course mth 272
7+7=14
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
Your solution, attempt at solution.
If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
020. ``q Query 20
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q Query 9.1.36 Ray MO U ray OM **** How do you express the intersection of the two rays?
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Your solution:
You would express it as MO because all of the elements on MO would be on OM.
Confidence Assessment:
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Given Solution:
`aSTUDENT SOLUTION:
The intersection of the two rays consists of the elements common to both sets, which would be MO.
However, a union symbol is used in the question and a union is composed of all the elements found in atleast one of the two sets, which would also be MO. **
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Self-critique (if necessary):
It would be he union of MO and OM
Self-critique Rating:
Question: **** `q Query 9.1.54 lines SR and TP intersecting at Q **** What are the names of the pairs of vertical angles for this figure?
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Your solution:
they would be < sqt and
Confidence Assessment:
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Given Solution:
`aSTUDENT SOLUTION:
The vertical angles are SQT and PQR; SQP and TQR **
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q Query 9.1.60 5x - 129 vert with 2x - 21 **** What is the value of x and how did you obtain it?
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Your solution:
if they are vertical then they are equal
5x-129= 2x-21
5x=2x+108
3x=108
x=36
Confidence Assessment:
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Given Solution:
`a *&*& Starting with 5x - 129 = 2x - 21 to get
3x - 129 = -21. Add 129 to both sides to get
3x = 108. Divide both sides by 3 to get
x = 36.
To check substitute 36 in for x in the equation and simplify, getting 51 = 51.
**** What equation did you solve to obtain x, and how did you get the equation?
Since the angles are vertical angles, they are equal to eachother, therefore, I set them up to be equal to eachother and then solved.To check myself, I then substituted my answer in for x on both sides of the equation to make sure they were equal.
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Self-critique (if necessary):
If angles are vertical then they are equal so set the equation up as equals and solve for the x
Self-critique Rating:
Question: **** `q Query 9.1.72 complement 10 deg less that 1/5 of suppl **** What is the measure of the angle and how did you get it?
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Your solution:
the complement is 90-the angle and the supplement is 180-angle and the angle is x so you would have 180-x for the supplement and 90-x for the compliment
90-x = 1/5( 180-x) -10
multiply by 5 because of the 1/5 450-5x= 180-x-50
450-5x=180-x-50
450-5x=130-x
-4x= -320
x= 80
Confidence Assessment:
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Given Solution:
`aLet x be the degree measure of the angle. Then the supplement is 180 – x; 10 deg less than 1/5 the supplement is 1/5(180 - x) – 10. The complement is 90 - x.
So the equation is
90 - x = 1/5(180 - x) – 10. Multiplying both sides by 5 we get
450 – 5 x = 180 – x – 50 so that
450 – 5 x = 130 – x. Adding x – 450 to both sides we get
-4x = -320 so thatx = 80.
The complement of 80 deg is 10 deg.
The supplement of 80 deg is 100 deg; 1/5 the supplement is 1/5 * 100 deg = 20 deg, so the complement 10 deg is 10 deg less than the supplement 20 deg. **
**** What equation did you solve to obtain the measure of the angle?
Student Response: I determined which equations represented the degree measure of the angle, complement, and supplement. I then substituted those in the equation using the worded problem.
90 - x (complement) = 10 (10 less than) - 1/5 (1/5 of the supplement) 180 - x (supplement).
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Self-critique (if necessary):
if you know that the compliment is 90-x and the supplement is 180-x then you substitute it in the problem in addition to the info you are provided
Self-critique Rating:
Question: **** `q Query Add comments on any surprises or insights you experienced as a result of this assignment.
The `q Query was basically what I expected it to be.
I didnt have any problems on this assignment
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If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
Your solution, attempt at solution.
If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
021. ``q Query 21
Liberal Arts Mathematics II
Asst # 21
03-25-2003
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q Query 9.2.6 sq must be rhombus **** Is the statement true or false and why?
