CK12 Calculus - Single Variable

Now we can solvethe problemby substituting into the originalequation:

Hence

and by substitution,

LessonSummary

1. We learnedto solveproblemsthat involvedrelatedrates.

Reviewquestions

1. a. Makeup a relatedratesproblemaboutthe area of a rectangle.
   b. Illustratethe solutionto your problem.


2. Supposethat a particleis movingalongthe curve Whenit reachesthe point
   the -coordinateis increasingat a rate of ft/sec.At what rate is the -coordinatechangingat that instant?


3. A regulationsoftballdiamondis a squarewith eachside of length ft. Supposea playeris runningfrom
   first baseto secondbaseat a speedof ft/sec.At whatrate is the distancebetweenthe runnerand home
   platechangingwhenthe runneris of the way from first to secondbase?


4. At a recentHot Air Balloonfestival,a hot air balloonwas released.Uponreachinga heightof ft, it
   was risingat a rate of ft/sec.Mr. Smithwas ft awayfrom the launchsite watchingthe balloon.At
   whatrate was the distancebetweenMr. Smithand the balloonchangingat that instant?


5. Two trainsleft the St. Louistrain stationin the late morning.The first train was travelingEast at a constant
   speedof mph.The secondtrain traveledSouthat a constantspeedof mph.At PM, the first train
   had traveleda distanceof mileswhilethe secondtrain had traveleda distanceof miles.How fast
   was the distancebetweenthe two trainschangingat that time?


6. Supposethat a ft ladderis slidingdowna wall at a rate of ft/sec.At whatrate is the bottomof the
   laddermovingwhenthe top is ft from the ground?