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Question

asked 2021-06-03

Let \(P(x)=F(x)G(x)\) and \(Q(x)=\frac{F(x)}{G(x)}\), where F and G are the functions whose graphs are shown.

a) Find \(P'(2)\)

b) Find \(Q'(7)\)

a) Find \(P'(2)\)

b) Find \(Q'(7)\)

asked 2021-06-09

Determine whether the given vectors are orthogonal, parallel,or neither:

\(u=(-3,\ 9,\ 6)\)

\(v=(4,\ -12,\ -8)\)

\(u=(-3,\ 9,\ 6)\)

\(v=(4,\ -12,\ -8)\)

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 2021-05-03

Two components of a minicomputer have the following joint pdf for their useful lifetimes X and Y:

\(f(x,y)=\begin{cases}xe^{-x(1+y)} & x\geq0\ and\ \geq0\\ 0 & otherwise \end{cases}\)

a) What is the probability that the lifetime X of the first component exceeds 3?

b) What are the marginal pdf's of X and Y? Are the two lifetimes independent? Explain.

c) What is the probability that the lifetime of at least one component exceeds 3?

\(f(x,y)=\begin{cases}xe^{-x(1+y)} & x\geq0\ and\ \geq0\\ 0 & otherwise \end{cases}\)

a) What is the probability that the lifetime X of the first component exceeds 3?

b) What are the marginal pdf's of X and Y? Are the two lifetimes independent? Explain.

c) What is the probability that the lifetime of at least one component exceeds 3?