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.
Step-by-step explanation:
Longest side of cuboid: 7cm
Height of cylinder:
2 × 7 = 14 cm
Volume of cuboid:
7x3x4=84
Volume of cylinder:
Surface area of the cylinder:
=128 cm^2
Answer:
S = 2π(4)^2 + 2π(4)(16)
Step-by-step explanation:
The surface area of a cylinder can be found using this equation: 2(πr^2) + 2(πrh). Therefore the answer would be the first one: S = 2π(4)^2 + 2π(4)(16)
Well you can simplify them by dividing by there greatest common factor.
In this case they can both divide by 12!
Thats the biggest number they can divide by...
Soo..
36 ÷ 12 = 3
----------------
48 ÷ 12 = 4
So your answer is 3/4!
Good Luck! :)
