The simplified expression is 
and the restriction is 
<h3>How to simplify the expression?</h3>
The expression is given as:
Express x^2 - y^2 as (x + y)(x - y) and factorize other expressions
Rewrite the expression as products
Cancel out the common factors
Express 4x^2 - y^2 as (2x - y)(2x + y)
Cancel out the common factors
Take the LCM
Hence, the simplified expression is and the restriction is
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11/20
Divide 11 by 20 to find the decimal value.
11/20 = 0.55
The decimal only contains two numbers, so it is a terminating fraction.
See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
Production would take place at a point inside the production possibility frontier
The Production possibilities curve is a curve that shows the various combination of two goods a company can produce when all its resources are fully utilised.
The PPC is concave to the origin. This means that as more quantities of a product is produced, the fewer resources it has available to produce another good. As a result, less of the other product would be produced. So, the opportunity cost of producing a good increase as more and more of that good is produced.
Points inside the production possibilities curve means that the nations resources are not being fully utilised
When the unemployment rate increases, it means that labour resources are not been fully utilized. As a result, production would take place at point inside the production possibilities curve
Point outside the curve or to the right of the curve means that the production level is not attainable given the level of resources
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