MATH Lecture ) February 1,2017

Transcription

1 MATH 1051 Lecture ) February 12017

2 Announcements HW # 2 due in class Friday February 3 HW # 3 due in class Wednesday February 8 Exam I : Friday February 10 in class Covering Sections A 2- A 3 & A 5- A 10

3 Agenda A 8 Word Problems ( continue d) Translating English to Math Uniform Motion Making a container

4 Tz Express Translating English to Math You have 7 more t-shirts than you have pairs T= J+7 of jeans Muffins cost $2 each of the number of muffins P= 2 M ( dollars ) your muffin bill in terms you buy Muffins cost $10 per dozen Express your muffin bill in terms of the number of muffins 10 p= ( dollars ) you buy

5 Translating English to Math That book Is on sale for 20% off S = B OR 5=0813 I run at a pace of 10 miles per hour Express distance spend running run the I in terms of the time D= lot Q : I run at a of pace my 10 miles hour per Express race time in terms of the race distance t =

6 distance Two Ex 5 ( P A 66 ) who is a Tanya long - Uniform Motion runner an average speed of 8 mi/h Tanya leaves house your and follow the same route runs at hours after you leave in your Honda your average speed is 40mi/h how long will it be before you catch up to Tanya? How far will each of you be from your home? If

7 Uniform Motion That's After A1 1 a * *ie Tanya goes 8 2=16 miles 8 miles away per hour 2 hours she is when car leaves to Call Tanya 's distance R C for runner ) & your distance C ( for Car )

8 Uniform Motion 16+8t Expression for Tanya 's distance from house : Expression for car 's distance from house : 40T * ti# == t 16

9 Uniform Motion Question asks for 1 after car leaves that Car catches Tanya Time 2 Distance of Car & Tanya from house at time t 1 Set Tanya 's distance equal to car 's distance 40T = t = 16 Units? t is in hours + = t= 's 1632 hour = 30 min

10 You Uniform Motion 2 Tanya is ) miles away = 16+4 = 20 miles away Car is 40Gt miles = 20 miles away away Ahs : you will catch up to Tanya after 30 min Will both be 20 miles away Check : Good that both distances are the same! Makes sense that car catches runner quickly

11 You Uniform Motion What Prob 51 p AH Suppose that you have entered an 87 - mile biathlon that consists of a run and a bicycle race the run your average speed is 6 miles per during the bicycle race your average speed mi/h finish the race in 5 hours the distance of the run? hour During and is 25 is

12 You Uniform Motion - What Let B be the distance of the bike race in miles R be the distance of the run Let in D) mile finish the race in 5 hours miles Q : Which equation correctly relates B &R? A) R +13=5 hours C) =87 miles B) = Suppose that you have entered an 87 that consists of a run and a bicycle race the run your average speed is 6 miles per during the bicycle race Milhr the distance of the run? R +13=87 miles your average speed biathlon hour During and is 25 is

13 Uniform Motion 5hr 187mi 1 Run distance = R Bike distance =B =5hrs R+B=87 miles / Runtime + Bike time :6mi Run Fliptoget hours / mile / lhr - Then Runtime of ( Rmi )=frmi I sameforbike time ) y IR =5

14 - Uniform Motion - So use 12+13=87 I R + Is 13=5 Solve one equation for one variable R = 87 - B then substitute f- ( 87 - B) tats B = 5 IB + Is B=3hf - FEB + ob = 013 = -5-5

15 Uniform Motion B = Had) ( )=75 Bike distance = 75 miles Run distance = 87-75=12 miles Reasonable? Yeah people run / bike those distances

16 They Making a Container Ex : You work for a company that sells cereal in a box that is 15in tall base Your company that holds 20% more cereal base dimensions the same with a 3in 10in wants to Make a Family Size box want to Keep the so the box takes up the Same shelf space box use? What's happening? How much cardboard Will the new : Draw & Ql label a picture Qj What Value does the problem ask for? What is the formula / equation for that value?

17 Making a Container : Draw & Ql label a picture Standard Box Family Size Box * Ft toile nil net Qj 3 " 3 " What Value does the problem ask for? What is the formula / equation for that value? Want : amount of cardboard in new box ( surface area) lwtlhtwtn ) SA2=2(

18 Making a Container Standard Box Family Size Box YOEIIP Taft KEY tt SAF :B " " We need h to find the surface area of the Family Size box h " Remember : Your company wants to Make a Family Size box that holds 20% more cereal "

19 Making a Container Q : When the problem says the new box " holds 20% More Cereal 20% bigger " which Value has to be for the new box? A) Volume in in C) Height in in B) Surface area in in ' D) Cost in $ Strategy : Find volume ~> find h - > find Surface area

20 Making a Container FindVdum= Findh:FindSurfa#a :

21 Making a Container

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