1. A new factory is being built in our Region on a lot that measures 50 metres by 30 metres. The nearest town's by-law states that a
lawn of uniform width must surround the factory such that the
area of the lawn is equal to the area of the factory. If the area of
the factory is 750 m² what must the width of the lawn be correct to
one decimal place?

21000

Step-by-step explanation:

Let x = the width of the lawn

Find the total area of the factory and the lawn: 200 * 210 = 42000 sq/ft

Factory area has to equal lawn area, therefore

21000 sq/ft = area of the lawn and the factory

The dimensions of the factory: (200-2x) by (210-2x)

Find x using the area of the factory

(200-2x) * ( 210-2x) = 21000

42000 - 420x - 400x + 4 = 21000

<=>  - 205x + 5250 = 0

<=> (x-30)(x-175) = 0

<=> x= 30 or x=175 but x = 30 ft is the solution that makes sense for the width of the lawn, so

Length: 210 - 2(30) = 150 ft

Width: 200 - 2(30) = 140 ft

Thus we have the area of the factory using these dimensions:

150 * 140 = 21000

Step-by-step explanation:

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: