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1.Show that the force field vec F =(2xy-4- 1 2 sin( x 2 )sin( y 2 )) hat i +(x^ 2 + 1 2 cos( ...

cos( x 2 )cos( y 2 )) hat j is conservative and obtain the potential function. Evaluate the work done by vec F in moving a particle along the curve C which is the portion of the circle centered at origin with radius 2 in the first quadrant with counter clockwise orientation, without using line integrals.
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2.1. One popular definition of economics is a). How firms maximize profits. b). How consumers maximize utility. c). The use of scarce ...

aximize utility. c). The use of scarce resources to satisfy our wants. d). The use of fiscal and monetary policies to achieve economic outcomes. Flag question: Question 2 Question 21 pts 2. In a capitalist economy a). The government plays the dominant role. b). Market forces coordinate most production activities. c). The prices of most goods and services are set by the government. d). All of the above are correct. Flag question: Question 3 Question 31 pts 3. In a capitalist economy a). Most producers are driven by the desire to make profit. b). The government regulates most economic activities. c). Foreigners play no role in the economy. d). The output of most goods are planned. Flag question: Question 4 Question 41 pts 4. In drawing the graph of two variables that are related a). The Y variable goes on the horizontal axis. b). The X variable goes on the vertical axis. c). The independent variable goes on the vertical axis. d). In most cases the dependent variable goes on the vertical axis.
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3.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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4. Proof by cases: Let x and y be two integers that are divisible by 4, and z be an ...

t divisible by 4. Then the sum of x, y, and z cannot be divisible by 4.
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5.3A(g) + X(g) → Z(g) ΔH° = -480 kJ/molrxn The equation shown above represents an exothermic reaction between A(g) ...

reaction between A(g) and X(g). What is the amount of heat released when 10 mol of A(g) reacts with an excess X(g) ? ΔH A -236kJ X -136kJ Y -167kJ Using the heats of formation found in the table above, calculate ΔH for the reaction below. 6A(aq) + 7X(g) → 6Y(l) Y + 2X → 4Z ΔH=-4 A + 3B → 2Z ΔH=-2 A → X +C ΔH=7 Using the thermodynamic data above, determine ΔH for the reaction below. 2C+ 6B → Y When 0.3 moles of A(s) (4 grams) is dissolved in 12 grams of water at 23°C, the temperature of the water increases to 31°C. The specific heat of water is 4.18 J/g°C. Calculate ΔH in kJ/mol. Report your answer to 1 decimal place.
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6.Using the picture above, determine coordinates (x1 and y1) of point a (the intersection of the rods) with respect to the ...

) with respect to the origin. Then determine the coordinates of the bead (x2 and y2) with respect to point a. Finally, put your answers together to get the x and y coordinates of the bead with respect to the origin.
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7.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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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics