Abox, with rectangular sides, base and top is to have a volume of 2 cubic feet. it has a square base. express the surface area a of the box in terms of the width w of the base. if the material for the base and top costs 40 dollars/ft2 and that for the sides costs 50 dollars/ft2 express the total cost c as a function of the width.

Total cost F (w) = 160/w + 200* √(2w)

Step-by-step explanation:

Volume in cubic feet

V (box) = x*y*w         and  square base means x=y so V= 2 = x^(2)*w

hence x^(2) = 2/w (1)

Area of base and top in square feet, and cost in $

Area(t+b) = 2*x*y = 2x^(2)       C(1) = Cost of ( base + top)  C(1) = 40*2x^(2)

                                                  C(1) =80*x^(2) and from eq. 1

                                                  C(1) = 80*2/w = 160/w

Area of sides = 4 * x* w = 4*√((2/w))*w

C(2) = Cost of sides. is:            C(2)= 50*4*√((2/w))*w    C(2) = 200* √2w

Total Cost = F(c) = 160/w +200*√2w

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752