Final answer:
To find the equation of the linear function p, determine the negative reciprocal of k(u)'s slope which gives 5/7. Use the point-slope form with the point (20, 14). Simplify the equation to get the final form of p(u).
Step-by-step explanation:
We need to find the equation of the linear function p such that p(20) = 14 and it is perpendicular to another linear function k(u) = -7/5u - 16.
First, we identify the slope of the given linear function k(u). The slope of k(u) is -7/5. A line perpendicular to k(u) will have a slope that is the negative reciprocal of -7/5, which is 5/7.
To find the equation of p, we use the point-slope form of a line equation, which is y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line. We know that p(20) = 14, so we have a point (20, 14).
Substitute the values into the point-slope form equation to get p(u) - 14 = (5/7)(u - 20). Simplifying this, we get p(u) = (5/7)u - (5/7)(20) + 14. Simplify further to complete the equation for p(u).