The average age of a groom in a wedding for the given age of the bride can be approximated by g(x)= -.0048x^2 +1.44x -3.316, 20≤x≤55, where y is the age of the groom and x is the age of the bride. For which age of the bride is the average age of the groom 30?
0 = -.0048 x^2 + 1.44 x - 3.316-30
.0048 x^2 -1.44 x + 33.316 = 0
x^2 - 300 x + 6941 = 0
x = [ 300 +/-sqrt(90,000 -27,764) ] /2
x = [300 +/- sqrt(62,236) ]/2
x = [ 300 +/- 249 ] / 2
x = 25.26 ignoring the unrealisic solution
perfect thanks Damon!
To find the age of the bride for which the average age of the groom is 30, we need to set g(x) equal to 30 and solve for x.
So the equation becomes:
30 = -.0048x^2 + 1.44x - 3.316
To simplify the equation, we move 30 to the other side:
-.0048x^2 + 1.44x - 3.316 - 30 = 0
Combine like terms:
-.0048x^2 + 1.44x - 33.316 = 0
Now, to solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a equals -0.0048, b equals 1.44, and c equals -33.316. Plugging these values into the formula, we get:
x = (-1.44 ± √(1.44^2 - 4(-0.0048)(-33.316))) / (2*(-0.0048))
After calculating the values within the square root, it becomes:
x = (-1.44 ± √(2.0736 + 0.639744)) / (-0.0096)
Simplifying further:
x = (-1.44 ± √2.713344) / (-0.0096)
Now, calculate the square root:
x = (-1.44 ± 1.6475) / (-0.0096)
Finally, we have two possible solutions:
x1 = (-1.44 + 1.6475) / (-0.0096)
x2 = (-1.44 - 1.6475) / (-0.0096)
Calculating each of these equations will give you the values of x1 and x2, which represent the age of the bride for which the average age of the groom is 30.