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Your solution:
true a square must be a rhombus because it has all sides equal
a square has all sides equal and the angles are right angles
a rhombus has all sides equal but no right angles
Confidence Assessment:
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Given Solution:
`aThis statement is true.
A parallelogram is a quadrilateral with two pairs of parallel sides and a rhombus is a parallelogram with all sides having equal length. All sides of a square have equal length. If a square were not a rhombus then all sides would not be of equal length.
It is not true that a rhombus must be a square. The angles of a rhombus do not have to be right angles, while the angles of a square do. **
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Self-critique (if necessary):
the difference in a rhombus and a square is that a square has all right angles
Self-critique Rating:
Question: **** `q Query 9.2.10 parallelogram must be rect and rect must be parallelogram **** Is the statement true or false and why?
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Your solution:
a rectangle is a parallelogram because it has two pairs of parallell sides but it has four right angles
a parallelogram does not always have four right angles so false
Confidence Assessment:
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Given Solution:
`aA rectangle is a parallelogram but a parallelogram is not necessarily a rectangle, so the statement is false. **
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Self-critique (if necessary):
a rectangle has 4 right angles and a paralleogram does not always have this feature
Self-critique Rating:
Question: **** `q Query 9.2.18 rb with 4 loops **** Is the curve simple, closed, both or neither?
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Your solution:
It is closed because you can draw 4 loops without taking your pencil off the paper but you will draw through some of the lines
Confidence Assessment:
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Given Solution:
`a This is only a closed curve because its starting point and ending point are the same and it can be drawn without lifting the pencil from the paper. It is not simple because some points are passed through twice.
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Self-critique (if necessary):
to be simple you cant pass through any points more than once and you cant take your pencil off the paper but to be closed you just have to have the same start and finish without taking your pencil off
Self-critique Rating:
Question: **** `q Query 9.2.24 ellipse **** Is the region inside the curve convex or not, and why?
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Your solution:
convex
an ellipse is like a circle so it is roundish and if you draw a line it woud be inside no matter where you start it
Confidence Assessment:
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Given Solution:
`a The region inside is convex because the line segment connecting any two points is completely inside the figure.
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Self-critique (if necessary):
to be convex any 2 points on a line segment have to be inside the figure
Self-critique Rating:
Question: **** `q Query 9.2.48 A 30 deg more than B which equals C **** What are the measures of the three angles?
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Your solution:
angles have to equal 180 so if a is 30 more than b and b = c then
a= 30+b b=c let x be b and c a=x+30
x+x+30+x=180 3x+30=180
3x=150
x=50 a=80 b= 50 c=50
Confidence Assessment:
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Given Solution:
`a Angle A + Angle B + Angle C = 180 deg. If x is the degree measure of B then angle A has measure x + 30 degrees and angle C has measure x degrees. So we have
x + x +30 + x = 180
3x + 30 = 180
3x = 150
x = 50
Angle B and Angle C are both equal to x, i.e., to 50 deg.
Angle A = 50 deg + 30 deg = 80 deg
To check, 80 + 50 + 50 = 180.
**** What equation did you solve to obtain your answer, and how did you use the solution to determine all angles?
Student Response: The definition for the angle sum of a triangle says the sum of the measures of the angles of any triangle is 180 deg.
I used x to represent angles B and C and x + 30 to represent angle A since it is 30 deg higher than the other two. All this equaled 180 deg. I solved for x to get the degree measure of angles B and C and then added 30 on to x to get the degree measure for angle A.
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Self-critique (if necessary):
all angles when added are 180
Self-critique Rating:
Question: **** `q Query Add comments on any surprises or insights you experienced as a result of this assignment.
There were no really big surprises.
I understood this assignment
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If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.
Your solution, attempt at solution.
If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
022. ``q Query 22
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q Query 9.3.12 area of parallelogram **** What is the area of the given parallelogram and how did you obtain it?
