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I suggest that you use this site. It is really good for questions like this.

Considering BS should be part of your name, it’s not a surprise you are familiar with the word and its correct spelling. 

It seems that you are better at spelling than math, anyway. 

How many positive integer divisors of 23,328 are perfect cubes?

23328^(1/3) = 28.573218935427587   Well less than 29 anyway.

1 is ok

factor(23328) = 2^5*3^6

\(2*2*2*2*2\quad * \quad 3*3*3*3*3*3\\~\\ 1^3,2^3,3^3,6^3,9^3,18^3 \;\;\text{that seems to be it.} \)

I just got those from visual examination of the factors.

So that is  6 of them.

/* Number of terms of arithmetic series */
(L - F) / D + 1, where L= Last term, F = first term, D = Common difference

(363 - 15) / 6 + 1 = 59 terms.

You are full of bulllshit!

The links are to images that don’t display clearly, not to the source of your answers. 

You are one of the biggest bullshiters to join this forum.

Did you come here to practice your bulllshitting skills?

I gave links to both of my answers...

in the response below, you didn't even spell bs correctly...

You plagiarized both of your answers.

I found your mistake. The sum of the first two equations is not 3y + 2z = -8.

       3x + 3y = 3

+    -3x - 2z = -11

______________

      3y - 2z = -8

Not 3y + 2z = -8.

The correct answers are x = 3, y = -2, and z = 1.

- PM

I checked both of your answers, and I found out that Guest's answers are correct.

If the first solution confuses you, here is a second solution. 

Create a trapezoid with inscribed circle O exactly like in the solution above, and extend lines AD and BC from the solution above and label the point at where they meet H. Because \(\frac{\overline{GC}}{\overline{BE}} = \frac{1}{9}\), \(\frac{\overline{HG}}{\overline{HE}} = \frac{1}{9}\). Let \(\overline{HG} = x\) and \(\overline{GE} = 8x\).

Because these are radii, \(\overline{GO} = \overline{OE} = \overline{OF} = 4x\). \(\overline{OF} \perp \overline{BH}\) , so \(\overline{OF}^2 + \overline{FH}^2 = \overline{OH}^2\). Plugging in, we get \(4x^2 + \overline{FH}^2 = 5x^2 \), so \(\overline{FH} = 3x\).Triangles OFH and BEH are similar, so \(\frac{\overline{OF}}{\overline{BE}}  = \frac{\overline{FH}}{\overline{EH}}\), which gives us \(\frac{4x}{18} = \frac{3x}{9x}\). Solving for x, we get \(x = 1.5\) and \(4x = \boxed{6}\).

Hope this helps,

- PM

Consider a trapezoidal (label it ABCD as follows) cross-section of the truncate cone along a diameter of the bases:

The radius is \(\boxed{6}\).

- PM

Good afternoon is correct.

3x + 3y = 3...........................(1)
-3x – 2z = -11.......................(2)
 y + z = -1.............................(3)
 From (3): z = -1 - y                                sub into (2)
3x + 3y =3.............................(1)
-3x -2 (-1 - y)= -11................(4)
-3x + 2 + 2y   = - 11..............(5)
-3x + 2y = - 13......................(6)             add this to (1) above
5y = - 10,
y = -10 / 5 = -2                                        sub this into (3) above:
-2 + z = -1
z =-1 + 2 =1                                            sub this into (2) above
-3x - 2(1) = - 11
-3x = - 9
x =-9 / -3
x = 3 ,     y = -2,     z = 1

Add the first two equations: 3y-2z=-8

y+z=-1

Now, multiply the second equation by 2, so 2y+2z=-2. Then, subtract the first equation from the second: y=-8+2, y=-6.

-6+z=-1, z=-1+6=5

And, x equals 3x+3(-6)=3, 3x-18=3, 3x=21, x=7.

Thus, the answer is \((x,y,z)=(3,-2,1).\)

\(n=2^k,~k=0,1,\dots,6\)

1/x + 1/y  =  1/12

x + y = xy/12

12(x + y) = xy

12x  - xy   =  -12y

x (12 - y)  = -12y

x ( y - 12)  = 12y

x =  12y / ( y - 12)

The smallest that y can be and still have x positive is when y = 13

(1) If y = 13  x = 156

(2) If y =14  x  = 84

3) If y = 15  x = 60

(4) If y = 16 x = 48

(5) If y = 18 x = 36

(6) If y = 20  x = 30

(7) If y = 24 x = 24      but x and y cannot be the same

(8) If x = 30  y = 20

And every other combo will be a repeat  of the sum of x and y for  (1) - (6)

So.....the smallest value of x  + y  =   50

I think you mean well afternoon.

We have \(\frac{x+y}{xy}=\frac{1}{12}, 12(x+y)=xy\) . \(12x+12y=xy\) . Try to plug in numbers!

Afraid I don't know this one, PM......

Maybe someone else does  ????