#$&* course MTH 173 10/28 00:15
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Given Solution: ** The bus only makes periodic stops, whereas the graph for III only comes to a stop once. I would matche the bus with II. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q describe the graph of the car with no traffic and no lights YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Problem submitted using text_13 assignment. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The car matches up with (I), which is a continuous, straight horizontal line representing the constant velocity of a car with no traffic and no lights. *&*& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q describe the graph of the car with heavy traffic YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Problem submitted under text_13 assignment. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** The car in heavy traffic would do a lot of speeding up and slowing down at irregular intervals, which would match the graph in III with its frequent increases and decreases. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q query 2.4.11 5th, 2.4.10 4th; 2.5.10 (was 2.4.8) q = f(p) (price and quantity sold)what is the meaning of f(150) = 2000? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Problem 2.4.11 and problem 2.4.10 submitted using text_13 assignment. Problem 2.5.10 The slope of the graph is always positive thus the value of f’(x) is always positive and the graph of the function is concave up thus the value of the second derivative will also be positive, thus f”(x) will be positive. Given that f(p) = q where q is quantity sold and p is the price, Thus f(150) = 2000 indicates that for a price of $150 the quantity sold is 2000. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: *&*& q = 2000 when p = 150, meaning that when the price is set at $150 we expect to sell 2000 units. *&*& &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q what is the meaning of f'(150) = -25? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: f’(p) indicates the rate of change of quantity sold at a particular price, thus f’(150) = -25 indicates that when the price is $150 the rate at which the quantity sold changes is -25 units/$ confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** f' is the derivative, the limiting value of `df / `dp, giving the rate at which the quantity q changes with respect to price p. If f'(150) = -25, this means that when the price is $150 the quantity will be changing at a rate of -25 units per dollar of price increase. Roughly speaking, a one dollar price increase would result in a loss of 25 in the number sold. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q query problem 2.4.23 5th; 2.4.18 4th; 2.4.7 graph of v vs. t for no parachute. Describe your graph, including all intercepts, asymptotes, intervals of increasing behavior, behavior for large |t| and concavity, and tell why the graph's concavity is as you indicate. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Problem 2.4.23, 2.4.18 submitted using text_13 assignment. It is known that as a person jumps out of the airplane without a parachute the velocity increases more rapidly initially and then less rapidly until the velocity reaches the terminal velocity. Thus the graph of the function will be a concave down function increasing until it reaches a terminal velocity and approaches the terminal velocity as an asymptote, that is the line y = terminal velocity is an horizontal asymptote to the graph. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** When you fall without a parachute v will increase, most rapidly at first, then less and less rapidly as air resistance increases. When t = 0 we presume that v = 0. The graph of v vs. t is therefore characterized as an increasing graph beginning out at the origin, starting out nearly linear (the initial slope is equal to the acceleration of gravity) but with a decreasing slope. The graph is therefore concave downward. At a certain velocity the force of air resistance is equal and opposite to that of gravity and you stop accelerating; velocity will approach that 'terminal velocity' as a horizontal asymptote. The reason for the concavity is that velocity increases less and less quickly as air resistance increases; the approach of the velocity to terminal velocity is more and more gradual ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q What does the t = 0 acceleration indicate? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: t = 0 acceleration indicates the acceleration of the person as soon as he jumps out of the airplane. Initially there is no air resistance and thus the acceleration of the person is the gravity of the earth which indicates a natural phenomenon of free fall for the person. This acceleration at t = 0 is nothing but the slope of the v vs. t graph at t = 0. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: ** t = 0 acceleration is acceleration under the force of gravity, before you build velocity and start encountering significant air resistance. Acceleration is rate of velocity change, indicated by the slope of the v vs. t graph. ** STUDENT QUESTION I understand how acceleration and vel. are related, just not the first part of solution INSTRUCTOR RESPONSE If it wasn't for air resistance, acceleration would be equal to that of gravity. When you first jump out you aren't falling very fast, so there isn't much air resistance to counter the acceleration of gravity, so you accelerate pretty much at the acceleration of gravity. You quickly speed up, and air resistance becomes more and more significant. So your acceleration becomes less than the acceleration of gravity. Assuming the ground is far away, this continues until air resistance is effectively equal to the force of gravity, at which point your acceleration will be zero. You will be at terminal velocity. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK ********************************************* Question: `q Query Add comments on any surprises or insights you experienced as a result of this assignment. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique Rating: OK #*&!