A woman wishes to rent a house within 9 miles of her work. If she lives x miles from her work, her transportation cost will be cx dollars per year, while her rent will be 4c x 1 dollars per year, where c is a constant taking various situational factors into account. How far should she live from work to minimize her combined expenses for rent and transportation

Combined cost C(x) = cx + 4c/(x+1)

minimum C(x) ==> C '(x) = 0

==> c - 4c/(x+1)2 = 0

==> 4c/(x+1)2 = c

==> (x+1)2 = 4

==> x +1 = 2

==> x = 1 mile

Hence she should live 1 mile from work to minimise comined costs.

Step-by-step explanation:

answer:  

123455421

step-by-step explanation: easy

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.