Solve the given differential equation by separation of variables.

$dy-(y-8)2dx=0$

pancha3
2021-09-04
Answered

Solve the given differential equation by separation of variables.

$dy-(y-8)2dx=0$

You can still ask an expert for help

Bentley Leach

Answered 2021-09-05
Author has **109** answers

Step 1

The differential equation is given as:

$dy-(y-8)2dx=0$

For finding the variable first we must put the same terms on one side and other terms on the other side of the equal to sign

$dy-(y-8)2dx=0$

$dy=(y-8)2dx$

$\frac{dy}{(y-8)}=2dx$

Step 2

Now integrating both sides we get,

Where c is the integration constant variable.

$\int \frac{dy}{(y-8)}=\int 2dx$

$\mathrm{ln}\left|(y-8)\right|=2x+c$

The differential equation is given as:

For finding the variable first we must put the same terms on one side and other terms on the other side of the equal to sign

Step 2

Now integrating both sides we get,

Where c is the integration constant variable.

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 2022-05-09

Most statements of Constraint Qualification I have found in the literature mention a locally "locally optimal solution" of the problem:

$\{\begin{array}{l}minf(x)\\ \text{s.t.}\\ {g}_{i}(x)\le 0\end{array}$

It is stated that when a C.Q. holds at a local optimum, then there exist Lagrange multipliers that satisfy KKT conditions.

But, I cannot get my head around this notion of local optimality. Does it mean locally optimal for the unconstrained problem? Does not local optimality imply the satisfaction of the KKT conditions?

$\{\begin{array}{l}minf(x)\\ \text{s.t.}\\ {g}_{i}(x)\le 0\end{array}$

It is stated that when a C.Q. holds at a local optimum, then there exist Lagrange multipliers that satisfy KKT conditions.

But, I cannot get my head around this notion of local optimality. Does it mean locally optimal for the unconstrained problem? Does not local optimality imply the satisfaction of the KKT conditions?

asked 2021-12-17

A camera shop stocks eight different types of batteries, one of which is type A7b.Assume there are at least 30 batteries.

of each type.a. How many ways can a total inventory of 30 batteries be distributed among the eight different types? b.

How many way can a total inventory of 30 batteries be distributed among the eight different types of the inventory must

include at least four A76 batteries?c. How many ways can a total inventory of 30 batteries be distributed among the eight

different types of the inventory includes at most three A7b batteries

of each type.a. How many ways can a total inventory of 30 batteries be distributed among the eight different types? b.

How many way can a total inventory of 30 batteries be distributed among the eight different types of the inventory must

include at least four A76 batteries?c. How many ways can a total inventory of 30 batteries be distributed among the eight

different types of the inventory includes at most three A7b batteries

asked 2021-11-19

Here is partial output from a simple regression analysis.

The regression equation is

EAFE = 4.76 + 0.663 S&P

Analysis of Variance

$$\begin{array}{cccccc}Source& DF& SS& MS& F& P\\ Regression& 1& 3445.9& 3445.9& 9.50& 0.005\\ Residual\text{}Error& & & & & \\ Total& 29& 13598.3& & & \end{array}$$

Calculate the values of the following:

The regression standard error,$s}_{e$ (Round to 3 decimal places)

The coefficient of determination,$r}^{2$ (Round to 4 decimal places)

The correlation coefficient, r (Round to 4 decimal places)

The regression equation is

EAFE = 4.76 + 0.663 S&P

Analysis of Variance

Calculate the values of the following:

The regression standard error,

The coefficient of determination,

The correlation coefficient, r (Round to 4 decimal places)

asked 2021-01-05

A concert promoter produces two kinds of souvenir shirt, one kind sells for $18 ad the other for $25. The company determines, the total cost, in thousands of dollars, of producting x thousand of the $18 shirt and y thousand of the $25 shirt is given by

$C(x,y)=4{x}^{2}-6xy+3{y}^{2}+20x+19y-12.$

How many of each type of shirt must be produced and sold in order to maximize profit?

How many of each type of shirt must be produced and sold in order to maximize profit?

asked 2021-11-20

(a) In a regression analysis, the sum of squares for the predicted scores is 100 and the sum of squares error is 200, what is $R}^{2$ ?

(b) In a different regression analysis, 40% of the variance was explained. The sum of squares total is 1000. What is the sum of squares of the predicted values?

(b) In a different regression analysis, 40% of the variance was explained. The sum of squares total is 1000. What is the sum of squares of the predicted values?