MWizard2k04

a)

x lesser than 6 = x more than 2

    (6 - x) = (2 + x)                          | - x

b)  Method 1

     (6 - 2x) = 2                                | + 2x

     6 = 2 + 2x                                 | - 2

     2x=4

     x = 2

     Method 2

     \(\tt \, Area\,of\,Desk\,1\rightarrow (x)(2+x) \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= (2x+x^2) \,ft^2 \\ Area\,of\,Desk\,2 \rightarrow (x)(6-x) \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;= (6x-x^2)\,ft^2\\ This\,should\,be\,true:(2x+x^2)=(6x-x^2)\quad|\,-(6x-x^2)\\2x^2-4x=0\\ Two\,possible\,results\,of\,x.x = 0\,and\,x=2.\\ As\,an\,area\,of\,0\,doesn't\,make\,sense,\,then\,x=2.\)

c) \(x=2,\\ 2(2x+x^2) = 2(2 \times 2 + 2^2) \\ = 2(4+4) \\ = 2(8) \\ = 16\)

Oops, wrong interpretation for question 2.

I meant:

12P7 = 3991680 ways

\(1 \, million \, \times \, 500 \, trillion = (1 \times 10^6) \times (500 \times 10^{12}) \\ = (1 \times 10^6) \times (5 \times 10^{14}) = (5 \times 10^{20})\)

(scientific notation) 

\(V = πr^2h \\ 100 = πr^2h \\ 100 = π \, \times \, (r)^2 \, \times h \quad |\; \times 4^2 \\ 1\,600 = π \, \times \, (4r)^2 \, \times \, h \quad | \; \times 12 \\ 19\,200 = π \,\times\,(4r)^2\,\times\,12h\)

\(\therefore \tt Container \, B \, can \, hold \, 19 \,200 \, ounces \, of \, water.\)    

from

MWizard2k04 AKA MathW0122

Jan 22, 2004 is not my birthday!

You took the photo... Backwards! I do not want to waste my time.

1. I cannot answer the first question.

2. Since order does not matter, we can arrange the order in any order. This is called a permutation.

\(30P12 = \frac{30!}{\left ( 30-12 \right ) !} \\ = \frac{30!}{18!} \\ = 41 430 393 164 160 000\)

∴ we have 41 430 393 164 160 000 ways.

\(2.4z + 1.2z - 6.5 = 0.7 \\ 3.6z - 6.5 = 0.7 | + 6.5 \\ 3.6z = 7.2 | ÷ 3.6 \\ z = 2\)  

\(a = 4 \\ b = -12 \\ \frac{2ab - b}{a} = \frac{2 \times 4 \times -12 - \left (-12 \right )}{4} \\ = \frac{8 \times -12 - \left (-12 \right )}{4} \\ \frac{-96 - \left ( -12 \right )}{4} \\ = \frac{-84}{4} \\ = -21\) 

{ x = -10

{ x = 8

\(3n - 3 = 4n + 1 | + 3 \\ 3n = 4n + 4 | - 4 \\ 3n - 4 = 4n \\ n = -4 \)