Time Unit Conversion 1 2 points Sheila drives her car for a time of tday every day. During her lifetime of tlife, she tday life drive spends a total time of tdrive driving her car. 41 minutes 88 years years Solution: Type your answer... The ratio time driven is the same for 1 day or for Sheila's lifetime: tday tdrive 1 day tlife 2 2 points Since tday will be given in units of minutes (not days), convert 1 day to minutes: tday life drive tday tdrive minutes 79 years 2.2 years 1 day) (1 baur ) (i'mmin) tlife Type your answer... Clean up numbers and units: tday tdrive 1440 min tlife Area per Time Unit Conversion 3 2 points A section of the Amazon Rainforest with an area of A, is destroyed in one year. At t field this rate, a section of rainforest with an area of As (the size of a soccer field) is Ar As destroyed in a time of t field. 10,274 km2 7,435 m2 seconds Solution: Type your answer... The ratio tired is the same during the time t field or for 1 year: As Ar 4 2 points t field 1 year AS field The left side of this equation will be given in units of and the right side in km? 10,176 km m2 21.4 seconds Convert units on the left side: As (1 km 2 365 day 24 hour (60 min 60 sec Ar Type your answer... field (1000 m ) 1 year 1 day 1 hour / (1 min ) 1 year Clean up numbers and units: 31.536 km As t field mz 1 yearDerived Unit Conversion 5 2 points Convert units (X 1 and X2 are numbers): X1 X2 X, gram.cm = X, kg.m 4.74 second2 12 hour? Type your answer... Solution: Convert units on the left side of the equation: 6 2 points X, gram.cm 1 second? 1000 gram (100 cm) (60 second ) 2 kg.m? 1 min (60 min ) 2 = X2 hour? X1 X2 5.65 Clean up numbers and units: Type your answer... X1 1.296 8.m = X,kg.m hour ? Since units match on left and right side, cancel the units: 1.296X1 = X2 2 Equations with 2 Unknowns 7 2 points Solve the equations for the variables x1 and X2 in terms of total and diff: Ctotal Cdiff C1+ x2 = Ctotal 206 75 X1 - X2 = Cdiff Type your answer... Solution: 8 2 points Solve 1st equation for 1: Ctotal xdiff C1 = Ctotal - 2 226 70 Plug result into 2nd equation: Type your answer... (total - 2) - 2 = diff Solve for 202: C2 = [total -Cdiff Plug result back into 1st equation: 21 + Ttotal -Zdiff = Xtotal Solve for 21: C1 = total + diffRelated Rates with Spherical Balloon Air is being blown into a spherical balloon - the volume of a sphere is V = 1377123. At some instant: The radius of the balloon is R. The radius of the balloon is increasing at a rate of mg. The volume of the balloon is increasing at a rate of 1-1/4 H int: Take the derivative of the volume equation with respect to time (t) and use the chain rule. Solution: Take the derivative of the volume equation V = gr}? with respect to time (t ) using the chain rule: _. ditdR alt Take the derivative of the volume equation to get 3}; = 4'II'R2 and plug in the symbols for the rate of volume increase (T'V = %) and rate of radius increase (m = %)= 1\"] = (47rR2)7'R 'I'R 'I'V E cm3 0.44 s T 2 points R TR TV cm 3 _ cm 0.46 T 634 % Type your