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If y is the midpoint of xz y is located at and z is located at

 
 

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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 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.In a city with a population of 100,000 people, the spread of an influenza epidemic follows the differential equation: dy / ...

rential equation: dy / dt = py (100000 - y) Where: y is the number of infected people at time t (measured in weeks) and p = 0.00001. If 10 people were ill, determine y as a function of t. How long will it take before half the population is infected?
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5.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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6.Rectangle LMNO is translated using the rule (x, y) → (x + 2, y + 2) to create rectangle L'M'N'O'. ...

If a line segment is drawn from point L to point L' and from point O to point O', which statement would best describe the relationship between segment L L prime and segment O O prime? They share the same midpoints. They are diameters of concentric circles. They are perpendicular to each other. They are parallel and congruent.
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7.1. A ball is thrown with an initial speed of 20 m/s at an angle of 60° to the ground. ...

ance is negligible, what is the ball’s speed at the instant it reaches its maximum height from the ground? A. - 20 m/s B. 0 m/s C. + 17.3 m/s D. + 10 m/s E. + 20 m/s 2. A rhino charges full speed at a car with an initial velocity of 15 m/s. When the rhino collides with the car, it crumples in by 1 m before the rhino comes to a complete stop. What acceleration did the rhino feel as it came to a stop? A. - 112.5 m/s^2 B. - 7.5 m/s^2 C. - 30 m/s^2 D. + 112.5 m/s^2 E. + 30 m/s^2 F. + 7.5 m/s^2 3. Two students want to determine the speed at which a ball is released when thrown vertically upward into the air. One student throws the ball into the air while the other student measures the total time that the ball is in the air. The students use a meterstick to measure the release height of the ball. Which of the following equations should the students use to determine the speed at which the ball was released? * A. Use y final = y initial+ v initial *t + (1/2)*a*t^2 from the moment in time in which the ball was released to the moment in time in which the ball reaches its highest point. B. v final^2 = v initial ^2 + 2a(????y) from the moment in time in which the ball was released to the moment in time in which the ball hits the ground. C. Use y final = y initial+ v initial *t + (1/2)*a*t^2 from the moment in time in which the ball was released to the moment in time in which the ball hits the ground. D. v final^2 = v initial ^2 + 2a(????y) from the moment in time in which the ball was released to the moment in time in which the ball reaches its highest point.
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8.The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells ...

ticket sells for $7 and each adult ticket sells for $10.50. The auditorium can hold no more than 110 people. The drama club must make no less than $840 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics