Month: September 2018

Week 3 Square roots

kaidenh2016 on

Changing entire radicals to a mixed radical is fairly simple, but is a very important concept.

Your first step is to find out what the number in side the radical divides into. Fifty four can become  \sqrt{2} & \sqrt{27}. (Which was from \sqrt{54})

Since two can’t be made smaller it is left alone. Next is to make \sqrt{27} smaller, \sqrt{27} can be turned into square root 3 and 9. So now you have \sqrt{2}, \sqrt{3},  \sqrt{9}, nine can become smaller again and turn into 3. Nine is a special number called a prime factor which are numbers that can be multiplied by the same number evenly twice. If you have a prime factor like nine it just becomes 3 instead of square root three.

Now that your left with 3 \sqrt{2}, \sqrt{3} you have to multiple the square root 2 and the 3 to make it one number. After words your left with the answer 3\sqrt{6}

Write the entire as a mixed radical

\sqrt{54}

\sqrt{54}  = \sqrt{2} *  \sqrt{27} ——>\sqrt{3} *\sqrt{9} *\sqrt{2} ——-> \sqrt{3} * \sqrt{2} * 3 = 3\sqrt{6}

Write the mixed as an entire radical

-2 ^3\sqrt{5}

= –^3\sqrt{8} * ^3\sqrt{5}

=^3\sqrt{40}

 

Arithmetic Sequence

kaidenh2016 on

Sequence: -13 -10 -7 – ….. +62      Determine the sum of the arithmetic sequence

62 = -13 + (n-1) (3)

+13    +13       —–> 75 = (n-1) (3) —–> \frac{75}{3} = (n-1) (\frac{3}{3}) ——-> 25=n-1  =    n = 26

/prt 2   S_{26} =  \frac{26}{2} (-13+62)   —–>   S_{26} = 13 (49)    —->    S_{26} = 637

 

Week 2 Convergent / Divergent

kaidenh2016 on

Convergent – Where an infinite geometric series that’s sum gets so small it is almost hardly changing the sum. There are two types of infinite geometric convergent series; the first series gets mutiplied by a number less than one, and gradually getting smaller and smaller, but never reaching 0. The second series, R is less than 0 but greater than -1, and makes the series gradually smaller almost reaching 0 dipping up and below the positive and negitive line. Convergent is easy to calculate, and can be using S = \frac{a}{1 - r}.

Ex: 2 + 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}…

——>   S = \frac{2}{1-1/2}    =     S = \frac{2}{1/2} = 4 ——->  S = 4

Divergent – Is the opposite of Convergent, divergent is an infinte geometric series that increases and becomes larger, so large that it becomes almost impossible to find the sum of the infinite series. Just like Convergent, there are two types of Divergent series that can apear; first is a series that increases constanly upward positively being mutiplied by a number grater than 1 2 + 4 + 8 + 16 + 32 + 64….; the second is one that dips into the red when multiplied by a number less than -1. 2 – 8 + 32 – 128 + 512….. It is impossible to calculate a infinite divergent geometric series, and can’t be used by the equation S = \frac{a}{1 - r}.

My Arithmetic Sequence

kaidenh2016 on

Sequence: 31 + 35 + 39 + 43…..       Find t_{50} & S_{50}

t_n= t_1+(n-1)(d)

Answer/ t_{50} = 31+ (50-1)(4)

=  t_{50} = 31+ (49)(4)

=  t_{50} = 31+ 196   =  t_{50} = 227

——-> S_{50} = \frac{50}{2} (31+227)

=   S_{50} = 25 (258)   —>   S_{50} = 6450