Unit 2 Blog Day 4

vertical angles are the angles across from each other are equivalent. a=b and d=c

multiplying radicals you break it up and 4x7 is 28 and 3x5 is 15

questions

1.  if a equals 50 degrees what is the other side.
2. what is b
3. what is 3 square roots of 4 times 2 square roots of 3
4. 

answers:

a=5o degrees on both sides

180-50=130 b=130

3x2 and 4x3  =six square roots of 12 so simplified 1 square root of 2

Unit 2 Blog Day 2

Pythagorean theorem

Every triangle equals 180 degrees. 60,30,90 equals 180 degrees.

from left to right, top to bottom

all angles acute, all angles and sides the same, two angles and sides the same, abtuse angle, isosceles with a 90 angle, a 90 angle

if some one gave you two points you could draw a triangle to find the distance between the two points.

questions:  

1. name this triangle
2. if a is 2 and b is 3 what is c
3. c is 4 and b is 3 what is a

answer

right triangle because it is a right angle

4+9=13   c is 3.6

16-9=5  a=2.2

Unit 2 Day 7

Define the real world meaning and formulas of prisms, pyramid, cylinder, cone, sphere

prisms: base X width X height

pyramid: area of base X 3d height divided by 3

cylinder: area of base X 3d height

cone: 1/3 area of base X 3d height divided by three

sphere: 4/3 X pi X radius cubed

The reason you would know these formulas is if you need to install a

pool or you need to help a neighbor, then you would need to know the volume. Another instance would be someone wants to know how much ice cream can fit in their cone. You would be able to figure it out.

QUESTIONS:

1. find the volume of the shape
2. if a pyramids area is 20, what are the dimensions
3. if the radius is 5 and height equals 6

ANSWERS:

(60 X 80)-(60 X 40)=2400 X 10=24000

20 X 3= 60   60 divided by 4 equals 15

25 X 3.14=78.5 X 6=471

Unit 2 Blog Day 8

Daily Objective: Volume of prism, pyramid, cylinder, cone and sphere.

Formulas: Volume of Prism- area of base x 3D height.
Volume of Pyramid- area of base x 3D height divided by 3.
Volume of Cylinder- area of base x 3D height.
Volume of Cone- area of base x 3D height divided by 3.
Volume of Sphere- 4/3 x pie x the radius3, or cubed.





QUIZ
1. what is the volume of this Prism?

2. what is the volume of this Pyramid?

3. what is the volume of this cone?

ANSWER KEY

1. The area of base will be 20 x 9, which equals 180 cm2. Then you multiply it by 8, giving you 1,440cm3. 

2. The area of base will be 440 x 440, = 193,600 units2. Then you multiply it by 280 because it is the height, = 54,208,000 units3.

3. The area of base will be 6x6=36 x 3.14= 113.04. x that by 14 = 1582.56cm2 divided by 3= 527.52cm3. 

Unit 2 Blog Day 6

special right triangles

30-60-90
45-45-90 are special right triangles.

on a 45-45-90 triangle the two legs are always the same. That means they are both X. To find the length of the hypotenuse  you multiply the square root of two times x. So, you end up with X square roots of two.

30-60-90 triangles

The short leg is X and the hypotenuse is 2X and to find the long leg you would have X time the square root of three.


Questions:

1. if x equals 5 then what is the hypotenuse
2. do the same on the 30-60-90
3. if the hypotenuse is 22 then what is the short leg on the 30-60-90

answers

X times the square root of two would be 5 square roots of 2

x times 2 is 10

22 divided by 2 would make X 11

Unit 2 Blog Day 5

Daily Objective: Addition and Subtraction of Radicals.

To add radicals,

To add radicals that are not similar, you
must divide the number in the square root
to it's simplest form. Then you multiply the
outside number by the reduced number, and
you should get a reduced radical that is similar
to the other radical. In this case it is 6+5=11.
The answer is 11square roots of 2. 

Subtracting radicals is the same process as adding, but you are subtracting. For example,

10 square roots of 6 - 5 square roots of 6. The answer is 5 square roots of 6. 

QUIZ
1. 3square roots of 6 + 2square roots of 6
2. 5square roots of 10 + the square root of 10.
3. 2 square roots of 3 - the square root of 3.

ANSWER KEY
1. 3 + 2=  5, then the 6's are the same, so 5 square roots of 6 is the answer.
2. 5 + 1= 6, then the 10's are the same, so the answer is 6 square roots of 10.
3. 2-1= 1, and the 3's are the same, so the answer is the square root of 3.

Unit 2 blog Day 3

Daily Objective: Simplify radicals; distance formula can be introduced

Radicals are also known as square roots. They do not need to be perfect square roots.

To find the reduced Radical form, there is a certain process. 

Example= square root of 75. you divide that number into a simpler form, like 25 x 3. you can't simplify 3, so you simplify 25. it can go down to 5. So in other words , the simplified form of the square root of 75 is 5 square roots of 3.   =  = 5.

The Distance Formula:Given the two points (x₁, y₁) and (x₂, y₂), the distance between these points is given by the formula:


This is an offspring of the Pythagorean thereon. It is a drawn triangle of the two points on a graph.

QUIZ

1. Reduce square root of 98.

2. Reduce square root of 60.

3. Reduce square root of 72.

ANSWER KEY

1. 98 divided by 2=49, 49 reduced = 7, the reduced form is 7 square roots of 2.

2. 60 divided by 2 is 30, 30 reduced to 15 makes 2 square roots of 15

3. 72 divided by 2=36, 36 is reduced to 6, making it 6 square roots of 2.