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# Equation of Solution, Marginal Cost and Maximum Height

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1.) You are shown a family of graphs each of which is a general solution of the given differential equation. Find the equation of the particular solution that passes though the indicated point.

dy/dx=-5x-2 point (0,2)

2.) Find the cost function for the marginal cost and fixed cost

marginal costs fixed costs (x=0)
dC/dx=85 \$5000

3.) Use a(t)=-32feet per sec. How high will the ball go?

A ball is thrown vertically upward with an intergral velocity of 60 feet per second. How high will the ball go?

##### Solution Summary

Integration Applications problems involving Equation of Solution, Marginal Cost and Maximum Height are solved. The solution is detailed and well presented.

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1.) you are shown a family of graphs each of which is a general solution of the given differential equation. Find the equation of the particular solution that passes though the indicated point.

dy/dx=-5x-2 point (0,2)

Solution. Since dy/dx=-5x-2 , we have
dy=(-5x-2)dx
Integrating it, we get
y = -5/2*x^2 - 2x + C
Since y(0)=2, we can ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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