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Your solution:
to find the area of a parallelogram you need to find the base and height the length is the base but the height is the width and you multiply Area = base * heigth
Confidence Assessment:
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Given Solution:
`a The formula for the area of a parallelogram is
A = bh ( area = base times height)
From the figure the base is 4 and the altitude is 2.5 so we have
A = 4 * 2.5 = 10.
The area is 10 in.
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Self-critique (if necessary):
I did not see a diagram but if you have a base of 4 and a height of 2.5 then the area would be 4* 2.5= 10
Self-critique Rating:
Question: **** `q Query 9.3.18 area of trapezoid **** What is the area of the given trapezoid and how did you obtain it?
The formula for finding the area of a trapezoid is A = 1/2h ( b + B )
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Your solution:
a trapezoid is half of a parallelogram so the formula is area = 1/2 of the height * (short base + long base)
I do not see any diagram for this problem
Confidence Assessment:
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Given Solution:
`a h = 3, b = 4, B = 5
A = 1/2 (3) (4 + 5)
A = 1/2 (3) (9)
A = 1/2 (27)
A = 13.5
The area is 13.5
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Self-critique (if necessary):
if the height is 3 and the short base is 4 and the long base is 5 then
area = 1/2 (3) *(4+5)
1/2 ( 27)
13.5
Self-critique Rating:
Question: **** `q Query 9.3.24 dim of rect with lgth 20 more than wdth and perimeter 176 **** What are the dimensions of the rectangle?
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Your solution:
the perimeter is P=2(length)+ 2(width)
176= 2( 20+x) + 2(x)
176=40+2x+ 2x
176=40+4X
136= 4x
x= 34
if the length is 20 more then width then the lenght is 54 and the width is 34
Confidence Assessment:
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Given Solution:
`aThe perimeter of a rectangle is P = 2l + 2w, where l and w are length and width.
From the given information
Length = 20 + w
Perimeter = 176
This gives us the equation
176 = 2 (20 + w) + 2w
which we proceed to solve for w:
176 = 40 + 2w + 2w by the Distributive Law. Simplifying we get
176 = 40 + 4w
Subtract 40 from both sides to get
136 = 4w
Divide both sides by 4 to get
w = 34
l = w + 20 so
l = 34 + 20 = 54
We have
Length = 54 and
Width = 34
Checking, we have perimeter = 2 * length + 2 * width so we should have
176 = 2(54) + 2(34).
The right-hand side does give us 176 so the solution checks out. **
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Self-critique (if necessary):
perimeter =2l+2w
Self-critique Rating:
Question: **** `q Query 9.3.48 trap bases x, x+4 alt 3 area 30 **** What is the value of x?
The formula for finding the area of a trapezoid is A = 1/2h ( b + B). We have
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Your solution:
30=area x=short base x+4=long base 3=height
30= 1/2(3) * (x+x+4)
30= 1/2(3)* (4+2x)
30= 1/2(12+6x)
30=6+3x
24=3x
x=8
Confidence Assessment:
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Given Solution:
`a A = 30
h = 3
B = x + 4
b = x
30 = 1/2(3) ( x + x+4)
30 = 1.5 ( x+x+4)
30 = 1.5x + 1.5x + 6
30 = 3x + 6 Subtract 6 from both sides
24 = 3x Divide both sides by 3
x = 8
The answer is 8.
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Self-critique (if necessary):
area= 1/2height* (short base+ long base)
Self-critique Rating:
Question: **** `q Query 9.3.54 $60 to paint ceiling of 9 x 15 rm, how much to paint if dimensions 18 x 30 **** What is the cost for the second ceiling? **** How did you use the results of exercise 53 to obtain your result?
