Conditionals

There are different conditionals that can be made, the conditional, the inverse, the converse, and the contrapositive

The conditional is the most frequently used statement in the construction of an argument or in the study of mathematicians.

The inverse is a negation of the conditional.

The converse is when you switch the conclusion and the hypothesis.

The contrapositive is doing both, the inverse and the converse.


Example:
 
The Conditional: If a number is even then it is divisible by two.

The Inverse: If a number is not even then it is not divisible by two.

The Converse: If it is divisble by two then the number is even.

The Contrapositive: If it is not divisible by two then is is not an even number.


Your turn:

1) Find the inverse of the conditional " If I dont go to school then I will not learn."

2) Find the converse of the conditional "If I am not hungry then I will not eat."

3) Find the contrapositive of the conditional "If I study then I will pass."

4) Find the conditional of the inverse "If I am not sleepy then I will not go to sleep."

Surface Area and Volume of a Sphere

A sphere is the set of all points in space equidistance from a given piont called the center.



Examples:

1) Find the Surface area of a Sphere whose radius equals 4. Leave your answer in terms of Pi.
         SA= 4 pi 4 squ.
         SA= 16 squ pi
         SA= 256 Pi

2) Fine the Volume of a Sphere whose radius equals 4. Leave your answer in terms of Pi.
         V= 4/3 pi 4 cubed
         V= 5.3 pi cubed
         V= 149.8 Pi

Your Turn:
Round all answers to the nearent tenth and leave answers in terms of pi.

1) Find the Surface Area and Volume of a sphere whose radius equals 11.

2) Find the radius of a sphere whose surface area equals 125.

3) Find the volume of a sphere whos surface area equals 300.



























                 

Area of Regular Polygons

Formula 1:

The a in the formula stands for apothem. the apothem is the perpendicular segment for the center to the side of the polygon

The p stands for the perimeter of the polygon

The A stands for the area of the entire polygon

Formula 2:

A= 1/2 nas

The n stands for the number of sides in the polygon

The a stands for the apothem

The s stands for the lenght of a side


Example:

1) A pentagon had an apothem of 3 inches. If a side measures 15 inches find the area

Formula 1:                                                                           Formula 2:
A=1/2 ap                                                                              A=1/2 nas
A= (1/2) (3) (75)                                                                  A= (1/2) (5) (3) (15)
A= 112.5 squ. in                                                                  A= 112.5 squ. in


You Try:

1) Find the area of a hexagon with an apothem of 6 and a side measuring 13

2) Find the apothem of a pentagon with an area of 115 and a perimeter of 5



Compositions of Transformations

In compositions of transformations the first step you do is the second transformation they give you. Then the first one they give you is the second one and your final answer. 

Example: Given point A(−2,3). State the coordinates of the 

image of A under the composition T(−3,−4)r x − axis

Step 1: When reflecting over the x-axis the you negate the y-value.

(-2,3) -----> (-2,-3)

Step 2: Using the new point created move the point left and right following the rule.

(-2,-3) ------> (-2+-3, -3+-4) -----> (-5,-7)

Final Answer: (-5.-7)

Questions:

1) Given Point A(5,3)find the transformation r x−axis r y=x

2) Given the point A(-8,-10) find the transformation   r x−axis r y−axis