Are a 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?
For the first problem don't you replace all the x with 5 and solve?
A(5)=5^2+5*5 + 6
On the second part,
1/2 b*h=answer in first part, solve for b.
To find the value of A(5), we substitute x = 5 into the function A(x) = x^2 + 5x + 6.
a) A(5) = (5)^2 + 5(5) + 6
= 25 + 25 + 6
= 56
Therefore, A(5) = 56.
To find the length of the base of the sail, we need to use the formula for the area of a triangle:
Area = (1/2) * base * height
Since the triangular sail has a height of x + 3, we can write the equation as:
A(x) = (1/2) * base * (x + 3)
We can rearrange the equation to solve for the base:
base = (2 * A(x)) / (x + 3)
b) Substitute the given function A(x) = x^2 + 5x + 6 and the height x + 3 into the equation:
base = (2 * (x^2 + 5x + 6)) / (x + 3)
So, the length of the base of the sail is (2 * (x^2 + 5x + 6)) / (x + 3).