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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.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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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 https://ibb.co/fGrxSvf . Thanks for any help!

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op
Speed = 37.529503 + 0.18599121 Drop
Sample size: 61
R (correlation coefficient) = 0.92132219
R-sq = 0.84883459
Estimate of error standard deviation: 4.4083553
Intercept 37.529503
Slope 0.18599121
Scatterplot has a positive direction.
Question as follows
Run another linear regression but use x = Drop (in feet) to predict y = Speed (in
miles per hour).
__________
Slope Interpretation:
__________

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seen an equation of a circle this is moved in both the x and y direction be converted to a polar equation.
For example, I know that the equation of a circle x^(2)+(y-2)^(2)=4 is r=4sin(theta) when converted to polar. Same thing for a translation with the x variable. However, I have never seen, nor do I know how to do, a conversion of a circle with both translations. For example, converting this equation of a circle to a polar equation: (x+3)^(2)+(y-4)^(2)=4. I have no idea how to do such a thing and cannot find any examples of such.
Hope you can shed some light on this, Thanks.

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8.the meaning of x time y i am having a hard time finding the meaning of x time y so ...

you could help me out for five day -clarissa
\

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9.Suppose that you run the following regression: Y i = β 0 + β 1 X 1 i + ...

i + β 4 X 4 i + β 5 X 5 i + μ i
You then decide to test the null hypothesis β 2 = β 3 = β 4 = 0.
What is your restricted model?

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formation: x commuters rode neither trains nor buses, y rode trains, and z rode only trains. How many people rode the following?
(a) trains and buses
(b) only buses
(c) buses
(d) trains or buses
I answered a easily but can't figure out b-d

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achine B. The nature of the machines makes their cost functions differ.
Total cost is given by C(x,y)equalsUpper C left parenthesis x right parenthesisplusUpper C left parenthesis y right parenthesis. How many units should be made on each machine in order to minimize total costs if xplusyequals19 comma 740 units are required?
The minimum total cost is achieved when
___ units are produced on machine A and
___ units are produced on machine B

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12.I how did this thing turned out i didn’t really understand can you explain? 1) x=y^2 ...

| Y
0-0
1-1
2-1.41
2– -1,41
2) y/3 =x+1
X | y
-2- -3
-1- 0
0-3
11-6
I dont know how’d they get that can u please explain the solution.

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14.I am wondering if we have a circle and someone goes around the circle three times. 1. the first time ...

me he goes around the circle X m/s
2. the second time he goes around the circle Y m/s
3. His average velocity is Z m/s
4. What is the velocity the third time.

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a tilebased game,
2D rectangle tiles with a size of 5000X5000 pixels per rectangle.
I make every rectangle know the 4 neighbouring rectangles in the map so starting from one you can generate an essentially infinite map.
I want to move this map around instead of moving the player around, the player stays centered on screen and since the map moves under him it looks like he's the one doing the moving.
So I know the following things:
Width and height of a single section:
5000X5000 pixels
the x and y location of the center section can be a value anywhere from -5000,-5000 to 5000,5000
The visible screen real estate is 1920 X 1080 pixels big
0X,0Y always stars top left, bottom right is 5000X5000
What I need to end up with:
A percentage value of howmuch this specific section is visible on screen, "inside the rectangle that is the scfeen)

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el of the flow in the coating zone x ∈ [0; L], y ∈ [0; h(x)] a lubrication approximation will be developed. If λ >> 1, and if α is close to, but less than 1 the coating zone appears plane. Use the equation of continuity to show by an order of magnitude estimate that |vy| << |vx|. Then state assumptions on flow and pressure field that reduce the Navier- Stokes equation locally to a form, from which the following approximate expression for the x-velocity in the slot for x ∈ [0; L] can be derived:
Se the attached.

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20.I dont understad these questions: For which value(s) of a does the curve y = x^2 + ...

ave a horizontal tangent line at x = 1 ? (Without using differentiation rules)
For each statement, explain why it must be true, or use an example to show that it can be false.
a)If y = f ( x ) has a horizontal tangent line at x = 1 then y = g ( x ) , where g ( x ) = f ( x − 1 ) + 1 , has a horizontal tangent line at x = 2 .
b)A tangent line always has exactly one point in common with the graph of the function.

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ike splitting into x and y

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r3> CreateCircle(float zValue, int points)
{
var vertices = new List();
float degrees = 0f;
float degreeChange = twoPi / points;
for (var i = 0; i < points; i++)
{
// Adding to degrees changes the rotation of the circles - adding nothing creates a straight tube
float x = (2f * Mathf.PI) * Mathf.Sin(degrees);
float y = (2f * Mathf.PI) * Mathf.Sin(degrees);
//Mathf.Sin(degrees + (GlobalVariables.tunnelDepth/2))
//Mathf.Cos(degrees + (GlobalVariables.tunnelDepth / 3))
vertices.Add(new Vector3(x, y, zValue));
degrees += degreeChange;
}
return vertices;
}

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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics