course MTH 163
id: qa pc1
001.
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Question: `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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Your solution:
3a + 3b = 9 [Mult. by -2]
-6a - 6b = -18
6a + 5b = 16
-6a - 6b = -18 [Subtract equations]
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0a - 1b = -2
b = 2
3a + 3(2) = 9 [Simplify]
3a + 6 = 9
3a = 6 [Divide by 3]
a = 2
Confidence rating: -[3]-
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q002. Solve the following system of simultaneous linear equations using the method of elimination:
4a + 5b = 18
6a + 9b = 30.
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Your solution:
4a + 5b = 18 [Common Factor of 12, Mult. by -3]
-12a - 15b = -54
6a + 9b = 30 [Mult by 2]
12a + 18b = 60
12a + 18b = 60 [Subtract equations]
-12a - 15b = -54
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0a + 3b = 6 [Divide by 2]
b = 2
4a + 5b = 18
4a + 5(2) = 18
4a + 10 = 18
4a = 8
a = 2
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q003. If y = 5x + 8, then for what value of x will we have y = 13?
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Your solution:
y = 5x + 8
13 = 5x + 8
5 = 5x
1 = x
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q004. Sketch a set of coordinate axes representing y vs. x, with y on the vertical axis and x on the horizontal axis.
*Plot the points (1, -2), (3, 5) and (7, 8).
*Sketch a smooth curve passing through these three points.
On your curve, what are the y coordinates corresponding to x coordinates 1, 3, 5 and 7? Estimate these coordinates as accurately as you can from your graph.
Retain your sketch for use in future questions.
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Your solution:
8 D
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5 D
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-01=3===7==0
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2D
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x y
1 -2
3 5
5 7
7 8
Confidence rating: -[3]-
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `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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Your solution:
8 D
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5 D
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-01=3===7==0
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2D
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x y
1.5 1
2 3
3 5
6 7
Confidence rating: -[3]-
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `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:
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Your solution:
*What would be the profit if the item is sold for 4 dollars?
Between 6 and 7 Cents
*What selling price would result in a profit of 7 cents?
Around 6 Dollars
*Why is this graph not a realistic model of profit vs. selling price?
Because the higehr you sell an item the less profit you gain, the logic for this should be the other way around: The more you sell an item for the more Profit you gain. Also, it starts to decay enough towards the top and head back downward in profit even as the price continues to rise.
Confidence rating: -[3]-
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `q007. On another set of coordinate axes, plot the points (-3, 4) and (5, -2). Sketch a straight line through these points.
We will proceed step-by-step 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 when you make this substitution?
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Your solution:
y = mx + b
4 = m(-3) + b
4 = -3m + b
Confidence rating: -[3]-
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `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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Your solution:
y = mx + b
-2 = 5m + b
Confidence rating: -[3]-
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution:
Self-critique Rating: OK
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Question: `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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Your solution:
-3m + b = 4
-5m - b = 2
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-8m = 6
m = -3/4
-3(-3/4) + b = 4
9/4 + b = 4
b = -7/4
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Self-critique (if necessary): OK
Self-critique Rating: OK
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Question: `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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Your solution:
y = -3/4x + 7/4
This equation can be used to determine that the points do in fact run through the graph that the equation creates.
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