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Jobisdone [24]
3 years ago
15

Solve the differential equation. x y^2 y' = x + 1

Mathematics
1 answer:
timurjin [86]3 years ago
5 0
x y^2 y' = x + 1 \ \Rightarrow\ y^2 \frac{dy}{dx} = \frac{x+1}{x}\ \Rightarrow\ y^2 dy = \left(1 + \frac{1}{x}\right) dx\ \Rightarrow \\
\\
\int y^2 dy = \int \left(1 + \frac{1}{x}\right) dx\ \Rightarrow \frac{1}{3}y^3 = x + \ln|x| + C\ \Rightarrow \\
y^3 = 3x + 3\ln|x| + 3C\ \Rightarrow\ \\ \\y = \sqrt[3]{3x + 3\ln|x| + K}, \text{ where $K = 3C$}
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A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for random sampleof 1044 pe
Evgesh-ka [11]

Answer:

A) D

B) B

C) C

D) B

Step-by-step explanation:

The complete question is:

A nutritionist wants to determine how much time nationally people spend eating and drinking. Suppose for random sampleof 1044 people age 15 or older, the mean amount of time spent eating or drinking per day is 1.44 hours with a standarddeviation of 0.57 hour. (A.) A histogram of time spent eating and drinking each day is skewed right. Use the result to explain why a large samplesize is needed to construct a confidence interval for the mean time spent eating and drinking each day.A. The distribution of the sample mean will never be approx. normalB. The distribution of the sample mean will always be approx. normalC. Since the distribution of time eating and drinking each is normally distributedthe sample must be large so that the distribution of the sample mean will be apprx. NormalD. Since the distribution of time spent eating and drinking each day is not normally distributed (skewed right), the sample must be large so that the distribution of the sample mean will be approx. normal.

(B) In 2010, there were over 200 million people nationally age 15 or older. Explain why this, along with the fact that that the data were obtained using a random sample, satisifies the requirements for constructing a confidence interval.A. The sampe size is greater than 5% of the population.B. The sample size is less than 10% of the populationC. The sample size is greater than 10% of the populationD. The sample size is less than 5% of the population.

(C.) Determine and interpret a 95% confidence interval for themean amount of time Americans age 15 older spend eating and drink each day.A. the nutritionist is 95% confident that the mean amount of time spent eatingand drinking per day is between blank and blank hours.B. the nutritionist is 95% confident that the amount of time spent eating or drinking per day forany individuals is between blank and blank hours.C. There is a 95% probability that the meant amount of time spent eating or drinking per day is between blank and blank hours.D. The requirements for constructing a confidence interval are not satisfied.

(D) Could the interval be used to estimate the mean amount of time a 9 year old spends eating and drinking each day?A. No, the interval is about individual time spent eating or drinking per day and cannot be used to find the mean time spent eating or drinking per day.B. No the intreval is about people age 15 or older. The mean amount of time spent eatinf or drinking per day for 9 year olds may differ.C. Yes, the interval is about individual time spent eating or drinking per dat and can be used to find the mean amount of time a 9 year old spends eating and drinking each day.D. Yes, the interval is about the mean amount of time spent eating or drinking per day for the 9 year olds.E. A confidence interval could not be constructed in part (C)D

A) a large sample size ensures normal distribution

B) a good sample size is around 10% of the population

C) confidence interval is a range of value and defines probability that mean of the population will lie with in the range

D) The data given is for 15 years and older so it can't be used for 9 years and younger

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Identify the equation that describes the line in slope-intercept form.
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Answer:

y=-2x-5

Step-by-step explanation:

slope (m)= -2, point (-4,3) put in y=mx+B

3 (y)= -2 [m](-4) + B

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3=8+B. - subtract 8

-8 -8

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Read 2 more answers
Geometry problem: Find the distance between the parallel lines y=-3/2x+1 and 2y+3x=10
s344n2d4d5 [400]

Answer:

d = 1.847

Step-by-step explanation:

To avoid any ambiguity, please enclose the slope -3/2 inside parentheses:

y = (-3/2)x + 1.  Next, solve the 2nd equation for y:  2y = - 3x + 10 => y = (-3/2)x + 5.  Notice how these two lines have the same slope (-3/2)?  Thus, the two given lines are parallel.

It's important to realize that the distance between these two lines is a line segment with perpendicular to both lines.  Thus, the segment representing this distance has the form y = (2/3)x + c.  Let's say that this segment passes through the y-intercept of y = (-3/2)x + 1; it thus passes through (0,1), and thus has the equation y = (2/3)x + 1.  

Find the point at which this y = (2/3)x + 1 intersects the line y = (3/2)x + 5.  Note that the xresultant point

Setting these two equations = to one another results in (2/3)x + 1 = (-3/2)x + 5.

Multiplying both sides by the LCD (6) will eliminate the fractions:

4x + 6 = -9x + 30.  Combining like terms:  13x = 24, and x = 24/13 = 1.846.

Substitute this x-value into   y = (2/3)x + 1 to find the y-coordinate of the point of intersection of y = (2/3)x + 1 and y = (-3/2)x + 5:

When x = 1.846, y = (2/3)(1.846) + 1 = 1.231.

Thus, the desired distance is that between (0,1) and (1.846, 1.231), and is:

d = √ [ (1.846 - 0)^2 + (1.231 - 1)^2 ] = √ [ (1.846)^2 + (0.053)^2 ]

This simplifies to                              d = √ [ 3.408 + 0.003 ] = √3.411, or

                                                          d = 1.847   (answer)

7 0
3 years ago
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