Solution below

asked 2021-05-14

Use the given graph off over the interval (0, 6) to find the following.

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)

b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)

c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)

d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)

e) The coordinates of the point of inflection. \((x,\ y)=\)

a) The open intervals on whichfis increasing. (Enter your answer using interval notation.)

b) The open intervals on whichfis decreasing. (Enter your answer using interval notation.)

c) The open intervals on whichfis concave upward. (Enter your answer using interval notation.)

d) The open intervals on whichfis concave downward. (Enter your answer using interval notation.)

e) The coordinates of the point of inflection. \((x,\ y)=\)

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 2021-09-04

Find the point(s) of intersection of the graphs of the equations.

\(x = 73 − y^2\)

\(y = x − 1\)

A point of intersection of the graphs of two equations is a point that satisfies both the equations. You can find the point(s) of intersection of the graphs of the given equations by solving their equations simultaneously.

Solve the first equation for \(y^2\).

\(x = 73 − y^2\)

\(= y^2\)

asked 2021-09-03

Given a set of parametric equations

\(\displaystyle{x}={1}+{\frac{{{1}}}{{{3}}}}{\cos{{\left({\frac{{{5}}}{{{2}}}}{t}\right)}}}{\quad\text{and}\quad}{y}=\sqrt{{{5}+{\cos{{\left({\frac{{{5}}}{{{2}}}}{t}\right)}}}}}\)

Eliminate the parameter t to obtain the equation in terms of x andy.

\(\displaystyle{x}={1}+{\frac{{{1}}}{{{3}}}}{\cos{{\left({\frac{{{5}}}{{{2}}}}{t}\right)}}}{\quad\text{and}\quad}{y}=\sqrt{{{5}+{\cos{{\left({\frac{{{5}}}{{{2}}}}{t}\right)}}}}}\)

Eliminate the parameter t to obtain the equation in terms of x andy.

asked 2021-09-04

Sketch the parametric curve for the following set of parametric equations. Clearly indicate direction of motion

1)\(\displaystyle{x}={5}{\cos{{t}}}\)

2)\(\displaystyle{y}={2}{\sin{{t}}}\)

3)\(\displaystyle{0}\ge{t}\ge{2}\pi\)

1)\(\displaystyle{x}={5}{\cos{{t}}}\)

2)\(\displaystyle{y}={2}{\sin{{t}}}\)

3)\(\displaystyle{0}\ge{t}\ge{2}\pi\)

asked 2021-09-10

Use the vector field:

\(\overrightarrow{F}=[-bx\ cy]\)

Use the following values: \(a=5,\ b=2,\ c=3\)