Modelling with Algebra

Hwk.: Pg 215:

#10

E=12mv2

2E=mv2

2Em=mv2m

2Em=v2

2Em=v2

2Em=v

#11.

Rocco: m=5 kg

E=4.2 J

Biff: m=5.5 kg

E=5.2 J

a)VRocco=2Em

=24.25

=8.45

=1.296ms

=1.3ms

VBiff= 2Em

=2 ×5.55.2

=15.2

=1.454ms

=1.5ms

Biff will reach the eucalyptus first since he has a greater speed.

b) E=12m VBiff2

=1251.4542

=5.285

So, Rocco should have a kinetic energy of 5.285 J in order for the bears to reach encalyptus at the same time.

Modelling with Algebra

When problems are solved with algebra, the first step is to translate the given facts into the language of algebra (equaons/expressions) and then solve the resulng equaon.

Example 1: Write an algebraic expression to represent each of the following situaons (translate words into algebraic expressions/equaons). Let x represent a number.

a) twice less than a number.

2x

b) five less than a number

x-5

c) half a number

x2 or 12x

d) three more than double a number

3+2x or 2x+3

e) six mes a number is 54

6x=54 (is means equal)

f) seven more than triple a number is 28.

7+3x=28

g) the sum of two consecuve numbers is 263.

x+x+1=263 (x+1 is the consecutive numbers of x)

Example 2: Millie is four mes as old as Marty. The sum of their ages is 65 years. Find how old the people are

Solution: Let x represent Marty`s age.

Millie`s age is 5x.

x+4x=65

5x=65

5×5=655

x=13

marty is 13 years old and Millie is 4 × 13=52 years old.

Example 3: At the season finale, you present the winner of Canadian Superstar with a recording‐and‐ tour contract.

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The contract states that the winner will be paid $5000 per month while on tour plus $2 per CD sold. a) Write an equaon that relates total earnings in terms of the number of months, m, on tour and the number, n, of CDs sold.

Let E represent the total earnings.

E=5000 m+2n… (*)

b) How much will the winner earn aer the first month if 500 CDs are sold?

m=1

n=500

Sub. m=1 and n=500 is (*)

E=5000m+2n

=5000 ×1+2 ×500

=5000+1000

=6000

The winner will earn $6000 after the first month.

c) Suppose aer the third month on tour the new recording arst earned a total of $74000. How many CDs were sold?

E=74000

m=3

Find n=?

Substitute E=74000 and m=3 in (*) and solve for n,

E=5000m+2n

74000=5000 ×3 +2n

74000=15000+2n

74000-15000=2n

2n=59000

2n2=590002

n=29500

d) In Canada, a record album or CD achieves gold status once it sells 50000 units. How much will the arst make if the CD goes gold aer 6 months?

m=6

n=50000

Substitute m=6 and n=50000 in (*)

E=5000 ×6+250000

=30000 +100000

=130000

The artist would make $130000