A. To find the x-intercepts of the function y = 50(x² - 18x + 31), we need to set y to 0 because x-intercepts occur when y = 0.
So, we have:
0 = 50(x² - 18x + 31)
Now, we can solve for x by factoring the quadratic equation or using the quadratic formula.
By factoring or using the quadratic formula, we get the x-intercepts in radical form.
B. The width of the window at its base can be found by determining the distance between the x-intercepts. Once you have found the x-intercepts in radical form as calculated in part A, you can subtract the smaller x-intercept from the larger x-intercept to find the width of the window at its base. This width will give you an approximate measure of how wide the window is at its base to the nearest tenth of a meter.
