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3 years ago

Solution for dy/dx+xsin 2y=x^3 cos^2y

1 answer:

3 0

Start by putting the dy/dx by itself
$\frac{dy}{dx}+xsin2y=x^3 cos^2y \\ \frac{dy}{dx}=x^3 cos^2y-xsin2y$
then multiply both sides by dx
$dy=(x^3cos^2y-xsin2y)dx$
which you can now integrate both sides with respect to their variable, so the left by y and the right by x
$y+ c_{1}= \frac{x^4}{4}cos^2y-\frac{x^2}{2}sin2y+c_{2}$
let c = c2-c1 and you find
$y= \frac{x^4}{4}cos^2y-\frac{x^2}{2}sin2y+c$

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Teresa will rent a car, she can choose between on of two plan. The first plan has an initial fee of $48 and costs an additional

nika2105 [10]

Answer:

plan 1

Step-by-step explanation:

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3 years ago

A manufacturer reported a sample mean = 22.0 g and a sample standard deviation = 2.5 g based on a sample of 20 of their products

tester [92]

Answer:

$n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5$

So the answer for this case would be n=5 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=22$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.5 represent the sample standard deviation

n represent the sample size

ME = 2 represent the margin of error accepted

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (2)

And on this case we have that ME =2 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

$n=(\frac{z_{\alpha/2} s}{ME})^2$ (3)

We can use as estimator for the population deviation the sample deviation $\hat \sigma = s$

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got $z_{\alpha/2}=1.640$ , replacing into formula (3) we got:

$n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5$

So the answer for this case would be n=5 rounded up to the nearest integer

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3 years ago

PLEASE HELP BRAINLIEST GIVEN TO CORRECT ANSWER

morpeh [17]

The solution to a system of (linear) equations is the point where the graphs intersect. Consider two parallel lines. By definition, two parallel lines never intersect each other, but all pairs of non-parallel lines will eventually intersect. That means they will also have a solution.

Let's consider what makes a line parallel to another line. It basically looks identical, having the same steepness (slope), but the graph is just shifted over. That is, a parallel line would have the same slope and a different y-intercept. For our equation $2y-4x=12$ , or $y=2x+6$ in slope-intercept form, a parallel line will be of the form $y=2x+b$ .

That describes the form of a parallel line, which we do not want. Any other line, however, will give a solution to our system, so we merely want a line where the slope does not equal 2.

We can have any equation of the form $y=mx+b, \ x \neq 2$ .