Algebra
(x+1)(x+2) = A x^2 + 3 x + 2 = A x^2 + 3 x + 2 = 56 x^2 + 3 x - 54 = 0 (x+9)(x-6) = 0 x = 6
Algebra
P = 42 x - 850 x intercept is when P = 0, break even
Algebra
2(2w+1) + 2 W = 35 4 w + 2 + 2 w = 35 6 w = 33 w = 5.5 then L = 2 w + 1 = 12
math
combinations of 20 taken 12 at a time = 20! / [ 12! (8!) ] = 125,970 ( I looked it up in a table of binomial coefficients )
Quadratic to vertex form
y = x^2 + 1 x + 1 y-1 = x^2 + 1 x y-1 + 1/4 = x^2 + x + 1/4 y - 3/4 = (x+1/2)^2 vertex at (-1/2 , 3/4)
Quadratic to vertex form
complete the square y=2x^2+12x+14 you need the coefficient of x^2 to be 1 so divide everything by 2 y/2 = x^2 + 6 x + 7 move the constant to the left y/2 - 7 = x^2 + 6 x add the square of half the coef of x to both sides, in other words 3^2 or 9 y/2 + 2 = x^2 + 6 x + 9 or y/2 ...
Calculus
well, work out from (0,0,0) as you move either way from there along the y axis, x goes up parabolicly as you move either way from there along the z axis, x goes down, again like a parabola
Calculus
a) when is v = 0? (t-5)(t-2) = 0 t = 5 or 2 b) a = 2 t - 7 put in t = 5 and t = 2 c) x = (1/3) t^3 - (7/2) t^2 + 10 t + c put in given point to find c d) when is x a minimum? When v = 0 so put in t = 5 and t = 2 and find the lower x value
physics
there may be a lot of stress but there is no strain if the length is constant.
Calculus
volume = v = x^2 h area = a = x^2 + 4 x h h = 108/x^2 a = x^2 + 4 x (108/x^2) a = x^2 + 432/x da/dx = 0 = 2 x -432/x^2 432 = 2 x^3 x^3 = 216 x = 6 h = 108/36 = 3
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