4x + 2y = 16 or y= -2r + 8 y=-2x + 8 only 5 points on the graph c T CONCon ss ROUTS 1400 DLDREN 1200 RI 3. Domain (x-values): 0, 1, 2, 3, 4 Range (y-values): 8, 6, 4, 2, 0 The domain is discrete because it consists of only the numbers 0, 1, 2, 3, and 4. y= -2x + 8 all points on line segment CHEESE FOR SALE Swiss: $41b Cheddar: $2/lb Domain (x-values): 0sx54 Range (y-values): 0sys8 The domain is continuous because it consists of all numbers from 0 to 4 on the number line.
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- The curve enters the window in the second quadrant, goes down and right, and exits the window nearly vertical at the approximate point (−7.2, −3). The curve reenters the window nearly vertical at the approximate point (−6.7, −3), goes up and right becoming less steep, crosses the x-axis at x = −5, goes up and right becoming more steep, and exits the window at the point (−3.3, 3). The curve reenters the window nearly vertical at the approximate point (−2.9, 3), goes down and right, changes direction at the approximate point (−1.5, 0.5), goes up and right, and exits the window nearly vertical at the approximate point (−0.1, 3). The curve reenters the window nearly vertical at the approximate point (0.2, 3), goes down and right, changes direction at the approximate point (1.6, −2), goes up and right, changes direction at the approximate point (4.3, 2.7), goes down and right, and exits the window nearly vertical at the approximate point (5.8, −3). The curve reenters the window nearly…Compute the abscissa of the minimum point of the curve y = x3 - 12x -9.There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows:P1=(10,15), P2=(20,25) ve P3=(40,5)To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the2two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively.Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move simultaneously in both directions.…
- Sketch the region that corresponds to the given inequalities. 2x + 4y ≥ 4 2x − 4y ≤ 4 x ≥ 0 The x y-coordinate plane is given. There are 3 lines and a region labeled "solution set" on the graph. The first line enters the window in the second quadrant, goes down and right, passes through the point (−4, 3), crosses the y-axis at y = 1 crossing the vertical line, crosses the x-axis at x = 2 crossing the second line, passes through the point (4, −1), and exits the window in the fourth quadrant. The second line enters the window in the third quadrant, goes up and right, passes through the point (−4, −3), crosses the y-axis at y = −1 crossing the vertical line, crosses the x-axis at x = 2 crossing the first line, passes through the point (4, 1), and exits the window in the first quadrant. The vertical line crosses the x-axis at the origin. The solution set is below the first line, below the second line, and to the right of the vertical line. The regions…Consider a manufacturing firm that occupies one hectare of land. The firm trans- ports over half of its output on trucks via an interstate highway four miles east of the city center (x = 4) and transports less than half its output on airplanes that leave from an airport seven miles east of the city center (x = 7). Draw the firm’s bid-rent curve for x = 0 to x = 10.Truck 1 is 40 km east of Truck 2 and starts to move west at 40 km/h, At the same time, Truck 2 Starts moving north 70 km/h. State the closest distance in km the trucks will be from eachother and at which time in hours, will that distance happen? (Optimization: need equation with one variable, drawing of problem with labelled variables, the critical #’s, the domain/boundary’s if possible, test values using orig equation, and therefore sentence. Didnt use any fancy math methods)
- If g left parenthesis x right parenthesis space equals space minus 2 left parenthesis 4 x plus 3 right parenthesis plus 1, what is g left parenthesis a right parenthesis simplified?Sketch the region that corresponds to the given inequalities. 3x − y ≤ 3 x + 2y ≤ 8 The x y-coordinate plane is given. There are 2 lines and a region labeled "solution set" on the graph. The first line enters the window in the third quadrant, goes up and right, passes through the point (−1, −6), crosses the y-axis at y = −3, crosses the x-axis at x = 1, passes through the point (2, 3) crossing the second line, and exits the window in the first quadrant. The second line enters the window in the second quadrant, goes down and right, passes through the point (−1, 4.5), crosses the y-axis at y = 4, passes through the point (1, 3.5), passes through the point (2, 3) crossing the first line, crosses the x-axis at x = 8, and exits the window in the fourth quadrant. The solution set is above the first line and below the second line. The regions outside the solution set are shaded. The x y-coordinate plane is given. There are 2 lines and a region labeled "solution…a) A region is called “positively invariant” if solutions in thatregion stay in that region as time increases. Which regions of your plot arepositively invariant? b) Use your answers to the previous parts (NOT the linearizationtheorem) to classify each equilibria as a source, a sink, a saddle, or noneof the above. c) describe the long-term behavior of everysolution in the plane. You should explain what can happen as t → ∞ andqualitatively describe which solutions have each behavior.
- The path of steepest ascent is usually computed assuming that the model is truly first order; that is, there is no interaction. However, even if there is interaction, steepest ascent ignoring the interaction still usually produces good results. To illustrate, suppose that we have fit the model ˆy =20+5x1−8x2+3x1x2ŷ=20+5x1−8x2+3x1x2 Using coded variables (−1 ≤ xi ≤ +1) a) Draw the path of steepest ascent that you would obtain if the interaction were ignored. b) Draw the path of steepest ascent that you would obtain with the interaction included in the model. Compare this with the path found in part (a).Can you show the step by step process of the first order conditions in order to get equation 8.9 , 8.10 and 8.11 Lagrange multipliers. L = Lagrangian Lagrange multipliers: Gamma and Lambda w_p = Portfolio weightLet S be the graph of f(x, y) = x2 + y2 - 2x + y for(x, y) ∈ D = {(x, y) : x2 + y2 ≤ 4 and x + y ≥ 0}. Let C1 be the curve along the edge of the graph of fover the straight edge of D – starting in the secondquadrant and ending in the fourth quadrant of D • Let C2 be the curve along the edge of the graph of fover the circular edge of D – starting in the secondquadrant and ending in the fourth quadrant of D. Let F(x, y, z) = ⟨x, y, y z⟩ Compute R: C1 F¯ · dr¯.