Friday, November 30, 2012

Test on Rational Number World Problems Question 1

1. A car uses fuel at a rate of 10.2L/100 km while travelling at 90 km/h. At this rate of fuel consumption, how many litres of fuel would the car use if it travels 480 km? Express your answer to the nearest tenth of a litre.

10.2L/100km = ______/480 km

How man litres of fuel would the car use if it travels 480 km?
Express your answer to the nearest tenth of a litre.
10.2L/100 km = 49.0L/480

480 litres of fuel is being used for 480 km.



Thursday, November 29, 2012

Transformation: Rotation


Order of Rotation
Its how many times a shape/image rotates before it finishes a rotation.
360° / 4 = 90°
360° / 2 = 180°
90° angle turns = order of rotation 4
180° _________ = ________ 2
If you divide 360° by the Order of Rotation, we get the angle at which we made our turns.

What is the Angle of Rotation?
It’s the minimum degree of the angle of our turns in one full rotation.

Rotation Symmetry
It has to have a center of rotation
When you turn/ rotate the image, at least part of the image has to fit on top of another part.
It has to have an order of rotation greater than 1.

Center of Rotation
Center of the image or shape that the image or shape has to rotate around.
The number of times an image reflects upon itself by rotating, before finishing one full rotation.

Sunday, November 25, 2012

Textbook Page 80 Question 22


The hypotenuse of an isosceles right triangle has a length of 20cm. What is the length of each leg of the triangle? Provide your answer to the nearest tenth of a centimeter.
The side length of each leg of the triangle is 14.1 cm.

Practice Test: Question 19 pg 85

Question 19: Ron buys 75 shares in a car company. A year later, he sells the shared for $15.64 each. The result is a loss of $260.25. How much did Ron pay for each share? State any assumptions you make.




Answer: For each share, Ron paid $19.11.










Textbook Page 80 Question 21


 A baseball diamond is square area of about 750m2. 
 what is the distance from first to second base. Give 
 your answer to the nearest tenth of a metre.


The distance from first base to second base is 27.4m.


Wednesday, November 21, 2012

Textbook: Page 81, Question 32

32. The total area of the shape is 52 centimetres squared. What is it's perimeter?

- I found the answer by dividing 52 by 2, which gets me 26. I did this to put the two squares at the side away to let me see the rectangle in the middle.

- I know that the rectangle's perimeter is 10, so I finish the equation by adding ten, getting me to 36, which is the answer.

Textbook: Page 81: Question 33








Textbook: Chapter 2.4 Page 79 Question 16

16 a) The label on a 1-L can of paint states that the paint will cover an area of 10m². What is the length of the largest square area that the paint will cover? Express your answer to the nearest hundredth of a metre.

You just squareroot using a calculator

√10m²= 3.16227766
          = 3.16m
Round of to the nearest hundredth of a metre.

b) what is the side length of the largest square area that a 3.79-L can of the same paint will cover? Express your answer to the nearest hundredth of a metre.

First off I rounded 3.79 to 3.80.

Then multiply 3.80 by 10

3.80x10 = 38
√38 = 6.164414003 round of to the nearest hundredth
       = 6.16m

c) Nadia is applying two coats of paint to an area that is 4.6m by 4.6m. How much paint will she use if she applies the same amount of paint for each coat? Express your answer to the nearest tenth of a litre.

4.6x4.6= 21.16
 21.16x2 = 42.32
42.32 ÷ 10 = 4.232 round to the nearest tenth of a litre
                  = 4.2L




Tuesday, November 20, 2012

Textbook pg 80 question 30


 



A square field has an area of 1000 m2. Laura wants to walk from one corner of the field to the opposite corner. If she walks at 1.5 m/s, how much time can she save by walking diagonally instead of walking along two adjacent sides? Express your answer to the nearest tenth of a second.

First you would find what the side length of the square is:


Now that you know its 63.24 s walking along the two sides you need to find the diagonal way.






Now you subtract both of them so you can find the difference. Then you have to divide 18.53 by 1.5
which is             
              12.353 because you know Laura walks 1.5 m/s.



The answer is:
If Laura walks diagonally instead of walking the two whole sides, she saves 12.3 s


 

Textbook Pg. 79, #17

My Question:

Some parks contain fenced gardens. Suppose that it costs $80 to build each metre of fence, including materials and labour. 

a) How much does it cost to enclose a square with an area of 120 m²? Express your answer to the nearest dollar.

b) Predict whether the total cost of enclosing two squares with an area of 60 m² each is the same as your answer for part a).

c) Test your prediction from part b) and describe your findings.

part a) The first step is trying to find the square root of 120 by using a calculator. The square root is also the same value as one side of the square garden.

√120 = 10.95

Because there are 4 sides in a square, you need to multiply 10.95 by 4.

10.95  x 4 = 43.8

Then, you need to multiply the number above by $80 to the the final answer.

43.8 x $80 = $3504

The cost of enclosing a square with an area of 120 m² is $3504

part b) Following the same procedure we used for part a), find the square root of one square with an area of 60 m²

√60 = 7.74

7.74 x 4 = 30.96

30.96 x 80 = 2476.8

And because we are finding the area of two 60 m² fenced gardens, multiply that previous answer by two.

2476.8 x 2 = $4953.6

As you can see, the results are Not The Same.

c) I predicted that the costs for the fenced gardens would not be the same because two 60 m² squares have a total of 8 sides, and a 120 m² only has four sides, therefore I knew that the area would of the 60 m² would be larger because of the greater amount of sides.


Textbook page 80 #28




Textbook Page 79 #20


20. Leon's rectangular living room is 8.2 m by the 4.5 m. A square rug covers 2/5 of the area of the floor. What is the side length of the rug, to the nearest tenth of a metre.

I first find the area of the living room.

A=  l x w
A = 8.2 (4.5)
A= 36.9

Then, I find 40% of the area of the living room (36.9m). I got 40% because 2/5 is equivalent to 40%. 40% of the area of the living room is 14.7. I got to this answer by:

0.40 x 36.9= 14.7

I then find the side length of the rug by getting the square root of 14.7 which equals 3.82.

A= l x w
√14.7 = 3.82

The side length of the rug is 3.82 m.


Monday, November 19, 2012

Textbook question 31 a)

31.

The area of a triangle can be determined using Heron's formula, which requires the side lengths of the triangle.
Heron's formula is A=√s(s-a)(s-b)(s-c). In the formula A is the area; a,b and c are the side lengths; and s is half the perimeter or a+b+c.
                                                          2
Determine the area of each triangle with the following side lengths. 
                                  
Express each area to the nearest tenth of a square centimetre.

a) 15cm, 12cm, 10cm

A=√s(s-a)(s-b)(s-c)

A=area

a,b,c=side lengths

s= half the perimeter  

-------------------------------------------------

15+12+10=37 

                =37/2

                =18.5

√18.5(18.5-15)(18.5-12)(18.5-10)

 

√18.5(3.5)(6.5)(8.5)

 

√18.5(22.75)(8.5)

 

√18.5(193.375)

 

√3577.4375

 

A= 59.81168364 

we have to round it to the nearest tenth of a square centimetre. 

so it's going to be 59.8cm2 

 

Textbook: Chapter 2.4 page 81, Question 34


























2.4 Textbook Question 24






For this question I had to find the distance of how much a person can see across the ocean to the horizon. I know that in order to find the distance you have to find the square root of 12.74 x h. The height is how much the person's eyes are above the water.

~First I re - wrote the formula.
~Then I found out the height of how much meters Adele's eyes are above the water which was 4.1 m.
~Next I multiplied 12.74 x 41. Then I got the answer of 52.234.
~Lastly now I have to find the square root of 52.234, so I got the answer of around 7.2273 km. Then I rounded my answer to 7.20 km.





