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For problem 1-10, determine whether the given set of
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- Use a system of linear equation to find the parabola y=ax2+bx+c that passes through the points (1,2), (0,1) and (2,6)arrow_forwardUse a software program or a graphing utility to write v as a linear combination of u1, u2, u3, u4, u5 and u6. Then verify your solution. v=(10,30,13,14,7,27) u1=(1,2,3,4,1,2) u2=(1,2,1,1,2,1) u3=(0,2,1,2,1,1) u4=(1,0,3,4,1,2) u5=(1,2,1,1,2,3) u6=(3,2,1,2,3,0)arrow_forwardDetermine whether each vector is a scalar multiple of z=(3,2,5). a v=(92,3,152) b w=(9,6,15)arrow_forward
- The zero vector 0 = (0, 0, 0) can be written a linear combination of the vectors v., v,, and v- because 0 = Ov, + 0v, + 0v3. This is called the trivia! solution. Can you find a nontrivial way of writing 0 as a linear combination of the three vectors? (Enter your answer in terms of v., v,, and v- If not possible, enter IMPOSSIBLE.) V1 = (1, 0, 1), V2 = (-1, 1, 2), V3 = (0, 1, 6)arrow_forwardA bird takes exactly two minutes to fly linearly from P(3,8,4) to Q(7,4,-3). Assuming that the bird maintains a constant speed, answer each of the following questions. What are the coordinates of the bird's position 45 seconds after leaving P? How many seconds after leaving P does the bird cross the xy-plane?arrow_forwardThere 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.…arrow_forward
- Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.arrow_forwardFor each problem, give an example of a set of vectors in R4 that meet criteria and briefly justify your answers. Give different examples than your classmates. 1. Linearly independent and spans all of R¹. 2. Linearly independent but does not span all of R4. 3. Linearly dependent and spans all of R¹. 4. Linearly dependent and does not span all of R4.arrow_forwardtotal commercial flight times between two cities (for jets) can be modeled by the following linear equation: time =rate (miles) + fixed where time is in hours and miles is the distance between the two cities. the fixed time in hours represents the time for the takeoff and landing phases of the flight. this fixed time is relatively constant for flights under normal conditions. given a 3-hour flight of 1,250 miles and a 4.5-hour flight of 2,100 miles, determine the rate (to 5 dec. places) and fixed time (to whole minute) for this linear model. rate = ________hours/mile. takeoff/landing time=_______min.arrow_forward
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