The circular area of the drum is (9x^2+30x+25)pi. What is the smallest diameter it can have?
(9x^2+30x+25)
(3x+15) (3x+15)
3(x+5) 3(x+5)
9(x+5)
9x+45 <--------
(9x^2+30x+25)PI
(3x+5) (3x+5)PI
(3x+5)^2 * PI=area
but area =PI r^2
r^2=(3x+5)^2
r= 3x+5
D=2r=6x+10
Thank you
To find the diameter of the circular area, we need to find the square root of the given expression and then multiply it by 2.
The given expression is (9x^2 + 30x + 25)π.
To simplify it, let's factorize the expression.
(9x^2 + 30x + 25) = (3x + 5)(3x + 5) = (3x + 5)^2
Therefore, the area of the drum is Pi(3x + 5)^2.
To find the diameter, we need to find the square root of Pi(3x + 5)^2, and then multiply it by 2.
So, the smallest diameter the drum can have is 2(3x + 5).
To find the smallest diameter of the drum, we need to find the smallest possible value of x that satisfies the equation (9x^2+30x+25).
First, let's find the smallest value of x by setting the expression equal to zero and then solving for x.
9x^2+30x+25 = 0
To solve this quadratic equation, we can either factor it if it is factorable, or use the quadratic formula.
However, we can see that the expression is a perfect square trinomial since it can be factored as (3x+5)(3x+5).
Therefore, the equation can be rewritten as (3x+5)^2 = 0
To find the smallest value of x, we set (3x+5)^2 = 0 and solve for x.
(3x+5)^2 = 0
Taking the square root of both sides:
3x+5 = 0
3x = -5
x = -5/3
So, the smallest value of x that satisfies the equation is x = -5/3.
Next, we need to find the corresponding diameter of the drum. The diameter is given by the expression 9x+45.
Plugging in the value of x, we have:
diameter = 9(-5/3) + 45
= -15/3 + 45
= -5 + 45
= 40
Therefore, the smallest diameter the drum can have is 40 units.