CPhill

3.   Perimeter  =  2 ( W + L)

So  we have

2 ( √13 + 7√13 )

2 (8√13)  =

16√13  units

4.  √20 + √45  - √5  =   

{ The trick here, NSS, is to try to write  each radical in terms of the last one}

√ [ 4 *5 ]  + √ [ 9 * 5 ]   - √5  =

√4 *√5  + √9 *√5  -  √5   =

2√5  +  3√5  - √5  =

5√5  -  1√5   =

4√5

7.

P  =  d^3/2

When  d  =  6.76, we have

P  =  (6.76)^3/2    ≈  17.58

8.   Hard to read this...but I think we have

³√x³

____

⁵√x²

Writing  in exponential form, we have

x^(3/3)                                   a^m

_____              using            _____        =    a^(m - n)         we  have  

x^(2/5)                                   a^n 

x ^( 3/3  - 2/5)  =

x^(1 - 2/5)  =

x^(5/5 - 2/5)  =

x^(3/5)

9.  We want to multiply top/bottom by the congugate of 2 - √5 ⇒  2 + √5

2 + √5        (2 + √5)

_____

2 -  √5        (2 + √5)

Let's do these separately

( 2 + √5 )  ( 2   + √5)  =

2(2)  + 2√5 + 2√5  +  √5*√5  =

4 + 4√5 + 5 =

9 + 4√5        (1)

( 2 - √5 )  ( 2   + √5)  =

2(2)  - 2√5 + 2√5  -  √5*√5  =

4 - 5 =

-1      (2)

Put  (1)  over (2)  and we have

[ 9 + 4√5 ]                      -9  - 4√5

________       =     

       -1

10.

(8a^-3)^-2/3   =   8^-2/3  *   (a^-3)^-2/3

Note, NSS.....

a^-m   =   1 / a^m           and       ( a^m )ⁿ    =  a^{m * n}

So we have

1 / 8^2/3    *   a^6/3

And  we can write

1 / ³√ [ 8 ² ]     *  a²

1 / ³√64  * a²  

1 / 4  * a²

a² / 4

EP  is correct.....

Using the guest's "formula"....   24  would be    (1 - 1) * 100%  =   0%  of itself !!!!

Happy Birthday, heureka.....!!!!!!

Second one :

Notice that if we let the normal sine graph have an amplitude of 1/2 and then  "flip" - reflect - it across the x axis, we get the "negative" sine graph with an amplitude of 1/2

So....the correct answer is

f(x)  = ( -1/2 ) sin (x)

The frequency  is    1 / period

We have 3 periods in 2pi.....so.....the period is  2pi / 3

So....the frequency is

1 / [ 2pi /3 ]  =

3 / [ 2pi ]

If we allow for repeats....we have

20 consonants to choose from to fill the first position

6 vowels to choose from for the second position

20 consonants to choose from  for the third position

10 digits to choose from for the last position

So....the number of possible plates is

20 * 6 * 20 * 10   =

24000

1st one  :

This is the graph of the cosine reflected across the x axis....and with an amplitude of 1/2

So......the correct answer is :

f(x)  =  -(1/2)cos (x)

2nd one :

This is the sine graph with a period half as long as normal.....thus....there are 2 periods in 2pi

So....the correct answer is

f(x)  =  sin (2x)