Maiclubk
2021-01-05
Answered

Let $z={e}^{{x}^{2}+3y}+{x}^{3}{y}^{2}$ , where $x=t\mathrm{cos}r{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r{t}^{4}$ . Use the chain rule fot multivariable functions (Cals III Chain Rule) to find $\frac{\partial z}{\partial r}$ and $\frac{\partial z}{\partial}t)$ . Give your answers in terms of r and t only. Be sure to show all of your work.

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Clelioo

Answered 2021-01-06
Author has **88** answers

asked 2021-09-08

Lynbrook West , an apartment complex , has 100 two-bedroom units. The montly profit (in dollars) realized from renting out x apartments is given by the following function.

$P\left(x\right)=-12{x}^{2}+2136x-41000$

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

To maximize the monthly rental profit , how many units should be rented out?

What is the maximum monthly profit realizable?

asked 2021-02-05

Use polar coordinates to find the limit. [Hint: Let $x=r\mathrm{cos}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}y=r\mathrm{sin}$ , and note that (x, y) (0, 0) implies r 0.]
$\underset{(x,y)\to (0,0)}{lim}\frac{{x}^{2}-{y}^{2}}{\sqrt{{x}^{2}+{y}^{2}}}$

asked 2022-05-14

for the function f(x,y)= $\sum _{i=1}^{n}[({x}_{i}{)}^{4\ast {y}_{i}}+(1-{y}_{i})ln{x}_{i}]$, y are binary variables, x nonnegative real values with fixed upper bound C. Does the minimization min f(x,y) have a unique solution or not?

asked 2021-01-10

Let $F\overrightarrow{\to}r=<x,y,z>$ and use the Divergence Theorem to calculate the (nonzero) volume of some solid in IR3 by calculating a surface integral. (You can pick the solid).

asked 2021-09-15

Solve the system of equation by the method of your choice.

${x}^{2}+{(y-9)}^{2}=49$

${x}^{2}-7y=-14$

asked 2021-02-09

Consider this multivariable function.

a) What is the value of

b) Find all x-values such that

asked 2022-06-14

The definition of a linear program is following:

Find a vector $x$ such that: $min{c}^{T}x$, subject to $Ax=b$ and $x\ge 0$.

Generally, $b$ is assumed to be a fixed constant. However is it possible to construct a program where values of $b$ are part of the optimization? Could I included b in the optimization by changing $Ax=b$ to $Ax-b=0$. If so, would I also be able to place constraints upon $b$ like $\sum b=1$ and $1>b>0$? Finally, would such a program be possible to solve efficiently?

I am trying to solve the linear program for Wasserstein Distance between two discrete distributions. In the standard case, b represents the marginals for each datapoint. I know the marginals for the target distribution but the marginals from my source distribution are unknown. I am wondering if there is an efficient way to optimize the marginals for my source distribution such that the Wasserstein distance is minimized.

Find a vector $x$ such that: $min{c}^{T}x$, subject to $Ax=b$ and $x\ge 0$.

Generally, $b$ is assumed to be a fixed constant. However is it possible to construct a program where values of $b$ are part of the optimization? Could I included b in the optimization by changing $Ax=b$ to $Ax-b=0$. If so, would I also be able to place constraints upon $b$ like $\sum b=1$ and $1>b>0$? Finally, would such a program be possible to solve efficiently?

I am trying to solve the linear program for Wasserstein Distance between two discrete distributions. In the standard case, b represents the marginals for each datapoint. I know the marginals for the target distribution but the marginals from my source distribution are unknown. I am wondering if there is an efficient way to optimize the marginals for my source distribution such that the Wasserstein distance is minimized.