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I am unsure on how to do my math homework and really struggling with proofs

 
 

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1.I am trying to figure out the optimal radius that will give the lowest surface area of a cylinder. I ...

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius. If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0. The website https://www.datagenetics.com/blog/august12014/index.html explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.
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4.I have a logic question, that has to do with truth tables. I am doing tautologies and contradictions, and we are ...

s, and we are converting sentences to truth tables, i have a sentence that only gives me one variable and i am unsure on how to start my truth table.
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5.I am looking for someone who is familiar with water resources engineering. I have to be able to determine size ...

rmine size of piping for a water, wastewater, and stormwater system for an addition to a building on our campus. I am given maps of the existing conditions. I have calculated the new water demand which has to be used to determine the size of the pipes, though I am not completely sure if I did that right. I have a lot of information which I have compiled into a one drive file that I can share. I am able to help provide any information that is necessary since I am familiar with what the files contain. I have attached a document which explains everything that I need to do. I am able to use the existing network for the most part so routing of it should be easy. The part I am unsure about is determining the size of the pipes. For the water, I believe I can use mannings equation. For wastewater, I am unsure. For stormwater, I am to use the rational method and I have an excel tool which makes that easy for someone who knows what they are doing. Please help ASAP. I have to be done with this before tuesday afternoon. I am in central time zone(11:20pm right now).
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

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