Answer:
2/5
Step-by-step explanation:
10/10 = 1 Whole
You need 4/10 to get 1 whole
4/10 is equivalent to 2/5 because when you divide the numerator and denominator by 2 you the 2/5.
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.
Answer:
X = 4, 1
Step-by-step explanation:
Multiplying out
X^2 - 2x - 3x +6 = 2
X^2 - 5x +4 = 0
Factoring:
X^2 - 4x - X +4
X(x-4) - 1(x-4)
(x-1)(x-4)=0
X= 1, 4
X^4 + x^3 + x^2 + x = 0
x(x^3 + x^2 + x + 1) = 0
x[x^2(x + 1) + 1(x + 1)] = 0
x(x + 1)(x^2 + 1) = 0 ⇔ x = 0 or x + 1 = 0 or x^2 + 1 = 0
x = 0 or x = -1 or x^2 = -1 -false
Answer: x= 0 or x = -1.
