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X y y find the vertex and one other points on a graph


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1.In Andrew’s Furniture Shop, he assembles both bookcases and TV stands. Each type of furniture takes him about the same ...

s him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit. Using the information in the problem, write the constraints. Let x represent number of bookcases, and y represent number of TV stands.
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2.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.Hello guys, I confess that I absolutely suck at math. Unfortunately my boss handed me what is basically a math ...

lly a math problem I gotta solve, and I have no idea how to do it cause of lack of my math skills. I am hoping someone can help me with this or I'm screwed. Co basically I've got this table in excel, where X (row) is a width and Y is a height (column) of a wooden sauna cabin, the X;Y is the price for a sauna with said dimensions. I need to find a relationship between the size of the sauna and the price And formulate ani equation. I can't seem to find it, the price seems to grow non linearly, I can't seem to find any coeficient. Again, I suck at math, maybe solution is simple, but I just don't see it. Can anyone help me please? Table Is at this link . Thanks for any help!
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6.Consider two random variable X and Y with following relation Y = 2X+3 The probability distribution of X is given as follows: X ...

tion of X is given as follows: X 3 4 6 p(X) 0.3 0.4 0.3 Find mean and variance of distributions X, Y.
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7.In a simple reaction A ↔ A*, a molecule is interconvertible between two forms that differ in standard free energy ...

ard free energy G° by 18 kJ/mole, with A* having the higher G°. Use the table below to find how many more molecules will be in state A* compared with state A at equilibrium. If an enzyme lowered the activation energy of the reaction by 11.7 kJ/mole, how would the ratio of A to A* change? Table: RELATIONSHIP BETWEEN THE STANDARD FREE- ENERGY CHANGE, ∆G°, AND THE EQUILIBRIUM CONSTANT Hint: ∆G° represents the free-energy difference under standard conditions (where all components are present at a concentration of 1 mole/litter). From this table, we see that if there is a favourable free-energy change of –17.8 kJ/mole for the transition Y→ X, there will be 1000 times more molecules of X than of Y at equilibrium (K = 1000).
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics