Power To A Power Law

When a power is raised to an exponent simply multiply the two exponents together to get a new power.

Power Of A Product Law

When a product is raised to an exponent you can re-write each number in the product to the same exponent.

Product Of A Quotient Law

When a quotient is raised to an exponent you can re-write each number in the quotient with the same exponent.

Anything to the exponent 0 is 1

Anything to the exponent 1 is to itself

1 to any exponent is 1

If there is a negative exponent in the numerator or in the denominator just simply flip it to turn it into a positive.

These are what these numbers are called when they are written like this.

Here is the question we did using BEDMAS

HW

All 3.4 textbook work

Melanie's Test Question #5

The question I was given:

To solve this question, you should know the rules of BEDMAS.

B rackets

E xponents

D ivision

M ultiplication

A ddition

S ubtraction

* Always work from left to right.

Using the rules of BEDMAS, I knew that I had to do the division part of the question first.

In order to do long division with decimals, you must change the decimals to whole numbers. The number of decimal places you move the decimal of the divisior, you must do the same to the dividend.

Now, you can use long division to figure out (-56) divided by 20. This game me an answer of 2.8.

The next step would be the multiplication.

Next, simply multiply the two decimals.

Please ignore the fact that I forgot the negative sign before 5.78.

Now that I have solved both the division and multiplication portions of the equation, I am left with:

To do the last step of this problem, what I did was use integer chips just to make it easier for myself. Then I subtracted 2.8 from 5.78. This gave me 2.98.

Homework:

-Chapter 3.1 and 3.2

-Get on Mangahigh

**I apologize for not having any colour on my post, for some reason I wasn't able to change the colours.

Question # 2- JohnChua

write an example of a rational number in a/b form.

A. the number has a value greater than -6 and a denominator greater than -3

Why?

because negative 5 is greater than negative 6 and negative 2 is greater than negative 3

B.the number is greater than zero and has a numerator less than the denominator

C.The number is between 1.4 and 1.5 with a denominator less than zero

Why? because -145 over -100 is between the two number and is less than zero, it is between because it has 2 negative sign which is positive, therefore in between.

Question # 3 - Ryan Bautista

# 3 Hakim and Joe bought a large pizza. They split it in half. Joe ate 7/10 of his half. Hakim ate 7/8 of his half. How much pizza did each person eat? Express your answers as fractions in lowest terms.

Since there is the word "of" , it means you have to multiply.

Joe

I multiplied 7/10 by 1/2 because 10 is half of what he ate. The amount of pizzas he ate is 7/20.

Hakim

I multiplied 7/8 by 1/2 because 8 is half of what he ate. The amount of pizzas he ate is 7/16.

Ivan's Test Question #1

Calculate the dimensions of the square that has the same area as a circle with a radius of 5.7cm. Round your answer to the nearest tenth of a centimeter.

CIRCLE <--> SQUARE = Same Area.

A=√(πr^2 )
A=√(π5.7r^2 )
A=√102.1
√102.1
10.1445449

SSA: The side length of the square is 10.1cm.

Multiplying and Dividing Powers

* All areas will always end up as a perfect square

* All volume will always be x cubic units

You can only add exponents if the base are alike.

Product Law:

When the bases are the same in a power simply add the exponents to find a new power.

Examples: 5^4 x 5^2 = 5^6

3^9 x 3^5 x 3^6 = 3^20

Quotient Law:

When bases are the same, simply subtract the denominator from the numerator to find the new power.

HOMEWORK:

1. Read pages 99-105 and do SYK
2. CYU # 1, 2 and 3
3. Practice odd or even
4. Apply and Extend (All)
5. 3.2 HWB
6. MANGA HIGH!

Chapter 3: Powers and Exponents

2^{5 = 2x2x2x2x2 = 32}

*choo-choo trains are only allowed FOR NOW*








Rule 1: Any number/variable to the exponent of 0 is always equal to 1
Rule 2: Anything to the exponent of 1 is itself
Rule 3: Anything squared makes a perfect square
Rule 4: Anything cubed, makes a perfect cube

HOMEWORK!!!
-all of 3.1 on homework book
- Go on Mr. Backe's blog for chapter 2 stash it assignment info

*DON'T FORGET TO GO ON MANGAHIGH!*

Krizna's Math Question

2.4 Question # 24

24.The distance d in kilometers , that a person can see a person can see across the ocean to the horizon is given by the formula d = square root of 12.74 x h. In the formula h is the height, in meters, of the persons eye above that the water.Calculate the distance that each of the following people can see across the ocean to the horizon. Express each answer to the nearest tenth of a kilometer.

A)Adele is sitting on a lifeguard station at the edge of the ocean. Her eyes are 4.1m above water.

Answer:14.6 km

D=square root of 12.74 x 4.1 m

D=14.634186 m

Nearest tenth:14.6 km

D=14.6 km

B)Brian is standing at the waters edge .His eyes are 165 cm above the water.

Answer:588.9 km

D=square root of 12.74 x 165 cm

D=588.9367538

Nearest tenth: 588.9 km

D=588.9 km

C)Yvonne is the pilot of an aircraft flying 5km above the coastline.

Answer:17.8km

D=square root of 12.74 x 5 km

D=17.8465683

Nearest Tenth: 17.8 km

D=17.8 km

Brandon's Math Question

My question was :

The width of a rectangle is 1/3 its length.

The area of the rectangle is 9.72cm^2.
What are the dimensions of the rectangle?

What we know :

The width of the rectangle is 1/3 it's length
The area of the rectangle is 9.72cm^2


The dimensions are 1.8cm by 5.4cm

Rowell`s Math Question 2.4 17 a.)

Diorella's Math Question #30 2.4

Question #30 2.4 : A square field has an area of 1000m². 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.

Step 1) Find the square root of the area or find the side length of the square

Step 2) Find the distance of the 2 adjacent sides

Step 3) Figure out how long it takes to walk the two adjacent sides

Step 4) Find out how long it takes to walk diagonally

Solution:

Subtract the time it takes to walk diagonally from the time it takes to walk the 2 sides.

42.25 - 29.85 = 12.4 seconds.

Laura saves 12.4 seconds by walking diagonally instead of walking the two adjacent sides.

Mark's Math Question

Math Homework Book - 2.4 #15

Since the whole square pool is 5.29m² , all you have to do is square root the number to find one side length.

√5.29m²= 2.3m

Math Textbook 2.4 #32

Marie's Blog Question

The question I was given for 2.4 was #21:

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






I knew that the distance between first base to second base is also equal to the side length of the baseball diamond. Since 750 m² is the area, all I needed to do was find the square root of 750m²















For the answer, I got 27.3861279 m.

I had to round it to the nearest tenth, and since .08 is greater than .05, I changed 27.3 to 27.4 m.

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

Ivan's Math Question 2.4 #29

Question: The speed of sound in air, s, in metres per second, is related to the temperature, t, in degrees Celsius, by formula s =√(401(273+t) ). How much greater is the speed of sound on a day when the temperature is 30◦C than on a day when the temperature is -20◦C? Express your answer to the nearest metre per second.

Since there are two temperatures, you can find two s's.

So find 30◦C first.273+30=303
303x401 = 121503
√121503 = 348.57

Then you find the second one -20◦C.
273+ -20 = 253
253x401 = 101453
√101453 = 318.52

Then I did.
348.57 - 318.52 = 30.05

S.S: The speed of sound on a day when the temperature is 30 degrees C is greater by 30m/s than on a day when the temp. is -20 degrees C.

Kevin's Math Question

I was told to answer question #27 in 2.4 of our textbooks.
The question states as follows :




My first reaction when I saw the question was confused, until I thought about the individual faces of the cube.

Here is my work :


























It may seem silly to show long division of a number that will result in a non terminating decimal. But it shows how a person can get such an answer.




So as a result, the edge length of a cube that has a surface area of 100cm^2 (rounded to the nearest tenth of a centimetre) is 4.1cm.

Ishaka's Math Question

The question that I was given was #22 chapter 2.4

The question said: The hypotenuse of an isosceles right triangle has a length of 20 cm. What is the length of each leg of the triangle? Provide your answer to the nearest tenth of a centimetre.

First I drew out the isosceles right triangle in the question

Then I just answered the question using this formula:

The length of each leg of this triangle is 14.1 cm

Tonie's Math Question

The question I was given:


To solve: First, I multiplied 8.2m by 4.5m and I got 36.90 or 36.9

Then I multiplied 36.9 by 2/5. But before I multiplied both numbers, I converted 2/5 into decimals to make it easier.


After, I multiplied 36.9 by 0.4 and I got 14.76



Lastly, I found the square root of 14.76 which equals to 3.8



S.S. The side lengths of the rug is 3.8m