Area of a sail. The area in square meters for a triangular sail is given by A(x) = x2 + 5x+ 6.
a) Find A(5).
b) If the height of the sail is x+3 meters, then what is the length of the base of the sail?
This is not calculus
a) Plug x = 5 into
A = x^2 + 5x + 6 = 25 + 25 + 6 = __
b) A(x) = (x+2)(x+3)
= (1/2)(base length)(height)
= (1/2)(base length)(x+3)
Base length = 2*A/(x+2)
Use the result of (a) for the area, A.
this don't make sense to me
To find the area of a triangular sail, you are given the formula A(x) = x^2 + 5x + 6.
a) To find A(5), you need to substitute the value 5 into the function:
A(5) = (5)^2 + 5(5) + 6
= 25 + 25 + 6
= 56
Therefore, A(5) = 56 square meters.
b) To find the length of the base of the sail, you need to use the formula for the area of a triangle, which is A = (1/2) * base * height.
Given that the height is x + 3 meters, and the area is defined by A(x), you can set up the equation:
A(x) = (1/2) * base * (x + 3)
You can rearrange the equation to solve for the base:
2 * A(x) = base * (x + 3)
Now substitute the formula for A(x) into the equation:
2 * (x^2 + 5x + 6) = base * (x + 3)
Simplify the equation:
2x^2 + 10x + 12 = base * (x + 3)
Now, solve for the length of the base by dividing both sides by (x + 3):
base = (2x^2 + 10x + 12) / (x + 3)
Thus, the equation for the length of the base of the sail is base = (2x^2 + 10x + 12) / (x + 3).