asked 2021-09-06

(a) \((0, -3, 0)\)

(b) \(\displaystyle{\left(-{1},{1},-\sqrt{{{2}}}\right)}\)

asked 2021-08-21

Change from rectangular to spherical coordinates. (Let \(\displaystyle\rho\geq{0},\ {0}\leq\theta\leq{2}\pi\), and \(\displaystyle{0}\leq\phi\leq\pi.{)}\)

a) \(\displaystyle{\left({0},\ -{8},\ {0}\right)}{\left(\rho,\theta,\phi\right)}=?\)

b) \(\displaystyle{\left(-{1},\ {1},\ -{2}\right)}{\left(\rho,\theta,\phi\right)}=?\)

a) \(\displaystyle{\left({0},\ -{8},\ {0}\right)}{\left(\rho,\theta,\phi\right)}=?\)

b) \(\displaystyle{\left(-{1},\ {1},\ -{2}\right)}{\left(\rho,\theta,\phi\right)}=?\)

asked 2021-05-14

a) \((0,\ -8,\ 0)(\rho,\theta, \phi)=?\)

b) \((-1,\ 1,\ -2)(\rho, \theta, \phi)=?\)

asked 2021-06-09

Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

asked 2021-05-27

Express the plane \(z=x\) in cylindrical and spherical coordinates.

a) cykindrical

\(z=r\cos(\theta)\)

b) spherical coordinates

\(\theta=\arcsin(\cot(\phi))\)

a) cykindrical

\(z=r\cos(\theta)\)

b) spherical coordinates

\(\theta=\arcsin(\cot(\phi))\)

asked 2021-09-14

Convert the point from rectangular coordinates to spherical coordinates.
\(\displaystyle{\left(-{3},-{3},\sqrt{{{2}}}\right)}\)

asked 2021-08-18

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

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}+{z}^{{{2}}}={8}\).

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

\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}+{z}^{{{2}}}={8}\).