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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.Following a method) 4.3 x 10^8 + 2.5 x 10^7 Choose bigger number in 10 and add the first 2 numbers 4.3+2.5 ...

4.3+2.5 : 10^8, 6.8 6.8 x 10^8 But the answer is 4.5 x 10^8 How do i get 4.5?
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5.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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8.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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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics