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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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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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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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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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) 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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8.Find the constant of proportionality. z is directly proportional to the sum of x and y. If x = 5 and ...

and
y = 2,
then
z = 56.

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9.y=xx+x+11 The value of y is a prime number when x = 0, 1, 2 and 3 The following statement is not ...

ot true.
y=xx+x+11 is always a prime number when x is an integer
(b) Show that the statement is not true.

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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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tion of X is given as follows:
X 3 4 6
p(X) 0.3 0.4 0.3
Find mean and variance of distributions X, Y.

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13.4x^2-16y=15-y Solve the equation for y and determine if the equation defines y as a function of x

ard free energy G° by 18 kJ/mole, with A* having the higher G°.
Use the table below to find how many more molecules will be in state A* compared with state A at equilibrium.
If an enzyme lowered the activation energy of the reaction by 11.7 kJ/mole, how would the ratio of A to A* change?
Table: RELATIONSHIP BETWEEN THE STANDARD FREE- ENERGY CHANGE, ∆G°, AND THE EQUILIBRIUM CONSTANT
Hint: ∆G° represents the free-energy difference under standard conditions (where all components are present at a concentration of 1 mole/litter). From this table, we see that if there is a favourable free-energy change of –17.8 kJ/mole for the transition Y→ X, there will be 1000 times more molecules of X than of Y at equilibrium (K = 1000).

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15.Suppose that f: A--> B is a function and that X and Y are two subsets of B such that ...

in Y. prove that f-1(X) is a subset of f-1(Y)

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= 4, y = 15, and dy/dt = 1.
x2 + y2 = 241
dx/dt= ??

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18.3. Given: x ∈ Q and y ∈ Q. Prove that 3x − 5y ∈ Q. You may use without proof: the ...

ference, and product of integers
is an integer.
4. Given: x ∈ R. Prove:
9x
2 + 5 > 12x.
At the idea stage, reduce the given inequality by setting it to 0. Then, it
should be helpful to complete the square.

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19.Engine 1 and Engine 2 are engines that move at the same speed and are the same length. Engine 1 ...

80 seconds to completely travel a distance of 1440 meters while Engine 2 took 100 seconds to completely travel a distance of 1700 meters. If Engine 1 is X meters long and Engine 2’s speed is Y meters per second, what is X + Y?

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n, y = 0.2x2 – 0.4x – 0.6, where x and y are measured in metres.
a) Find the x intercepts
b) Find the vertex.
c) What is the minimum height of the hammock?

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By 5 Table 1st Row 1st Column x 2nd Column 1 3rd Column 2 4st Column 3 5st Column 4 2nd Row 1st Column y 2nd Column 1.86 3rd Column 3.75 4st Column 6.12 5st Column 11.3 EndTable
Select the correct choice below and fill in the answer boxes to complete your choice.
x: 1,2,3,4
y:1.86,3.75,6.12,11.3
(Type integers or decimals rounded to the nearest hundredth as needed.)
f=_()square root of x
f=_+(_) ln x
f(x)=_
1+(_)e suqare root -(_)x

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24.Consider the following LP, where the value of has not yet been ascertained maxz = c1x + y s. t . ...

t . 2x + 2y ≤ 12
2x + 4y ≤ 10
x ≥ 0,y ≥ 0
(a) What value of will result in a unique optimal solution to this LP and what is the corresponding optimal solution? You need to give a comprehensive answer.
(b)What value of will result in infinitely many solutions to this LP? You need to give a comprehensive answer.
(c) What value will result in no optimal solution to this LP? You need to give a comprehensive answer.

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is the middle of the DrawingPanel. Ask the user to enter an x
and a y coordinate for a DrawingPanel. Your program will draw a line from the last
coordinates to the current coordinates the user enters. If the user enters an x value or y value
out of bounds of the DrawingPanel, then end the program.

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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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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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29.(1,5) , (2,10) and (3, 19) are points on the curve y = ax^2 + bx + c. Found a, ...

-1 and c = 4.
So quadratic function is y = 2x^2 - x + 4.
Next question is: suppose that the 3rd point is written as (3, t). Find all values for t that will change the quadratic function y =ax^2 + bx + c into a linear function.

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30.hello can you please help to solve this system of equations k == (Sqrt[y^2 - 2 y^3 - y^4 + ...

+ Sqrt[2 - 2 y] -
k)/((y + 1) Sqrt[1 - y^2]),
Sqrt[2]/2/m == k/(k - Sqrt[2 - 2 y]), n ==
Sqrt[2 - 2 Sqrt[1 - m^2]], z == Sqrt[2 - 2 y]/f ==
Sqrt[(zn)^2 - 2 + 2 y]/
Sqrt[n^2 - f^2], t == (Sqrt[g^2 - 2 g^3 - g^4 + 2 g + 1] +
Sqrt[2 - 2 g] - t)/((g + 1) Sqrt[1 - g^2]),
Sqrt[2]/2/h == t/(t - Sqrt[2 - 2 g]), q ==
Sqrt[2 - 2 Sqrt[1 - h^2]], l == Sqrt[2 - 2 g]/p ==
Sqrt[(lq)^2 - 2 + 2 g]/
Sqrt[q^2 - p^2], (z + 1) x == (l + 1) 2 x == (y + 1) Sqrt[1 - y^2]/
Sqrt[2] == Pi/4, q == m and determine true it or false thank you

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31.If sin(x) = 1/3 and sec(y) = 29/21 , where x and y lie between 0 and π/2, evaluate the expression ...

n using trigonometric identities. (Enter an exact answer.)
cos(x + y)

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l unemployment rate dropped to about 4%.
Find the average decline/year in unemployment rate from 2010 to 2018.
Let x be the year since 2010 and y be the unemployment rate. Write an equation for unemployment rate versus year.
Use your equation to estimate the unemployment rate in 2020.

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he also pays $0.10 of tax every dollar she spends. Write an expression that shows how much tax she pays. Then expand the expression.

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35.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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ned online. Using technology, with x representing the ratings and y representing price, we find that the regression equation has a slope of 130 and a y-intercept of negative 363. Complete parts (a) and (b) below.
a. What is the equation of the regression line? Select the correct choice below and fill in the answer boxes to complete your choice.

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37.Given the points on a line below : x (2,4) y (10,16) (i) Find the values of m and c (ii) ...

hat is the equation of the line passing through the points ?
(iii) Using the equation of the line. For a y value of 28, what is the x value?

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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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ike splitting into x and y

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43.2. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value ...

s of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
5. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
9. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
22. What is the greatest value of c for which the roots of the equation x^2 + 4x + c = 0 are real?
24. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
7, 24 and 25
A._________________ (smaller value)
B._________________ (larger value)

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44. 1. What is the greatest value of c for which the roots of the equation x^2 + 4x + ...

2. Find the two acute angles in the right triangle whose sides have the given lengths. Express your answers using degree measure rounded to two decimal places.
A._______________________ (Smaller Value)
B. _______________________ (Larger Value)
3. A flagpole casts a shadow 200 feet long. At the same time, a boy standing nearby who is 5 feet tall casts a shadow 20 feet long. Find the number of feet in the height of the flagpole.
4. If (k, 3) is a point on the line whose equation is 4x + y = -9, what is the value of k?
5. If 8 ounces of a sports drink contains 130 milligrams of sodium, what is the total number of milligrams of sodium in 20 ounces of the sports drink?
6. If the mean of the numbers 9, 10, 11, 12, and x is 12, what is the value of x?

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46. Value: 1 equation image indicator a. (x - 2)2(x - 3)2 b. (x2+ 4)(x2+ 9) c. (x - 2)(x + ...

2)(x - 3)(x + 3)
d. (x2 - 4)(x2+ 9)
Value: 1
The table below shows the cost of purchasing a standard stapler at five office supply stores, A through E. If the median cost of purchasing a standard stapler for these stores was $17.99, which of the following could NOT have been the cost of the stapler for Store A?
staplergraph.jpg
a. $19.95
b. $18.95
c. $16.95
d. $19.25
Value: 1
If equation image indicator then x =
a. 7
b. 1/5
c. 5
d. 1/7
Value: 1
A six−sided die, with sides numbered 1,2, 3,4,5, and 6, is tossed. What is the probability of tossing a number less than three?
a. 1/3
b. 0
c. 1/2
d. 1/4
Value: 1
If 6m + 4 = 8m, then 4m =
a. 6
b. 2
c. 8
d. 4
Value: 1
In the xy-plane, what is the y-intercept of the graph of the equation equation image indicator?
a. 2
b. 4
c. 16
d. There is no y-intercept.
Value: 1
Which of the following equations has both 2 and −4 as solutions?
a. x2 + 6x + 8 = 0
b. x2 - 2x - 8 = 0
c. x2 + 2x - 8 = 0
d. x2 - 2x + 8 = 0
Value: 1
The perimeter of a square is 20 ft. If you increase the length of the square by 2 feet and decrease the width by 1 foot, what is the area, in square feet, of the new figure?
a. 22
b. 28
c. 35
d. 40
Value: 1
(3x-2y4)-3 =
a. equation image indicator
b. equation image indicator
c. equation image indicator
d. equation image indicator
Value: 1
A softball is tossed into the air upward from a first floor balcony. The distance of the ball above the ground at any time is given by the function, distance function.png, where h(t) is the height of the softball above the ground (in feet) and t is the time (in seconds). What was the maximum height, in feet, of the softball above the ground after it was thrown?
a. 28
b. 30
c. 32
d. 34
Value: 1
A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. If the total paid, for all 100 people, was $1300, how many students attended the museum opening?
a. 20
b. 50
c. 70
d. 80
Value: 1
The ratio of Sam's age to Hank's age is 5 to 3. If the sum of their ages is 24, how old is Hank?
a. 21
b. 15
c. 19
d. 9
Value: 1
In the xy−coordinate plane shown below, point P has coordinates (8, −6). Which of the following is an equation of the line that contains points O and P?
O and P graph.jpg
a. equation image indicator
b. equation image indicator
c. equation image indicator
d. equation image indicator
Value: 1
The variables x and y are inversely proportional, and y = 2 when x = 3. What is the value of y when x = 9?
a. 54
b. 6
c. 2/3
d. 3/2
Value: 1
A farmer has 1235 trees to be planted on a rectangular parcel of land. If there are 24 trees planted in each row and each row must be complete before it is planted, how many trees will be left over after planting?
a. 21
b. 11
c. 0
d. 55

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ups need one hour in Machine 1; whereas glasses need one hour. The company has exactly ten hours available in Machine 1. Use the method of substitution to find the maximum values of X and Y and the maximum value for the objective function. Show all the steps in the method.

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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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dog. John charges $17.50 up front, plus $13 per dog. Write the system of linear equations that describes this situation.
hannah: y = 10.5 x 25
john: y = 17.5x + 13
For how many dogs would they both charge the same price, and what would that price be? Describe when Hannah would be cheaper and when John would be cheaper.

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

mathematicsalgebra Physics