In this question it is very similar to the first one. The only thing different I have to do in convert the height  which was 165 cm into m. I did this by dividing 165 by 100 because there is 100 cm in 1 meter.

First I re - wrote the formula.
Then I found the height that Brian was above the water, which was 165 cm then converted in 1.65 m.
Then I finally multiplied 12.74 by 1.65 and got the answer of 21.021.
Lastly I found the square root of 21.021 and I got around 4.5848 km, and rounded this answer to 4.6 km.




In this question I converted the height of Yvonne's eyes above the water into meters by multiplying 5 ( The height in km. ) by 1000 because there is 1000 meters in 1 kilometer.

First I re - wrote the formula.
Then I found the height that Yvonne's eyes were above the water, which was 5 km then I converted it to 5000 m.
Then I multiplied 12.74 by 5000 and got a product of 63700.
Lastly I found the square root of 63700 and got an answer of around 252.2885 km and then I rounded it to 252.4 km.

Textbook 79, Question 19

A square picture with an area of 100cm² is mounted on a square piece of matting. The matting has 2.5 times the area of the picture. If the picture is centered on the matting, what width of matting is visible around the outside of the picture. Give your answer to the nearest tenth of a centimeter.

So we know that the picture in the middle is 100cm²

So I if we find out what 100cm² x 2.5 is we get 250. Now we need to find the square root of 250 which we get 15.8cm.

 The space between the 10cm and 15.8cm line is 5.8cm
if we move the square in the middle to the very center, that is like splitting that space in half, so 5.8÷2 you get 2.9cm








Chapter 2.4 Page 80 Question 29


You would replace 't' by 30 and (-20) and solve such as the following:



Then you would find the difference:


Lesson Today 11/19/12

In today's Math class we found out how square roots work.
Examples that was given by Mr. Backe are:

√121=11               √81 =9                         √36=6


√12.1 ≠1.1  because if you use a calculator the answer will be 3.48. But if you estimate it, the easy way to figure it out is to find the closest perfect square in this case √12.1 is close to √9 and √16. Then you find out the distance between √9 and √16 and it will be 7 so the answer will be close to 3 and 3/7. Which is 3.428.

The same thing will happen for √8.1 and √3.6. But √8.1 ≠0.9 and √3.6 ≠0.6, and √3.6 equal to 1.897 and √8.1 equals to 2.846

Here are the other examples:

√1.21=1.1                   √0.81=0.9              √0.36=1.6
√0.121=0.348             √0.081=0.2846      √0.036=0.1847
√0.0121=0.11             √0.0081=0.09        √0.0036=0.06
√0.00121=0.0348

You might realize that there is a pattern. And the pattern is that even amount of even numbers are perfect squares and the ones that have odd amount of decimals are surds. They move one place value.

11²= 11x11=121
1.1²= 1.1x1.1= 1.21
 0.11²= 0.11x0.11= 0.0121

Those are perfect squares.

Another thing we learned is to know how to square root a fraction.

25=    √25  = 5
   49      √49      7

 √64  =  8
  81      9


36 = 2     √36 = √4=2
   9               9

Homework:
Textbook: pg 72-77
Do Practise: 6,7,9,10,11,13,14
Apply: 15,16,17,18,19,20,22,24,25,27,28,30,31
Extend Any 2 plus 36

Textbook - Chapter 2.4 Page 79 Question 18

A frame measures 30 cm by 20 cm. Can you mount a sqaure picture with an area of 500 cm² in the frame? Explain.
 
√500 = 22.36 cm

Picture = 22.36 cm
Frame = 30 cm x 20cm
No you cannot mount a square picture on the frame because one side of the picture is too big for the frame so it won't fit.

