Even numbers can’t be simplified
Answer:
Step-by-step explanation:
We have the equations
4x + 3y = 18 where x = the side of the square and y = the side of the triangle
For the areas:
A = x^2 + √3y/2* y/2
A = x^2 + √3y^2/4
From the first equation x = (18 - 3y)/4
So substituting in the area equation:
A = [ (18 - 3y)/4]^2 + √3y^2/4
A = (18 - 3y)^2 / 16 + √3y^2/4
Now for maximum / minimum area the derivative = 0 so we have
A' = 1/16 * 2(18 - 3y) * -3 + 1/4 * 2√3 y = 0
-3/8 (18 - 3y) + √3 y /2 = 0
-27/4 + 9y/8 + √3y /2 = 0
-54 + 9y + 4√3y = 0
y = 54 / 15.93
= 3.39 metres
So x = (18-3(3.39) / 4 = 1.96.
This is a minimum value for x.
So the total length of wire the square for minimum total area is 4 * 1.96
= 7.84 m
There is no maximum area as the equation for the total area is a quadratic with a positive leading coefficient.
1/2 ( -3/2 + 6x + 1) - 3x
Simplify:
= 1/2 (-1/2 + 6x) - 3x
Apply distributive property:
= -1/4 + 3x -3 x
Simplify:
= -1/4
If you would like to know how many hours will Lena need to work before she can afford to buy the computer, you can calculate this using the following steps:
$900 - $473 = $427
$427 / $7 = 61 hours of yard work
Result: Lena will need to work 61 hours before she can afford to buy the computer.
Answer:
-16
Step-by-step explanation:
