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.
<h3>
Answer:</h3>
see attached for a graph
domain and range: all real numbers
<h3>
Step-by-step explanation:</h3>
The function is written in slope-intercept form, showing that it has a slope of -3 and a y-intercept of +7. The y-intercept (0, 7) is a point on the line, as is a point 1 unit to the right and down 3 units, (1, 4).
The graph will be the line through these two points.
_____
As with any odd-degree polynomial function, both domain and range are all real numbers: (-∞, ∞).
Answer:
Step-by-step explanation:
1. Put y on the other side - 200x + 500 = y
y= 200x +500
See, this works because -y, when bringing it to another side, you would be adding it. That cancels out the negative, giving you your slope-intercept form. All you have to do is flip it into y=mx + b form, and that's how you get y=200x + 500
4 feet? 20/5=4? Not too sure