Textbook: Chapter 2.4 page 81, Question #36


Question: Determine √√√65 536

1. √65 536 = 256
√65 536 is a perfect square because when you multiply 256 x 256, it equals 65 536.
√65 536 = 256 x 256

2. √256 = 16
√256 is a perfect square because when you multiply 16 x 16, it equals to 256.
√256 = 16 x 16

3. √16 = 4
√16 is a perfect square because when you multiply 4 x 4, it equals to 16.
√16 = 4 x 4


  • Since there are three square root signs (radicals), that means you keep square rooting the given number three times.
  • The final answer of √65 536 should be 4.



Here is a picture of perfect squares:



















URL: http://www.math.com/school/subject1/images/S1U1L9DP3.gif

Textbook: Chapter 2.4 page 80 Question 25

25.) What is the length of the longest line segment you can draw on a sheet of paper that is 27.9 by 21.6? Express your answer to the nearest tenth of a centimeter.

1.) First you would need to square both the numbers.

27.9 cm² = 778.41

21.6 cm² = 466.56

2.) Add them together.


778.41 cm² + 466.56 cm² = 1,244.97

3.) Find the square root of 1,244.97


1,244.97 = 35.28 cm

4.) Round to the nearest tenth of a centimeter.

35.28 cm rounded to the nearest centimeter would be 35.3 cm.


The length of the longest line segment would be 35.3 cm.



Textbook: Chapter 2.4 page 79

14. Given the area of square, determine its side length. Express your answer to the nearest hundredth of a unit.

      a) 0.85 m²                       b) 60 cm²
 





Textbook: Chapter 2.4 Page 80 Question #26

26. A bag of fertilizer will cover an area of 200m. Determine the dimensions of a square that 3/4 of a bag of fertilizer will cover. Express your answer to the nearest tenth of a metre.

 


















So, the dimensions of a square that 3/4 of a bag of fertilizer will cover are 12.2m by 12.2m. 


Link

  

Textbook- Chapter 2.4, Page 79, Question # 15

Kai needs to replace the strip of laminate that is glued to the vertical faces on a square tabletop.
The tabletop has an area of 1.69 m². What length of laminate does she need?















SOLUTION:

Area of a square = Side x Side (length x width)

A = 1.69 m²


Length = area of square

L = 1.69 m²

L = 1.3 m   


Verify:  1.3² = 1.3 m x 1.3m
                     =  1.69 m²



SSA:  The length Kai needs for the laminate is 1.3 m long.

Tuesday, November 6, 2012

question pg.69 #14

Question: Li and Ray shared a vegetarian pizza which was cut into eight equal pieces and the Hawaiian pizza into six equal pieces. Li ate two  slices of vegetarian pizza and one slice of Hawaiian pizza. Ray ate two slice of Hawaiian pizza and one slice of vegetarian pizza.

A) Who ate more pizza?

  Ray ate more because:

Li: Veggie pizza- 2/8 and Hawaiian pizza 1/6

Ray: VP- 1/8 and Hawaiian pizza 2/6

I found the lowest common denominator for 6 and 8. Which was 24.
Then also multiplied the numerator with the same number which I multiplied with the denominator.

Li:  VP   2/8 x 3/3 = 6/24
    
       HP   1/6 x 4/4 = 4/24
 4/24 + 6/24= 10/24

Ray: VP  1/8 x 3/3= 3/24

        HP  2/6 x 4/4 = 8/24
3/24+ 8/24= 11/24

Also 6ths are much bigger pieces than 8ths so if you had more sixths you probably had more pizza because they were bigger pieces.

B) How much more pizza did that person eat?

1/24


C)  How much pizza was left over?

13/24 or 5/8 of veggie pizza and 3/6 of Hawaiian pizza.












Monday, November 5, 2012

Textbook: Page 70 Question 22

22. Taj has three scoops for measuring flour. The largest scoop hold 2 1/2 times as much as the smallest one. The middle scoop holds 1 3/4 as much as the smallest one.

Describe two different ways in which Taj could measure each of the following quantities. He can use full scoops only.

a) 3 1/4 times as much as the smallest scoop holds

b) 1/2 as much as the smallest scoop holds

                                                                                                                                                      

Before we can find out what what the other cups are we need to find out what the smallest cup is.

