The area of a tennis court can be represented approximately by the function A(x) = 10x2 + 3x - 1, and its length can be represented by l(x) = 5x - 1, where x is a distance, in metres.
a) Write and simplify a function, w(x), to represent the width of a tennis court. (2 marks)
b) If x represent 5 m, what is the approximate width of the court? (2 marks)
well, 10x^2+3x-1 = (5x-1)(2x+1)
now the rest is a cinch.
a) To find the width of a tennis court, we need to subtract the length from the area. The width can be represented by the function w(x) = A(x) - l(x).
Substituting the given functions A(x) = 10x^2 + 3x - 1 and l(x) = 5x - 1, we have:
w(x) = (10x^2 + 3x - 1) - (5x - 1)
To simplify, we combine like terms:
w(x) = 10x^2 + 3x - 1 - 5x + 1
w(x) = 10x^2 - 2x
Therefore, the function representing the width of the tennis court is w(x) = 10x^2 - 2x.
b) To find the approximate width of the tennis court when x = 5m, we substitute x = 5 into the function w(x) and evaluate it:
w(5) = 10(5)^2 - 2(5)
w(5) = 10(25) - 2(5)
w(5) = 250 - 10
w(5) = 240
Therefore, when x represents 5m, the approximate width of the tennis court is 240m.