Equation in the indicated coordinate system is written below

Laaibah Pitt

Answered 2021-09-02
Author has **26434** answers

asked 2021-09-01

Write an equation in the indicated coordinate system. Also write a parametric equation
and a vector equation for the following equation

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={25}\in{R}^{{{3}}}\), cylindrical coordinates, sherical coordinates

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}={25}\in{R}^{{{3}}}\), cylindrical coordinates, sherical coordinates

asked 2021-09-10

Write an equations in indicated coordinate system. Also write a parametric equation and a vector equation for each of the following equations.

1) \(\displaystyle{\frac{{{x}-{1}}}{{{2}}}}={\frac{{{y}-{5}}}{{{3}}}}={\frac{{{z}-{2}}}{{{4}}}}\) cylindrical coordinates, sherical coordinates

2) \(\displaystyle{3}{x}+{4}{y}+{5}{z}={6}\) cylindrical coordinates, sherical coordinates

3) \(\displaystyle{x}^{{2}}+{y}^{{2}}+{z}^{{2}}={100}\) cylindrical coordinates, sherical coordinates

4) \(\displaystyle{x}^{{2}}+{y}^{{2}}={100}\) cylindrical coordinates, sherical coordinates

asked 2021-09-14

asked 2021-09-12

Surface s is a part of the paraboloid \(\displaystyle{z}={4}-{x}^{{2}}-{y}^{{2}}\) that lies above the plane \(z=0\).\((6+7+7=20pt)\)

a) Find the parametric equation \(\displaystyle\vec{{r}}{\left({u},{v}\right)}\) of the surface with polar coordinates \(\displaystyle{x}={u}{\cos{{\left({v}\right)}}},{y}={u}{\sin{{\left({v}\right)}}}\) and find the domain D for u and v.

b) Find \(\displaystyle\vec{{r}}_{{u}},\vec{{r}}_{{v}},\) and \(\displaystyle\vec{{r}}_{{u}}\cdot\vec{{r}}_{{v}}\).

c) Find the area of the surface

asked 2021-09-05

Write in Cartesian coordinates the parametric equations of the curve with polar equation
\(\displaystyle{r}{\left({t}\right)}={<}\sqrt{{t}},\frac{\pi}{{8}}{>}\).

asked 2021-09-06

Which of the following polar coordinate pairs does not represent the point with rectangular coordinates (-2,-2)?

(A)\(\displaystyle{\left({2}\sqrt{{2}}.−{135}°\right)}\)

(B)\(\displaystyle{\left({2}\sqrt{{2}}.{225}°\right)}\)

(C)\(\displaystyle{\left(−{2}\sqrt{{2}}.−{315}°\right)}\)

(D)\(\displaystyle{\left(−{2}\sqrt{{2}}.{45}°\right)}\)

(E)\(\displaystyle{\left(−{2}\sqrt{{2}}.{135}°\right)}\)

(A)\(\displaystyle{\left({2}\sqrt{{2}}.−{135}°\right)}\)

(B)\(\displaystyle{\left({2}\sqrt{{2}}.{225}°\right)}\)

(C)\(\displaystyle{\left(−{2}\sqrt{{2}}.−{315}°\right)}\)

(D)\(\displaystyle{\left(−{2}\sqrt{{2}}.{45}°\right)}\)

(E)\(\displaystyle{\left(−{2}\sqrt{{2}}.{135}°\right)}\)

asked 2021-09-05

The letters \(\displaystyle{r}{\quad\text{and}\quad}θ\) represent polar coordinates. Write each equation using rectangular coordinates \((x, y)\).

\(\displaystyle{r}= \sin{\theta}- \cos{\theta}{r}= \sin{\theta}- \cos{\theta}\)

Help, please.