course Mth 163 assignment #001001. Precalculus I 01-29-2009
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14:17:43 `questionNumber 10000 `q001. Note that this assignment has 10 questions Solve the following system of simultaneous linear equations: 3a + 3b = 9 6a + 5b = 16.
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RESPONSE --> This system can be solved by using the addition of the appropriatemultiple of one equation to eliminate one of the two variables. By multiplying the first equation by -2, you can make the equations opposite and equal. Then you add both the equations together and you get b=2. After this step you substitute 2 into the first equation which will give you the solution a=1. The ending solution for this system is a=1 and b=3. You can check your answer by substituting both of the values into the second equation. confidence assessment: 3
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14:23:33 `questionNumber 10000 `q002. Solve the following system of simultaneous linear equations using the method of elimination: 4a + 5b = 18 6a + 9b = 30.
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RESPONSE --> First in the method of elimination you have to multiply the first equation by 3 and the second equation by -2 to eliminate a. Then you take the products of both equations and add them together to get the solutions for the variables. After doing this you will find that b=2, then you substitute this into the first equation to find that a=2. To check your work you substitute a into the second equation. confidence assessment: 3
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14:26:43 `questionNumber 10000 `q003. If y = 5x + 8, then for what value of x will we have y = 13?
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RESPONSE --> First, substitute 13 in for y into the equation. Then, you subtract 8 from both sides and divide by 5 on both sides which will solve the equation. The solution is x-=1. confidence assessment: 3
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14:39:15 `questionNumber 10000 The x coordinates 1, 3 and 7 match the x coordinates of the three given points, the y coordinates will be the y coordinates -2, 3 and 8, respectively, of those points. At x = 5 the precise value of x, for a perfect parabola, would be 8 1/3, or about 8.333. Drawn with complete accuracy a parabola through these points will peak between x = 3 in and x = 7, though unless you have a very fine sense of the shape of a parabola your sketch might well peak somewhere to the right of x = 7. The peak of the actual parabola will occur close to x = 6, and the value at x = 7 will be just a bit greater than 8, perhaps 8.5 or so. If your peak was to the right of x = 7, your x = 5 value will be lass than 7.
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RESPONSE --> I'm not exactly sure what kind of answer you were wanting on this one. self critique assessment: 1
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14:45:19 `questionNumber 10000 `q005. Using your sketch from the preceding exercise, estimate the x coordinates corresponding to y coordinates 1, 3, 5 and 7. Also estimate the x values at which y is 0.
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RESPONSE --> The x coordinates coreesponding to each were: (1.5,1) (2.5,3) (3,5) (6,7). Y cannot be 0 because the curve does not pass through the origin. confidence assessment: 2
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14:52:41 `questionNumber 10000 `q006. Suppose the graph you used in the preceding two exercises represents the profit y on an item, with profit given in cents, when the selling price is x, with selling price in dollars. According to your graph what would be the profit if the item is sold for 4 dollars? What selling price would result in a profit of 7 cents? Why is this graph not a realistic model of profit vs. selling price?
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RESPONSE --> To find the profit if the item is sold at 4 dollars, then you sketch a line on x=4. This allows you to find the x value or the profit in cents, which is about 7. This graph is not a realisitic model because there are no real given profit numbers. confidence assessment: 2
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14:59:09 `questionNumber 10000 `q007. On another set of coordinate axes, plot the points (-3, 4) and (5, -2). Sketch a straight line through these points. We will obtain an approximate equation for this line: First substitute the x and y coordinates of the first point into the form y = m x + b. What equation do you obtain?
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RESPONSE --> When you substitute -3 in for x and 4 for y, you get the equation -3 m + b = 4 confidence assessment: 3
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15:00:49 `questionNumber 10000 `q008. Substitute the coordinates of the point (5, -2) into the form y = m x + b. What equation do you get?
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RESPONSE --> When you substitute (5,-2) into the equation you get 5 m + b = -2 confidence assessment: 3
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15:04:21 `questionNumber 10000 `q009. You have obtained the equations -3 m + b = 4 and 5 m + b = -2. Use the method of elimination to solve these simultaneous equations for m and b.
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RESPONSE --> Using the elimination method, we first, subtract the first equation by the second equation to obtain the solution of m= - 3 / 4. Then we substitute this value into the first equation to get the solution b= 7 / 4. To check the work substitute both solutions into the second equation. confidence assessment: 3
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15:06:59 `questionNumber 10000 `q010. Substitute your solutions b = 7/4 and m = -3/4 into the original form y = m x + b. What equation do you obtain? What is the significance of this equation?
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RESPONSE --> When you substitute m= - 3 / 4 and b= 7 / 4 into the original form, the equation you get is y= - 3 / 4x + 7 / 4. This is significant because it is the equation of the straight line that goes through the points (-3,4) and (5,-2). confidence assessment: 3
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15:07:28 `questionNumber 10000 end program
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RESPONSE --> OK self critique assessment: 1
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