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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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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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chets and sells baby blankets, b. Each blanket requires 3 skeins of yarn, and the total number of skeins Facundo uses, y, varies directly as the number of blankets he crochets, b.
Write an equation that models this relationship.
2. The weight of an object, w, varies inversely as the square of its distance from the center of Earth, d. When an astronaut stands in a training center on the surface of Earth (3,960 miles from the center), she weighs 155 pounds. To the nearest tenth of a pound, what will be the approximate weight of the astronaut when she is standing on a space station, in orbit 240 miles above the training center?
3. The square of g varies inversely as h. When g = 16, h = 2. What is the value of h when g = 40?
4. The number of days, d, it will take Manny to read a book varies inversely as the number of pages, p, he reads per day. If k is the constant of variation, which equation represents this situation?
5. The battery life for Bruhier’s cell phone is longer when he has fewer apps running. When only one app is running, the battery will last for 16 hours. When four apps are running, the battery will only last for 4 hours.

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seen an equation of a circle this is moved in both the x and y direction be converted to a polar equation.
For example, I know that the equation of a circle x^(2)+(y-2)^(2)=4 is r=4sin(theta) when converted to polar. Same thing for a translation with the x variable. However, I have never seen, nor do I know how to do, a conversion of a circle with both translations. For example, converting this equation of a circle to a polar equation: (x+3)^(2)+(y-4)^(2)=4. I have no idea how to do such a thing and cannot find any examples of such.
Hope you can shed some light on this, Thanks.

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e a look at this spreadsheet so I can properly explain:
https://docs.google.com/spreadsheets/d/1lEJIPiSZJk9LYUTSA4oeDwyLXCVd18Zdewm6gnjxcXo/edit?usp=sharing
Ok, so for the sake of simplicity We'll just go with row two here. Cell A2 represents the hours worked freelancing, where B2 is for the minutes of the recorded time frame. C2 is the net amount earned in that time. Over in cell N10 I need to figure out an equation using the =SUM() function (treats it as a normal math problem) where it prints the hourly income based on those three integers. I'll admit i was never great at math, but in my defense I've been up since 6 am yesterday (currently 3 pm) and have been running solely on caffiene and nicotine haha... The sheet is editable and I can see any changes you make in realtime. Is there any way you could help me out on this one? It's for a work report type thing.

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rt. How does it make u pay less interest and have less interest:
Vn+1 = 1.00405Vn - 1817.35, Vo= 34400
The term of the loan is 30 years with monthly payment of 1817.35 at an interest rate of 4.86 p.a
Pls tell me the answer regarding this particular equation
Q2) How much of the principal has been repaid? Fv - Vo is this the correct formula
Q3) Superannuation
Something like if u add money without tax why does it benefit your super account
I’m sorry to disturb you but I was hoping you could help as tmrw is my last writing lesson for my sac

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ed to design the water, wastewater, and stormwater systems for an addition to a building at our university. I have the maps of the existing systems and I am planning to use these existing systems as much as possible to avoid extra work. I have calculated a water demand and fire flow for the building. I believe I have to use mannings equation for the water pipes to determine flow, etc. I am not sure how to deal with the wastewater. I have to use the rational method for stormwater. I have attached a document which explains what I need to do overall. I need help on this ASAP as I have to present it Tuesday evening.

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12.I don't understand how to graph a sin or cos equation by just looking at it. Vice versa, I have ...

dea how to write an equation looking at the graph.

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raneous solution. Use the equation below as a model.
a√x+b]+c=d
In the document, I need help with Tasks 2 & 3. Thanks.

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics