course Mth 163 assignment #002002. Precalculus I 01-29-2009
......!!!!!!!!...................................
15:51:28 `q001. Note that this assignment has 8 questions Begin to solve the following system of simultaneous linear equations by first eliminating the variable which is easiest to eliminate. Eliminate the variable from the first and second equations, then from the first and third equations to obtain two equations in the remaining two variables: 2a + 3b + c = 128 60a + 5b + c = 90 200a + 10 b + c = 0. NOTE SOLN IS -1, 10, 100.
......!!!!!!!!...................................
RESPONSE --> First, you eliminate the c out of the system because it will be the easiest. You do this by subtracting the first equation from the third equation, then you replace the second and third equations with the corresponding results. Then subtracting the first equation from the second equation will give you a new equation to use as your replacement of the old second equation. You repeat this method to get the new replacement for the third equation. confidence assessment: 2
.................................................
......!!!!!!!!...................................
15:56:12 `q002. Solve the two equations 58 a + 2 b = -38 198 a + 7 b = -128 , which can be obtained from the system in the preceding problem, by eliminating the easiest variable.
......!!!!!!!!...................................
RESPONSE --> First, you eliminate one of the two variables. I chose to eliminate b. To do this you multiply the first equation by -7 and the second equation by 2. Then, you solve the equations by adding them together and you get a= - 1. confidence assessment: 3
.................................................
......!!!!!!!!...................................
16:00:23 `q003. Having obtained a = -1, use either of the equations 58 a + 2 b = -38 198 a + 7 b = -128 to determine the value of b. Check that a = -1 and the value obtained for b are validated by the other equation.
......!!!!!!!!...................................
RESPONSE --> You simply substitute - 1 into the first equation to find the solution for b. Once this is completed, you will find that b= 10. confidence assessment: 2
.................................................
......!!!!!!!!...................................
16:03:26 `q004. Having obtained a = -1 and b = 10, determine the value of c by substituting these values for a and b into any of the 3 equations in the original system 2a + 3b + c = 128 60a + 5b + c = 90 200a + 10 b + c = 0. Verify your result by substituting a = -1, b = 10 and the value you obtained for c into another of the original equations.
......!!!!!!!!...................................
RESPONSE --> Substitute -1 and 10 in for a and b in the first equation and solve it. The solution we obtain is c= 100. To check your work substitute these solutions into either the second or third equations. confidence assessment: 2
.................................................
......!!!!!!!!...................................
16:06:18 `q005. If a graph of y vs. x contains the points (1, -2), (3, 5) and (7, 8), as was the case for the graph you sketched in the preceding assignment, then what equation do we get if we substitute the x and y values corresponding to the point (1, -2) into the form y = a x^2 + b x + c?
......!!!!!!!!...................................
RESPONSE --> First, you substitute -2 in for y and 1 in for x. When you do this the solution obtained is a + b + c = - 2. confidence assessment: 2
.................................................
......!!!!!!!!...................................
16:27:03 `q006. If a graph of y vs. x contains the points (1, -2), (3, 5) and (7, 8), as was the case in the preceding question, then what equations do we get if we substitute the x and y values corresponding to the point (3, 5), then (7, 8) into the form y = a x^2 + b x + c?
......!!!!!!!!...................................
RESPONSE --> To calculate the second point you substitute 5 in for the y value and 3 in for the x value. From doing this you get 9 a + 3 b + c = 5. Then to get the solution for the third point you substitute 8 in for y and 7 in for x. The equation you get is 49 a + 7 b + c = 7. confidence assessment: 2
.................................................
......!!!!!!!!...................................
16:34:43 `q007. If a graph of y vs. x contains the points (1, -2), (3, 5) and (7, 8), as was the case in the preceding question, then what system of equations do we get if we substitute the x and y values corresponding to the point (1, -2), (3, 5), and (7, 8), in turn, into the form y = a x^2 + b x + c? What is the solution of this system?
......!!!!!!!!...................................
RESPONSE --> The same method is used to solve this system like you did in the last question. However, in this system the solutions came out in decimals, not whole numbers. a = - 0.45833, b = 5.33333 c = - 6.875 confidence assessment: 2
.................................................
......!!!!!!!!...................................
16:37:24 `q008. Substitute the values you obtained in the preceding problem for a, b and c into the form y = a x^2 + b x + c. What function do you get? What do you get when you substitute x = 1, 3, 5 and 7 into this function?
......!!!!!!!!...................................
RESPONSE --> I couldnt figure this one out. confidence assessment: 0
.................................................