Blog post week 16 sine law

Formula for sin law: sin(A)/a + sin(B)/b + sin(C)/c

this formula will only work for a triangle if you have 3 clues and 2 angles with an opposite side, if you do not have an angle with the length of the opposite side, it will not work

for example: ABC

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here is an example of the sine law with ABC using 2 angles opposit of sides but only one side.

Factoring week 7 blog post

factoring is expanding or simplifying binomials or trinomials, such as; 6x+3   and   x^{2} +11x +24

these can be simplified

6x+3, can  both be divided by 3, if you divide 3 from both sides, you are left with 2x+1, but this is still not finished, since we divided the 3, we have to add it out front: 3(2x+1)

x^{2} +11x +24, is more complicated, we have 3 terms, the x^{2} will always be an x*x, we will use this as our base

(x+_)(X+_)   from here, we have to look at all the numbers that multiply into the last number. 

In this case, we have to look at factors of 24

24*1

12*2

8*3

6*4

then we have to look at the single X value, and see if any of these factors add up into the x value, here 8 & 3 add up into 11.

So our equation would look like (X+8)(X+3)

Method of substitution(system of equations)

method of substitution is isolating one variable, finding out the rearranged equation, and substituting it into another one.

Ex: 2x+3y=6 and x-y=4

you can change the second one to x=y+4 and then substitute it into the first one

2(y+4)+3y=6

5y+8=6

5y=-2

y=-2/5

x-2/5=20/5

x=22/5

solution: (22/5,-2/5)

process of elimination

if you have 2 equations

Ex: 2x+3y=14

x-3y=4

you would be able to cancel out the 3y, because one of them are negative and the other is positive.

next step:

3x=18

x=6

then we can substitute it into the one of the equations:

6-3y=4

-3y=4-6

-3y=-2

y= 2/3

the solution is (6, 2/3)

if none of the numbers add up, you can multiply them to let them even out

Slope y-intercept

Ex: y=_x+#

the slope(x) goes infront of the x spot, when looking at an equation this is where you want to look first, giving you the slope and most important information about the equation.

the number is where the line connects on the Y axis at (x=0)

If it is a positive number with a slope of 3

Y = 3x + 2

if it is a negative number, the number will be negative, indicating that the (Y axis meets 0) is a negative.

What if there was a change in UV radiation?

Video link:

UV radiation has many different effects on us.

If the UV radiation lowers, it will make it colder, and will lower our production of vitamin D.

if the UV radiation increases, the chances of skin cancer, sunburns and sun burning on the whites of your eyes will start to occur, and it will get much more intense.

Too intense for sunscreen to protect our skin fully from the effects of radiation.

It will also cause people to wrinkle faster and seems to make us age faster.

This will not happen if we have less UV radiation, but we will lose the production of most of our Vitamin D from the sun.

Slope basics

Finding the slope of a straight line in any direction is fairly simple

Ex:

The rise is on the Y axis, it is 3 in the example, the run is on the X axis, in the example is 4

the Slope=rise/run

in the example: 3/4

the slope will be positive only if both the rise and the run are positive numbers, or both negative. The slope will always go upwards towards the right

negative slopes:

negative slopes will always have either a negative run or rise, if both are negative, it will be positive.

Ex:

In the example, the rise goes down by 3, and over by 1.

rise=-3

run=1

equation: -3/1 = -3

the slope is -3

if the run is a negative number, the negative will switch over to the top. A negative run means the slope is going backwards, therefore having a negative slope equation

Ex: 3/-1 =-3/1 = -3

Undefined and 0 slopes

Zero slopes are all slopes with a 0 Y axis.

Ex: (1,0)(4,0)(7,0)

anything with one or more different Y axis, even if all the other ones are the same, it will not be a 0 slope, because it will not be a perfectly straight line along the X axis, it will have a little bump

0 slopes will always only be perfect straight lines along the X axis.

Undefined slopes are all slopes with a 0 X axis

Ex: (0,1)(0,4)(0,7)

If any coordinates have the same X axis, it will not be undefined, all the X axis have to be the same or it will be a defined slope.