Gummy Bears after Lunch

Thursday, June 21, 2007

Pre-Calculus 20S, Gummy Bears After Lunch '07

posted by NCC-74656 Intrepid Class at 6:01 PM

Myspace Glitter Graphics, MySpace Graphics, Glitter Graphics

Pre-cal Grade 10 is doooonnneeee!!!!!!!!!

Exams are done toooo!!!!!!!!

now it's time for....

Vacation and jobs!!!!

Seee you next semester!!!!!

See you too Ms. Armstrong!!!!!:-)

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Tuesday, June 12, 2007

Arithmetic Sequences

posted by NCC-74656 Intrepid Class at 5:22 PM

Hello there Gummy Bears!!!!

Ms. Armstrong has taught us a totally new topic, the Arithmetic Sequence. An Arithmetic Sequence is a sequence of numbers such that the difference of any two sequential numbers is a constant.

For example, the sequence:

(5, 10, 15, 20...) is an Arithmetic Sequence with a common difference of 5.

The formula to calculate the value of an arithmetic sequence consisting of n terms is:

n= the number of terms
d= the common difference
t1= the first term

tn= the last term

Red Alert!!! All Hands, Battle Stations!!! We are under attack by Arithmetic Sequencing spaceships and the only thing to do to defeat them is to understand how they operate...

Now, let's learn how to calculate the SUM of the first 25 terms...

For example, if we have: (-2, 1, 4, 7...), 25 terms...
we have the following:

n=25
d=3
t1=-2
tn=?

Substituting the information, we should have:

S25=(25/2)(2(-2)+3(25-1))

S25=(12.5)(-4+3(24))

S25=(12.5)(-4+72)

S25=(12.5)(68)

S25= 850

Thus, the sum of the first 25 terms of (-2, 1, 4, 7...) is 850.

Shields are down to 70%!! Arm torpedoes and fire multiple-phasers!!

Now, to solve for tn using the information we have,
tn=t1+(n-1)d

tn= -2+3(25-1)

tn= -2+3(24)

tn= -2+72

tn= 70

Their torpedoes are ripping right through our shields!!! I think we should learn more about them...

Finding the SUM of all multiples of 7 between 232 and 677.

t1= 238

tn= 672

d= 7

n= ?

First, we must find the value of n

tn=t1+(n-1)d

672= 238+7(n-1)

434= 7n-7

441=7n

63=n

The environmental controls and life support are failing. Shields are down to 0%.. We've lost 9 decks, main computer is down, multiple breaches across the ship, phasers and torpedo launchers are down... What are we going to do? Continue to learn...

S63= (63/2)(2(238)+7(63-1))
S63= (31.5)(476+7(62))

S63= (31.5)(476+434)

S63= (31.5)(910)

S63= 28665

Computer.... Initiate Self-Destruct Sequence....

Please the following sites if you are still having problem with this topic: Arithmetic Sequence and Sequences.

The images came from Star trek Data Base. Copyright Paramount Pictures.

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Saturday, June 9, 2007

Relations,Functions, Domain and Range

posted by NCC-74656 Intrepid Class at 5:30 PM

Hello there Gummy Bears!!!

We are now on our last unit and Ms. Armstrong is now teaching us Relations. Relations is a shared property of associations: a property of association such as "greater than" or "less than", shared by ordered pairs of terms or objects.

In this post of mine, I will talk about function. Now, don't be confused with "Relations" and "Function". Relation is a connection between sets of information while a Function is a kind of relation that has only one output for every input.

The way we simplify equations is based on the fact that the function always give the same result when applied to the same input.

For example,

y=2x+3

For each value of x there is only one value of y. The value that x may assume is called the Domain and the values of y are called the Range. Thus if x=3, y=2(3)+3, y=9.

If you have more questions about this topic please see: Relations and Functions.
Ms. Armstrong assigned Exercise#50

Remember!!!! Exams is 1 week within our reach!!! Study!!!:-)

Labels: Anthony, Domain, Functions, Range, Relations, Scribe

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Saturday, June 2, 2007

Solving Rational Equations

posted by NCC-74656 Intrepid Class at 6:21 PM

Hello there Gummy Bears!!!

We now have another somewhat like a review on how to solve rational equations. Please remember that rational equations have variables in the numerator/denominator or both.

Steps:

If you can, first factor the fractions on the both sides of the equation. Then/or, simplify the expressions by getting the LCD (least common denominator).

Solve the remaining expression/Check for Restrictions.

Simplify/Check for Extraneous Roots. (If you don't remember what Extraneous Roots is, it means that the restriction to the equation is also the answer which also means that the equation is not possible to solve. An imaginary number, not relevant or essential)

Now let's have a practice;
Solve the following equation:

Since, we cannot factor this equation anymore, we get the common denominator which is 6x.

29=x

Restrictions: x cannot equal to 0.

Let's have another one,

x cannot be equal to -2

I hope you find my explanation and examples understandable. If you still have problems in this topic please see, Rational expressions, Purple Math and Solving Equations.

Labels: Anthony, Rational Equations., Scribe

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Wednesday, May 30, 2007

Simplifying Compound Algebric Fractions

posted by NCC-74656 Intrepid Class at 4:12 PM