)}$$ b) $$\displaystyle{\left(-{9},{9}\sqrt{{{3},{6}}}\right)}$$ c) Use cylindrical coordinates. Evaluate $$\displaystyle\int\int\int_{{{E}}}{x}{d}{V}$$ where E is enclosed by the planes $$\displaystyle{z}={0}$$ and $$\displaystyle{z}={x}+{y}+{10}$$ and by the cylinders $$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={16}$$ and $$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={36}$$ d) Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone $$\displaystyle{z}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}$$ and the sphere $$\displaystyle{x}^{{{2}}}+{y}^{{{2}}}+{z}^{{{2}}}={8}$$.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Is it true that the equations r=8, $$\displaystyle{x}^{{2}}+{y}^{{2}}={64}$$, and $$\displaystyle{x}={8}{\sin{{\left({3}{t}\right)}}},{y}={8}{\cos{{\left({3}{t}\right)}}}{\left({0}\le{t}\le{2}\pi\right)}$$ all have the same graph.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Let C be the curve described by the parametric equations x(t)= t, y(t) =$$\displaystyle{t}^{{3}}$$ a) sketch a graph of C b) find the vector-valued function f(t) associated with this parameterization of the curve C.

Parametric equations, polar coordinates, and vector-v
ANSWERED ### Graph the sets of points whose polar coordinates satisfy the equations and inequalities $$\displaystyle{r}\ge{1}$$
ANSWERED 