# Week 15 – Solving Rational Equations

This week, we have learned about solving rational equations.

First of all the most important part when solving multiple rational equations is to see whether the denominator’s the same.

For example, lets look at this equation.

We can see that to make the equation the same on both sides, (x+6) was multiplied on the left side and (x+3) was multiplied on the right side.

Then, to make sure we have one equation, 8x+24 was moved to the left side and we could see that there is a common of Xs’.

We’ve calculated 6x-8x (-8x is when 8x was moved to the left) and got the result as shown above.

At last, we factored the equation having 2 Xs’

X=6, X=-4

# Wave Phenomena Part 1 – Wave Interferance

Constructive Interferance

Constructive Interferance occurs when waves come together so that they are in the same point with each other. This means that their movement at a given point are in the same direction, due to the result of the amplitude at that point being much larger than the amplitude of an individual wave. As the waves meet, the amplitude between wave to the crest becomes much larger. For two waves of equal amplitude interfering together, the resulting amplitude is twice as large as the amplitude of an individual wave. After the collision, the wave came back to the original point. In conclusion, due to the constructive interferance, we were able to find a significant increase in amplitude.

Destrictive Interference

When two waves interfere together, they have the same amplitude in opposite directions, But then, there are more than two waves interfering. The situation gets a little more complicated. When the two waves meet in this following example, the collide and go apart as crests and troughs. When the two amplitude have opposite signs, they will also form a wave with a lower amplitude. The following diagram shows two pulses interfering destructively. Again, they move away from the point where they combine as if they never met each other.

Step 5

When we try to listen to music on an airplane, problem might occur. Headphones that block out the noise and let you enjoy to your music are called noise cancelling headphones. The shape of the headphones and the material they are made of can physically block certain sound waves from reaching your ears. As we learned in this lesson, if the soundwave is 180 degrees, it means that the wavelenght is zero, which result in silence.

# Week 14 – Rational Expressions and Equations

This week, we learned about rationalizing expressions and equations; linear or quadratic.

We learned that denominator can’t be 0 and because of that there is restrictions, which is also called non-permissible values.

If we look at this expression

We know that x can’t be either 0 or 5 and when we factor both sides, we can see that there is a common of x-5. So, it gets canceled.

This chapter needs alot of practice with factoring.

# Week 13 – Graphing Reciprocals of Linear and Quadratic Functions

Every number has a reciprocal except 0.

The reciprocal is shown as 1/x.

1 and -1 has the same reciprocal as the original.

Reciprocal is an inverse of natural number.

For example,

# Week 12 – Absolute Value Functions

Absolute Value is a magnitude of real number without regarding to its signs.

The absolute value has the form of y =  |f(x)|, where f(x) is a function.

The x-intercept of the graph of y = f(x) is a critical point also known as point of reflection.

So when there is an absolute value symbol, the line always reflects.

As long as we know the concept of an Absolute Value, it is easy to solve problem solving questions.