Question

real life problem

Answer 1

http://boingboing.net/2013/06/21/math-textbook-attempts-to-solv.html

Answer 2

what do you think guys

Answer 3

pretty easy. do you actually want a solution for each part? @Jonask

Answer 4

a and b will be enough thanks

Answer 5

is this normal calculus (single) or multivariate

Answer 6

Just a question Ik this is this isn;t in my frame of math but is a'(s) read "a prime of s"?

Answer 7

derivative a'(t)

Answer 8

or rate of change at t

Answer 9

\[a^2(t)+b^2(t)=c\implies 2a(t)a'(t)+2b(t)b'(t)=0\]

Answer 10

a.) is just chain rule/implicit differentiation:\[\bf a^2(t)+b^2(t)=c \implies 2a(t)(a'(t))+2b(t)(b'(t))=0\]\[\bf \implies a(t)a'(t)+b(t)b'(t)=0 \implies a(t)a'(t)=-b(t)b'(t)\]

Answer 11

using implicit differentiation
okay good

Answer 12

thanx @genius12

Answer 13

b.) Case 1: if we are find the rate of change in his affection for angela which is given as:\[\bf b'(t)=-a(t) \ and \ a(t)>0 \implies b'(t) < 0\]This must mean that if Angela likes Brian then Brian starts losing his love for angela, i.e. Brian's affection for Angela is decreasing.

Case 2: If Angela dislikes brian then:\[\bf b'(t)=-a(t) \ | \ a(t) <0 \ and \ -a(t) >0 \implies b'(t) >0 \]This means that when Angela dislikes him, Brian starts to like her more, i.e. Brian's affection for Angela increases. @Jonask