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$\sum_{1}^{40}$ 7n-12

Oh wait, nobody is online. LOVELY! >:(

Great sol, EP! I understand it much better, now!

The area of the WHOLE figure is 1/2 b h    = 1/2 ( 36)(24) = 432 cm^2

Now subtract the small right triangles in the corners

-  2  x 1/2 x 6 x FG     

via similar triangles

CH/HB = FG/6    

24/18 = FG/6

FG = 8

- 2 x 1/2  x 6 x 8 = -48

Pentagon area = 432 - 48 = 384 cm^2

The sin of a 90 degree angle is  1  .

Since ABC is isosceles, angles ACB  and ABC  = 45°

Since ABC is trisected, then angle DBE  = 15°

Note that angle BEA  =  90 - EBA =  90 - 15  =  75°

So....by the Exterior Angle Theorem , Angle BEA  =  angle DBE + angle BDE

So

75  =  15 + angle  BDE        subtract   15 from both sides

60° =  angle BDE

Since it is an isoc right triangle angle  ABC (and ACB) are each 45 degrees .   Trisecting the 45 degree angle results in three 15 degree angles  . Angle ABD includes two of these so it is 30 degrees.

The resulting triangle (ABD) is 30 degrees + 90 degrees  +   60 degrees.  BDEA = 60 degrees.

I THINK the second question is as follows

each switch controls one bank , so there is EIGHT ways to have ONE bank on

  then for TWO banks there is  8 C 2 ways = 28 ways

28+8 = 36 ways to have either one bank or two banks on,    

~EP

That may be true, but on the left you still have a LOG (negative number)    .....So I am confused.

  2 Log (a-2b)   =  log(a-2b)^2    

       seems invalid as the left side of the equation is invalid if (a-2b) is negative  

Does anyone know for SURE?

Help !

  ~EP

Please let me know what the correct answer is when you find out :)

Take your FUCKING spam and shove it up your A S S !!!

Happy that you managed to solve this problem yourself and you hadn't to wait so long for the right answer.

CPhill always got the best explanation! 

Just wanted to thank you for all your help. :) 

you are more than welcome!

thank U!! ur thebest phill

Long ago, your ship sailed and sank. No one thought it worthy of salvage— then or now.  It needs warning buoys because of the toxic waste that it leaches.   

An arsonist thinks all fires start because of arson.

A thief thinks all missing items are stolen.

An embezzler thinks any missing funds are embezzled. 

A plagiarist thinks every posted solution is plagiarized.

 I wasn’t accusing you of plagiarism, Mr. BB. However, you didn’t cite the Mathematica program from which you copied your pasted SLOP.  The slipper fits because it belongs to you. _{You are what you are, Mr. BB.}

You are gifted Mr. BB, you are the only person I know that takes a brilliantly integrated mathematical program and finds a noxious use for it.  Another example of throwing slop on a diamond.

GA

7 ways to chosse the middle one

Put another down anywhere

5! ways to order the rest 

So that is 840

that takes care of rotation but not relfections

There are six axes of symmetry so I'll have to divide by something...not sure what.   

2 of the places are fixed before the other 5 get included so maybe there is only really one reflection that counts.

So maybe

840/2 = 420      But that is a bit of a guess but is seems right .... well maybe anyway.    

-----------------

I do not understand the second question - I do not know what is being asked. 

I don't agree that that the function $\frac{p^2-4p-32}{p+4}$ is undefined at p = -4.  Its value is just -12 there.  Use L'Hopital's rule for example to find the limit.

Although the denominator goes to zero at p = -4, so too does the numerator - at the same rate.  This negates the effect of the denominator going to zero.

You wouldn't say the function $\frac{x}{x}$ is undefined at x = 0 simply because the denominator is zero there.  The function is clearly 1 for all values of x.

If the numerator goes to zero as fast as, or faster than the denominator then the function will have a well defined value. It's only if the denominator goes to zero faster than the numerator that the function will have a singularity.

Of course, there might well be numerical problems in evaluating a function like $\frac{p^2-4p-32}{p+4}$ at p = -4 if the numerical procedure first calculates numerator and denominator separately.  However, the function is mathematically well-defined there!

http://www.pleacher.com/mp/probweek/p2003/a011303.html

https://web2.0calc.com/questions/andy

[plagiarized?  Or was it conjured from "Set Theory"? As phony as a 3-dollar bill !. Utterly Shameless!]

First calculate the probability, q, that no two dice show the same number:

first die:  any number

second die:  prob 5/6 that it is different from first

third die:      prob  4/6 that it is different from first two

fourth die:    prob  3/6 that it is different from first three

fifth die:       prob  2/6 that it is different from first four.

Hence;  q = 5*4*3*2/6^4

Porbability, p, that at least two show the same number is p = 1 - q

p = 1 - 5*4*3*2/6^4             (You can crunch the numbers!).

No I don't think so as squaring a negative gives a positive

ie 2log(a-2b) =log (a-2b)²

P(top 3 spades) = 1/4*12/51*11/50

                          =  11/850

Sorry Tetre but I agree with guest. x=5

but the question asks what is the smallest value of the other interger is and that is the pronumeral 'a'

The smallest possible value of a is 10

This is how I did it.

The lowest common multiple of 2 numbers a and b is    $\frac{ab}{HCF(a,b)}$

SO we have

$GCD(a, 50) = x + 5\\ LCM(a, 50) =x(x + 5)=\frac{50a}{x+5}\\ x(x + 5)=\frac{50a}{x+5}\\ x(x+5)^2=50a\\ a=\frac{x(x+5)^2}{50}\qquad \text{where a and b } \in Z \ge 1\\ $

I want the smallest positive integral value of a and I can see that as x isncreases a will increase

So I want the smallest possible value of x

Straight off I can see that x must be a multiple of 5

Try x=5       a=5*100/50 = 10  which is an integer

so the smallest value of the second number is 10

(Just as our guest already found)

Wondering if  a/b =1 might be considered an extraneous (invalid) solution, as it would result in a

LOG (negative number)   ??