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Your solution:
if length of each side of a rectangle is multiplied by x then the area is multiplied by x^2
so if the lengths multiplied by 2 then the area is 2^2=4
60*4=240 240 dollars
Confidence Assessment:
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Given Solution:
`a The sides doubled from 9 ft. to 18 ft. and from 15 ft. to 30 ft. When the sides are doubled the area increases by a factor of 4. So the cost is
$60 * 4 = $240
The cost for the second ceiling is $240
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Self-critique (if necessary):
if your length of the rectangle is multiplied by n then the area is multipled by n^2
Self-critique Rating:
Question: **** `q Query 9.3.60 triangle alt 9 on top of 10 x 4 rect; parallelogram alt 3 under **** What is the area of the given figure and how did you obtain your result?
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Your solution:
area of triangle= 1/2 (10)*9
1/2*90=45 for triangle
rectangle area= length*width
10*4= 40
parallelogram area= base*height
3*10=30
if all of these figures are connected tehn you must add them together so
45+40+30= 115 area
Confidence Assessment:
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Given Solution:
`aHere's a solution by a student from a previous semester:
I found the area of each figure and then added those three results together.
Area of Triangle = 1/2bh
A = 1/2 (10) (9)
A = 1/2 (90)
A = 45
Area of Rectangle = lw
A = (10) (4)
A = 40
Area of Parallelogram = bh
A = (10) (3)
A = 30
45 + 40 + 30 = 115
Area = 115 **
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Self-critique (if necessary):
yoiu must find sthe area of each figure and then add them together
Self-critique Rating:
Question: **** `q Query 9.3.67 26 m diam circle inscribed in sq; area outside circle **** What is the area of the shaded region and how did you obtain it?
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Your solution:
the radius is 1/2 of diameter so radius is 13 area of circle = pi*r^2 3.14*13^2
3.14* 169 = 530.66 m^2
area of square= side^2 26^2= 676 m^2
since the area of the square is counting the circle and everything then you must subtract the circle
676- 530.66= 145.34 m^2
Confidence Assessment:
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Given Solution:
`aThe circle has diameter 26 m so its radius is 13 m and its area is
A = pi r^2 = pi * (13 m)^2 = 169 pi m^2 = 531 m^2.
The area of the square is the square of its side
A = (26 m)^2 = 676 m^2.
The area of the shaded region is the difference
}
676 m^2 - 531 m^2 = 145 m^2. **
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Self-critique (if necessary):
you must find the area of the circle then the square and subtract the two to find the area of the shaded region
Self-critique Rating:
Question: **** `q Query 9.3.72 10, 12, 14 in pizzas for 11.99, 13.99, 14.99 **** Which pizza is the best buy and how did you
obtain your result?
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Your solution:
area= pi*radius^2 3.14(5)^2= 3.14* 25= 78.5 11.99/78.5= $0.15
3.14(6)^2= 3,14*36= 113.04 13.99/113.04= $0.12
3.14(7)^2= 3.14*49= 153.86 14.99/153.86= $0.10
the cost per square inch tells you that the 14 inch pizza is the best deal at 10 cent per inch
Confidence Assessment:
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Given Solution:
`a Student Solution: The thickness is about the same for all three pizzas so the amount of pizza can be measured by its area. I therefore found the area of each.
A = 3.14 * r^2 and radius is 1/2 the circumference. So we get areas
A = 3.14 (5)^2 = 78.5
A = 3.14 (6)^2 = 113.04
A = 3.14 (7)^2 = 153.86
I then divide the prices and these answers to get the price per square inch.
$11.99 / 78.5 = 15.3
$13.99 / 113.04 = 12.4
$14.99 / 153.86 = 9.7
Since 9.7 is the least, and since this is the result for the 14 inch pizza, the 14 in. pizza for $14.99 is the best buy.
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Self-critique (if necessary):
you must find the area of each pizza then divide by the cost of the pizza to see how much each inch costs. Then compare price per inch to see what is cheaper
Self-critique Rating:
Question: **** `q Query Add comments on any surprises or insights you experienced as a result of this assignment.
There weren't any big surprises.
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