Say for $$1$$ for $$x$$ and $$99$$ for $$y$$?

omgespit9q
2022-10-14
Answered

In a function like $f(x,y)={x}^{2}+y$, are $$x$$ and $$y$$ independent of each other and are we allowed to pick values for each deliberately?

Say for $$1$$ for $$x$$ and $$99$$ for $$y$$?

Say for $$1$$ for $$x$$ and $$99$$ for $$y$$?

You can still ask an expert for help

Finnegan Stone

Answered 2022-10-15
Author has **11** answers

In general

$$f(x,y):D\subseteq {\mathbb{R}}^{\mathbb{2}}\to \mathbb{R}$$

is defined in a subset $D$ of ${\mathbb{R}}^{\mathbb{2}}$ that is the real plane.

In your case

$$f(x,y)={x}^{2}+y$$

is defined for each value of $$(x,y)$$ thus $D\equiv {\mathbb{R}}^{\mathbb{2}}$.

$$f(x,y):D\subseteq {\mathbb{R}}^{\mathbb{2}}\to \mathbb{R}$$

is defined in a subset $D$ of ${\mathbb{R}}^{\mathbb{2}}$ that is the real plane.

In your case

$$f(x,y)={x}^{2}+y$$

is defined for each value of $$(x,y)$$ thus $D\equiv {\mathbb{R}}^{\mathbb{2}}$.

asked 2021-09-08

There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in dollars) realized from renting out x apartments is given by the following function.

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

How many units should be rented out in order to optimize the monthly rental profit?

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 2021-11-17

Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y produced after t hours of production is

$y=10t+\frac{1}{2}{t}^{2}-{t}^{3}$

$0\le t\le 8$

1) After how many hours will the hourly number of units be maximized?

2) What is the maximum hourly output?

asked 2021-10-09

For a marketing analysis,you want to 125 people how they
like the colours red,green and blue.After your questions,your
questions,you discover that.
55 people like red.
60 people like blue.
50 people like green.

asked 2021-02-22

Multivariable optimization. Find the demisions of the rectangular box with largest volume if the total surface are is given as 64 $c{m}^{2}$

asked 2022-05-02

use squeeze theorem find the following $\underset{}{\mathrm{lim}}x,y-0,0{y}^{2}(1-cos2x)/{x}^{4}+{y}^{2}$

asked 2021-11-16

The response area during an analysis of compound A in river water samples for five replications using HPLC-DAD were tabulated below.

$$\begin{array}{|cccccc|}\hline \text{No. of trial}& 1& 2& 3& 4& 5\\ \text{Area of metoprolol}& 424& 540& 428& 431& 532\\ \hline\end{array}$$

(I) Based on the tabulated data, calculate the % RSD

(II) Comment on the precision obtained from the analysis.

(I) Based on the tabulated data, calculate the % RSD

(II) Comment on the precision obtained from the analysis.