#$&*
Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Graphing 10june13
** **
** **
Question `q001: Sketch a set of coordinate axes, with the x axis horizontal and directed to the right, the y axis vertical and directed upwards.
Sketch the point P = (-3, -1) on a set of coordinate axes.
Sketch the point you get if you shift this point -1 units in the horizontal direction. What are the coordinates of your point?
Sketch the point you get if you shift the original point 3 units in the vertical direction. What are the coordinates of your point?
Sketch the point you get if you move the original point 4 times as far from the x axis. What are the coordinates of your point?
If you move the original point 4 times as far from the x axis, then shift the resulting point -1 units in the horizontal direction, and finally shift the point 3 units in the vertical direction, what are the coordinates of the final point?
Your solution:
Confidence rating:
Given Solution:
Shifting the point -1 units in the horizontal direction we end up at the point (-3 + (-1), -1) = (-4, -1).
Shifting the point 3 units in the vertical direction we end up at the point (-3, -1 + ( 3)) = (-3, 2).
The point (-3, -1) is -1 units from the x axis.
If the point is moves 4 times further from the x axis, the y coordinate will become 4 * -1 = -4.
The x coordinate will not change.
So the coordinates of the new point will be (-3, -4).
If you then shift the resulting point -1 units in the horizontal direction, it will end up at (-3 + (-1), -4) = (-4, -4).
If you shift this new point 3 units in the vertical direction, it will end up at (-4, -4 + 3) = (-4, -1).
NOTE: We can express this sequence of transformations in a single step as
(-3 + (-1), 4 * -1 + 3) = (-4, -1).Question `q001: Sketch a set of coordinate axes, with the x axis horizontal and directed to the right, the y axis vertical and directed upwards.
Sketch the point P = (-3, -1) on a set of coordinate axes.
Sketch the point you get if you shift this point -1 units in the horizontal direction. What are the coordinates of your point?
Sketch the point you get if you shift the original point 3 units in the vertical direction. What are the coordinates of your point?
Sketch the point you get if you move the original point 4 times as far from the x axis. What are the coordinates of your point?
If you move the original point 4 times as far from the x axis, then shift the resulting point -1 units in the horizontal direction, and finally shift the point 3 units in the vertical direction, what are the coordinates of the final point?
Your solution:
Confidence rating:
Given Solution:
Shifting the point -1 units in the horizontal direction we end up at the point (-3 + (-1), -1) = (-4, -1).
Shifting the point 3 units in the vertical direction we end up at the point (-3, -1 + ( 3)) = (-3, 2).
The point (-3, -1) is -1 units from the x axis.
If the point is moves 4 times further from the x axis, the y coordinate will become 4 * -1 = -4.
The x coordinate will not change.
So the coordinates of the new point will be (-3, -4).
If you then shift the resulting point -1 units in the horizontal direction, it will end up at (-3 + (-1), -4) = (-4, -4).
If you shift this new point 3 units in the vertical direction, it will end up at (-4, -4 + 3) = (-4, -1).
NOTE: We can express this sequence of transformations in a single step as
(-3 + (-1), 4 * -1 + 3) = (-4, -1).
** **
If you started at (-3,-1) going up 4 units would would max be 3, please explain this too me.
self-critique rating
rating #$&*:
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#$&*
Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
11June13 1:29
** **
To eliminate b we will multiply the first equation by -7 and the second by 2, which will make the coefficients of b equal and opposite. The first step is to indicate the multiplications:
-7 * ( 58 a + 2 b) = -7 * -38
2 * ( 198 a + 7 b ) = 2 * (-128)
Doing the arithmetic we obtain
-406 a - 14 b = 266
396 a + 14 b = -256.
Adding the two equations we obtain
-10 a = 10,
so we have
a = -1.
** **
Why is -7, but the 2 on the outside stays positive?
@&
That's so you can add the two equations rather than subtracting, which when negative signs are already present can be an additional source of error.
*@
#$&*
Mth163
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
typo?11jun13 16:44
** **
The variable c is most easily eliminated. We accomplish this if we subtract the first equation from the second, and the first equation from the third, replacing the second and third equations with respective results.
Subtracting the first equation from the second, are left-hand side will be the difference of the left-hand sides, which is
2d eqn - 1st eqn left-hand side: (60a + 5b + c )- (2a + 3b + c ) = 58 a + 2 b.
The right-hand side will be the difference 90 - 128 = -38, so the second equation will become
new' 2d equation: 58 a + 2 b = -38.
The 'new' third equation by a similar calculation will be
'new' third equation: 198 a + 7 b = -128.
You might well have obtained this system, or one equivalent to it, using a slightly different sequence of calculations. (As one example you might have subtracted the second from the first, and the third from the second).
** **
** **
subtract the first equation from the second, and the first equation from the third, replacing the second and third ...Is this a typo? If not I am very confused
@&
The new' 2d equation is
58 a + 2 b = -38.
and the 'new' third equation is
198 a + 7 b = -128.
The first was obtained by subtracting the first equation from the original second equation, the third by subtracting the first equation the original third.
*@