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bry7474
05.05.2020 •
Mathematics
A rectangle has sides measuring (2x + 7) units and (5x + 9) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (4 points)
Part B: What are the degree and classification of the expression obtained in Part A? (3 points)
Part C: How does Part A demonstrate the closure property for polynomials? (3 p
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Ответ:
First of all, let's analyze this equation. There is no restriction for
x since the domain of a function sin
( x )
is all real numbers.
Secondly, we can introduce an intermediary variable y = sin ( x
and express this equation in terms of y : y 2 2 y + 3 or y 2 − 2 y 3 = 0
This equation has solutions: y 1 , 2 = 2 ± √ 4 + 12 2 or y 1 = 3 and 2 = − 1
Now we have to take into consideration that y = sin ( x )
and, as such, is restricted in values from − 1 to 1
(inclusive).
Therefore, solution y 1 = 3
would not lead to any value of x .
The second solution y 2 − 1
can be used to find x : sin ( x ) = 1
implies that x= − π 2 + 2 π N , where N - any integer number or, in degrees, x = −
90 o +
360 o ⋅
N
This is a final solution to the problem