16000000=10r-r^2. Calculate the maximum value of r.
To find the maximum value of r in the equation 16,000,000 = 10r - r^2, you need to rearrange the equation in quadratic form, set it equal to zero, and then use the quadratic formula.
First, rearrange the equation:
r^2 - 10r + 16,000,000 = 0
Now use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our equation, a = 1, b = -10, and c = 16,000,000. Substituting these values into the quadratic formula, we get:
r = (-(-10) ± √((-10)^2 - 4(1)(16,000,000))) / (2(1))
Simplifying further:
r = (10 ± √(100 - 64,000,000))/2
The term inside the square root (√) is less than zero, which means the quadratic equation has no real solutions. Therefore, there is no maximum value of r that satisfies the given equation.
Thus, the equation 16,000,000 = 10r - r^2 has no maximum value for r.