The yawn factor is a measure of the ability for an instructor to put their students to sleep during a lecture. The relationship between the yawn factor y of an instructor and the number of students who attends lectures s is given by:

(1920/((y)(s))) = (sqrt(y + s))

(a) Validate that a yawn factor of 4 will result in an attendance of 60 students.
(b) Use a linear approximation to estimate the attendance if the instructor works really hard to decrease their yawn factor to 3.

for (a) you can use two approaches
1. just plug in what is stated and you get (1920/(4*60))=8=sqrt(4+60)
2. assume you do not know the number of students, then you have

(1920/(4*s))=sqrt(4+s) -> 480/s=sqrt(4+s) -> 480^2/s^2=4+s -> 480^2=s^3+4*s^2 etc [btw, cube-root(480^2)=61.304...]

not sure which approximation you are supposed to use, personally i would start with the same as in the last line

(1920/(3*s))=sqrt(3+s) => 640/s=sqrt(3+s) -> ... -> 640^2=s^3+3*s^2 and here the cube-root(640^2)=74.265...

for the linear approximation part, you must take the derivative wrt s to find the slope of the line
after that,write the line equation and plug in 3

this^^
using implicit differentiation I found the derivative at s = 60, y=4 is (-495)/(47)
and the constant needed to make that work for the data point given is (4800)/(47)

giving:

S(y) = (-495)/(47)*y+(4800)/(47)

man this seems complex.