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The graph at the right shows a proportional relationship between x and y why does this mean all the x

 
 

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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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3.Please check options and pictures within the file attached. If the questions can be answered within a free demo session ...

hin a free demo session as I have my answers, but just want to confirm them, that would be greatly appreciated. Question 1: A block of mass M = 0.10 kg is attached to one end of a spring with spring constant k = 100 N/m . The other end of the spring is attached to a fixed wall. The block is pushed against the spring, compressing it a distance x = 0.04 m . The block is then released from rest, and the block-spring system travels along a horizontal, rough track. Data collected from a motion detector are used to create a graph of the kinetic energy K and spring potential energy Us of the system as a function of the block's position as the spring expands. How can the student determine the amount of mechanical energy dissipated by friction as the spring expanded to its natural spring length? Question 2: The Atwood’s machine shown consists of two blocks connected by a light string that passes over a pulley of negligible mass and negligible friction. The blocks are released from rest, and m2 is greater than m1. Assume that the reference line of zero gravitational potential energy is the floor. Which of the following best represents the total gravitational potential energy U and total kinetic energy K of the block-block-Earth system as a function of the height h of block m1? Question 3: A 2 kg block is placed at the top of an incline and released from rest near Earth’s surface and unknown distance H above the ground. The angle θ between the ground and the incline is also unknown. Frictional forces between the block and the incline are considered to be negligible. The block eventually slides to the bottom of the incline after 0.75 s. The block’s velocity v as a function of time t is shown in the graph starting from the instant it is released. How could a student use the graph to determine the total energy of the block-Earth system? Question 4: A block slides across a flat, horizontal surface to the right. For each choice, the arrows represent velocity vectors of the block at successive intervals of time. Which of the following diagrams represents the situation in which the block loses kinetic energy?
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5.You need to create a 3 piece, piecewise defined function that includes a point of discontinuity and a jump discontinuity. ...

a jump discontinuity. You then need to write and find the limit at that point of discontinuity and jump discontinuity. You also have to find the limit at a point on your piecewise defined function that is continuous. Each limit needs to be justified using the graph and the limit notation. Your piecewise defined function needs to have a beginning and end. That means that the domain cannot go to infinity. You will state the domain and the range using interval notation.
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6. If NASA launches a model rocket from the grounds of Cape Canaveral at the same time a Navy fleet shoots ...

hoots a laser beam in a straight path from a deck 14 feet above sea level off the coast of Florida, is it possible the laser beam will cross the path of the model rocket? Use a piece of graph paper to write/model equations f ( x ) to represent the path that models the rocket and g ( x ) to represents the path that models the laser beam.
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7.The cost of gym membership, C, in Australian dollars (AUD), in Paolo’s Gym can be modelled by the function C = 65t ...

function C = 65t + 30 where t is the time in months. (a) Calculate the gym membership cost over a six month period. (b) Sketch the graph of the function C = 65t + 30 for t ≥ 0. (c) Calculate the time, t, in months, when the total cost reaches 290 AUD. In the neighbouring Nicolo’s Gym, the initial payment is 75 AUD higher than in Paolo’s Gym, however the monthly fee is lower at 30 AUD per month. (d) Determine the number of months it takes for the total cost to be less by attending Nicolo’s Gym in comparison to Paolo’s Gym.
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8.A weather balloon has a capacity of 11 ft3 . It is filled with hydrogen at a constant rate. Initially, the balloon ...

itially, the balloon contains 4 ft3 of hydrogen and it takes 14 seconds to com- pletely fill the balloon. (a) At what rate is the balloon filled? (b) Find a linear function V that models the volume of hydrogen in the balloon at any time t. (c) What can you say about the graph of V ? (You do not need to sketch the graph.)
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics