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Asad,

Rom was not trying to bully you. 

He was responding in anger to what he saw as rudeness from you.

I thought what you wrote was rude too but I do not think you intended to be rude.

However, no matter what degree of intent you had, your post was rude.

It was understandable for Rom to respond the way he did.

Now accept Rom's response as a lesson and learn from it !

Hi Lightning,

A right square pyramid with base edges of length units each and slant edges of length 10 units each is cut by a plane that is parallel to its base and 3 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?

You have the edge slant height 10, and the base length  8sqrt2 

Using pythagoras you can get the slant height in the middle of each triangle (not that the sides are isoceles triangles)

this will be 

\(\sqrt{10^2-(4\sqrt2)^2}=\sqrt{100-32}=\sqrt{68}\;units\)

Now you can use pythagoras again to get the perpendicular height of the entire pyramid.

\(=\sqrt{68-(4\sqrt2)^2}=\sqrt{68-32}=\sqrt{36}=6 units.\)

sionce you are halving the height when you cut the top off, you can halve all the other dimensions for the little pyramid too.

\(volume\;\;of \;\;little\;\;pyramid\\ =\frac{1}{3}*(4\sqrt2)^2*3\\ =\frac{1}{3}*32*3\\ =32\;\;units^3\)

See if you can draw the pics that should go with tihs explanation :)

LMFAO!! I knew it! I knew it!

We have another Troll. And this one can do math at least as well as Nauseated.

There’s now a triple sprite dynamic on the forum. A Chimp, A Gorilla, and a ??? 

What kind of Troll is Rom?   Whatever. We have a quorum!

ok then, idc about you, as long as you keep your bullying ways to urself, LOL!

Let a and b be real numbers such that the equation 6x^2 - axy - 3y^2 - 24x + 3y + b = 0 represents two lines, whose intersection lies on the x -axis. Enter the ordered pair (a,b). 

If the intersection is on the x axis then that is when y=0

sub in y=0 and I get

\(6x^2 - axy - 3y^2 - 24x + 3y + b = 0\\ when\;\;y=0\\ 6x^2 - 24x + b = 0\\ x=\frac{24\pm\sqrt{24^2-24b}}{12}\\ \text{if there is only one solution then}\\ 24^2-24b=0\\ 24-b=0\\ b=24\)

if b=24 then we have

\(6x^2 - axy - 3y^2 - 24x + 3y + 24 = 0\)

I have used a Desmos graph to determine that a=1.5 approx

So    (a,b) = (1.5,24)        

BUT I have not worked out how to get the value of a without using the graphing calculator.

My knowledge of conics is not great.   

We can equate slopes to find p

[ -14 - -5 ] / [ p  - 2 ]    =  [ -17 -  - 5 ] / [p + 2 - 2]

[ -9] / [ p - 2] =   [ -12 ] / p         cross-multiply

-9p  = [ -12 ] [ p  - 2 ]   simplify

-9p = -12p + 24       add 12p to both sides

3p = 24       divide both sides by 3

p = 8

So....the slope   is       (-12) / (8) =  -3/2

And the equation of the line is

y = (-3/2)(x - 2) - 5

y = (-3/2)x + 3 - 5

y = (-3/2)x - 2

So....when x = 13

q = (-3/2)(13) - 2    =  (-39/2) - 2 =  -43/2  =  - 21.5

So

p + q =

8 + (-21.5)  =

-13.5

An arithmetic sequence 2,5,8, 11, 14,... is written in order in a book, one hundred numbers per page, beginning on page one. On which page will the number 11,111 appear?

The common difference is 3

So....we want to find what term 11,111 might be

11,111 = 2 + 3(n - 1)    subtract 2 from both sides

11,109 = 3(n - 1)    divide both sides by 3

3703 = n - 1         add 1 to both sides

3704 = n

So  11,111 will appear on page =   ceiling [ 3704/100]  =  page  38 

What is the largest three-digit number in the arithmetic sequence 1,4,7,10,13, 16, ...?

The common difference is  3

So....we'd like to solve this

1 + 3(n - 1) < 1000

3(n - 1) < 999

n - 1 < 333

n < 334

So....n = 333

So...the largest three-digit term is

1 + 3 ( 333 - 1)   =

1 + 3(332) =

997

D) Find all the real zeros of f(x) = 3x^5 - x^4 - 6x^3 + 2x^2

Factor out x^2

x^2 (3x^3 - x^2 - 6x + 2)

One zero = 0

Factors of 2 =  1 , 2

Factors of 3 = 1 . 3

So...The other possible rational roots are   ± [ 1,  2, 1/3 , 2/3 ]

A little trial and error shows that the only other rational root = 1/3

The other two roots are non-rational reals

Please explain your problem further.

Consider the function f(x) = 2x^2 + 5x^3 - 21x^2  - 36x

A) Explaing why the rational zero theorem cannot be directly applied to this function.

The last term must be a constant to apply the theorem

B) Factor out the common monomial factor of f.

 x (2x + 5x^2 - 21x - 36) = 0

x ( 5x^2 - 19x - 36) = 0

The possible rational zeoroes  are all the possible divisors of 36   ovet all the possibe divisors of 5

However....the only rational zero here is x =0

The other two solutions involve non-rational  (but real) answers

Type them using a backslash like this: 1/2, or 1/4.

f(2)  = 2^2 - 8(2) + 6  =   -6

f(-5) = (-5)^2 - 8(-5) + 6  =  71

1.196 x 10^0   in   sci not

i need it written in scenitifc notation . Do you know how i would do that?

OK....thanks for catching my error....!!!!

Oh right... Thank You

Oops...I shouldn't have included 4   !!!!

See my edited answer

Not much on Science...but

1 mole = 6.022  x 10^23 molecules 

So

[7.2 x 10^23]  /  [ 6.022 x 10^23 ]  =    7.2 / 6.022  ≈ 1.196  moles

The function f satisfies

f(sqrt(x+1)
for all x>=-1, x isn't equal to 0. Find f(2).

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

This notation looks odd to me. There is a bracket messing but even with that it does not make a lot of sense to me.

Could you check it please?

All I can say is that  if  you want f(sqrt(x+1))  and sqrt(x+1)=2 then

\(\sqrt{x+1}=2\\ x+1=4\\ x=3\)

I cannot find f(2) becasue the function is not defined. There are no equal signs.

Sorry for the inconvenience, but your answer, 30, is incorrect.

I looked through your great explanation to see if I can figure out what you did wrong, but I came out empty-handed. I you please try again, I would be very thankful. 

Again sorry.

1/3 < 3/x < 3/4  

We have that

1/3 < 3/x            and      3/x < 3/4

             cross - multiply

x < 9           and                12 < 3x           divide both sides by 3

                                           4  < x

So....the integer solutions are 5, 6, 7, 8    

And their sum is   26  !!!!

Someone please help???

The numbers are:

(-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21) =225

225/25 = 9 - the average of the 25 numbers