Smallest cup = X.... So 2 1/2 ÷ X = 2 1/2 or 1 3/4 ÷ X = 1 3/4.
X = 1
Smallest cup = 1
Large cup = 2 1/2 or 5/2
Medium cup = 1 3/4 or 7/4

ANSWER..
a) First way: 1 large scoop + 1 medium scoop - 1 small scoop
            
Second way: 2 large scoop - 1 medium


ANSWER
b) First Way: 1 large scoop - 2 small scoop


Second Way: 2 medium scoops - 3 small scoop


Textbook: Page 61 Question 18


18. Determine the mean of each set of numbers. Express your answer to the nearest hundredth, if necessary.

a) 0, -4.5, -8.2, 0.4, -7.6, 3.5, -0.2

To determine the mean, I first add all the numbers together:
0 + -4.5 + -8.2 + 0.4 + -7.6 + 3.5 + -0.2= -16.6

I then divide the sum with how many numbers I used to add it with.

-16.6/7= -2.37

b) 6.3, -2.2, 14.9, -4.8, -5.3, 1.6


6.3 + -2.2 + 14.9 + -4.8 + -5.3 + 1.6= 10.5

10.5/6= 1.75




Textbook: Page 60, Question 12

12. A pelican dives vertically from a height of 3.8 m above the water. It then catches a fish 2.3 m underwater.

a) Write an expression using rational numbers to represent the length of the pelican's dive.

- 3.8 - ( -2.3) because 3.8 represents the height above the water the pelican is at and 2.3 represents how deep the the fish underwater is.

b) How long is the pelican's dive?

- The pelican's dive is 6.1 m because you add the two numbers together (3.8 and 2.3), which is the pelican's dive altogether (it dove 3.8 above water and 2.3 underwater).

Sunday, November 4, 2012

Textbook (pg.68, #11)

In everyday speech, in a jiffy means in a very short time. In science, a specific value sometimes assigned to a jiffy is 1/100 s.
Naima can type at 50 words/min. On average, how many jiffies does she take to type each word.


She takes up to 120 jiffies to type each word.
Please make any suggestions. This was kind of rushed.

Textbook- Page 69: Question 15

15) Predict the next three numbers in each pattern.

A) -1 1/2, -7/8, -1/4, 3/8, 1, 1 5/8, 2 1/4, 2 7/8

B) 1 1/3, -2/3, 1/3, -1/6, 1/12, -1/24, 1/48, -1/96

Textbook - Page 68: Question 12

12. In the table, a positive number shows how many hours the time in a location is ahead of the time in London, England. A negative number shows how many hoursthe time is behind the time in London.

A) How many hours is the time in St. John's ahead of the time in Brandon

St. John's: -3 1/2
Brandon: -6

-3.5 - (-6) = 2.5 hours

B) How many hours is the time in Victoria behind the time in Mumbai?

Victoria: -8
Mumbai: +5 1/2

+5.5 - (-8) = 13.5 hours

C) Determine and interpret the time difference between Tokyo and and Kathmandu.

Tokyo: +9
Kathmandu: +5 3/4

+9 - (+5.75) = 3.25
Tokyo is  3.25 hours ahead of Kathmandu.

D) Determine and interpret the time difference between Chatham Islands and St. John's.

Chatham Islands: +12 3/4
St. John's: -3 1/2

+12.75 - (-3.5) = 16.25
Chatham Islands is 16.25 hours ahead of St. John's.

E) In which location is the time exactly halfway between the times in Istanbul and Alice Springs?

Istanbul: +2
Alice Springs: +9 1/2

9.5 + 2 = 11.5
11.5 / 2 = 5.75

Kathmandu: +5 3/4

Kathmandu is location with the time that is exactly halfway between istanbul and Alice Springs.

Textbook: Page 62: Question 28