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Is it possible to create a mapping diagram for a function whose domain has fewer elements than the range


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3.Hi. If 2 electrodes, both made of pure silver, were used as the cathode and anode, in a solution of ...

sodium hydroxide, with 5 volts applied to the circuit to produce hydrogen and oxygen, via electrolysis, would the pure silver electrodes react with anything or be completely unreactive? Im guessing the electrodes will be unreactive, but since electricity is part of the equation, it seems possible for there to be reactions between the silver metal and maybe oxygen or something else depending on the voltage level, but to be honest, i never had a chemistry class, so i dont really know what might happen at all besides guessess i could make according to the little knowledge about all this i got here and there over the years. So here i am, in hopes of a person who does know what will occur.
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4.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 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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5.I have a doubt about on whether it is possible to integrate logarithmic spirals to find the area of certain ...

certain objects. So in this case, I derived a log spiral equation in polar coordinates to model an spiral galaxy. I plan on finding the area as well as volume of the galaxy using the function which I have derived. So is there any way, I could integrate these spiral functions to find area?
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7.600m of fencing is used to construct 6 rectangular animal pens as shown.. how do I show that the area ...

a of each pen is A=x((600-8x)/9)m^2? then I need to find the dimensions of each pen so that it has the maximum possible are. then I need to know what is the area of each pen in this case
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8.Objective​: To write a “newspaper” article based on the events in Alice’s Adventures in Wonderland. Characteristics of a Main News Story: 1. ...

erland. Characteristics of a Main News Story: 1. General Content:​ Start with the facts: who, what, when, where, how (feel free to fabricate unknown details for the purpose of this project) 2. Interviews:​ Provide no less than one “interview” in which characters involved are quoted in response to the event 3. Tone:​ Be objective in tone. A quality news story is devoid of opinion or conjecture. Represent both sides of the issue if multiple viewpoints exist. It may mean getting interviews from differing parties. 4. Headline: ​Don’t underestimate the importance of the headline. Reporters use sensationalized and emotionally charged language to catch the reader’s attention. This can be a challenge because you also keep a headline concise. 5. Structure:​ ​Inverted pyramid ​structure​. Journalists usually describe the organization or ​structure​ of a ​news story​ as an inverted pyramid. The essential and most interesting elements of a​ ​story​ ​are put at the beginning, with supporting information following in order of diminishing importance. 6. Length:​ CPS: 500 words minimum; Hon: 600 words minimum 7. Format: ​MLA, submit a Google doc Possible events: 1. The Pool of Tears
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics