CPhill

1.1x + 1.2 x - 5.4 = (-10)    let's make this more simple by mutiplying through by 10 to clear the decimals....so we have......

11x + 12x - 54  = -100      combine like terms

23x - 54 = -100     add 54 to both sides

23x = - -46      divide both sides by 23

x = -46/23 = -2

If we're rounding to the nearest tenth, it's 3.3.......if we're rounding to the nearest hundredth, it's 3.29

28 = 7 x 4   = 7 x 2²

Yep......N + 500%(N)   =  N + 5(N)  = 6N

C(31,7) = 2,629,575

No prob......

x+3/4+1/3  =

x + 9/12 + 4/12  =

x + 13/12

2/10 = 11/x      cross-multiply

2x = 10*11

2x = 110    divide both sides by 2

x = 55

√567 = about 23.81

We could use the Quotient Rule here......however....I generally like to use the Product/Power/Chain Rules, whenever possible....

Note that  √x^2+1/(x-9)^2   =  (x^2 + 1)^(1/2) * (x - 9)^(-2)

And taking the derivaive, we have

(1/2)(2x)(x^2 + 1)^(-1/2)* (x - 9)^(-2) +  (x^2 + 1)^(1/2)* (-2)(x - 9)^-3    (simplify)

x(x^2 + 1)^(-1/2)*(x - 9)^(-2)  - 2 (x^2 + 1)^(1/2)* (x - 9)^-3    (factor)

[(x^2 + 1)^(-1/2) * (x - 9)^(-3) ] * [ x(x-9) - 2(x^2 + 1)] =

[(x^2 + 1)^(-1/2) * (x - 9)^(-3) ] * [ x^2 - 9x - 2x^2 -2] =

[(x^2 + 1)^(-1/2) * (x - 9)^(-3) ] * [ -(x^2 + 9x + 2)]

And this is the same result that Melody and Radix found......!!!