Given:
The area model.
To find:
The area as a sum and area as a product.
Solution:
The four terms of the area model are
.
The area as a sum is the sum of all the terms of given area model.
Area as a sum = 
= 
The area as a product is the factor form of sum of all the terms of given area model.
Area as a product = 
= 
= 
Therefore, the area as a sum is
and the area as a product is
.
an isosceles triangle is a triangle with two twin sides, and therefore two twin angles.
if one angle is 98°, well, we can't have another 98° angle because that makes 98+98 = 196°, and the sum of all interior angles in a triangle cannot be more than 180°.
so the other remaining angles must be the twin smaller angles, namely 180 - 98 = 82, and each twin takes half of that, namely 41°.
Check the picture below.
Total cost, C = 8x^2 + 12xz
volume, V = (x^2)*z = 10
C = 8x^2 + 12x*10/x^2
= 8x^2 + 120/x
dC/dx = 16x - 120/x^2 = 0
16x = 120/x^2
x^3 = 120/16
x = 1.957 ft
d^2C/dx^2 = 16 +240/x^3 = +ve for x = 1.957
so, C is minimum when
x = 1.957 ft z = 2.61 ft
Length of the base x is 1.957 ft and height of side z is 2.61 ft
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I am making one________________
Katy has 5 cakes with each cake having 1/4 of a whole left. How many pieces does Katy have in all?