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**Unformatted text preview: **ed and write expressions for all important quantities.
2) Write the system of equations that models the situation described in the problem.
3) Solve the system of equations.
4) Answer the problem. Your answer must be what the problem is asking you to find. example: A mounted police officer is riding his horse at his top speed of 10 m/s toward
the bank, and is 100 m away when a bank robber begins to accelerate away
from the bank going in the same direction as the officer. The robber's
distance, d in metres, away from the bank after t seconds can be modelled by
the equation d = 0.2 t 2.
When and where will the
d
officer catch the robber?
Answer to 1 decimal place.
d
100 m
1) d represents the distance from the bank in metres.
t represents the time from when the bank was robbed in seconds. 2) The bank robber ........................................................
The mounted police officer ....................................... 0.2 t 2 = 10t − 100
0.2 t 2 − 10t + 100 = 0
t 2 − 50t + 500 = 0 3) t=
When − (−50) ± (−50)2 − 4(1)(500)
2(1) t = 25 − 5 5 ≈ 13.8 d = 10 ( 25 − 5 5 ) − 100
= 150 − 50 5 4) d = 0.2 t 2
d = 10t − 100 ≈ 38.2 or = 25 ± 5 5 t = 25 + 5 5 ≈ 36.2, d = 10 ( 25 + 5 5 ) − 100
= 150 + 50 5 ≈ 261.8 The officer should catch the robber ( 25 − 5 5 ) s or about 13.8 s after the
robbery and (150 − 50 5 ) m or about 38.2 m from the bank. Unit 3: Day 4 notes - Solving Problems with Systems of Equations Page 2 of 2 exercise: A 20-m tall parabolic arch is being constructed on level ground. Its bases will
be 10 m apart. To support this arch, another parabolic arch 5-m tall with
bases 20 m apart is going to be attached. How high above the ground will the
two arches be joined? [Answer: 4 m] PRE-CALCULUS 11 Unit 3 – Day 5: LINEAR INEQUALITIES IN TWO VARIABLES INEQUALITIES
An inequality is a mathematical statement that compares values that may not be equal.
• < is the symbol for "is less than"
• > is the symbol for "is greater than" 8 < 12
−8 > −12 • ≤ is the symbol for "is less than or equal to"
• ≥ is the symbol for "is greater than or equal to" The same rules for equations can be applied to inequalities with one exception!
When multiplying or dividing both sides of an inequality by negative number,
the direction of the inequality symbol must be reversed.
8 < 12 is a true statement, when 8 is multiplied or divided by −1 the result is −8
when 12 is multiplied or divided by −1 the result is −12
−8 is not less than −12 −8 ≮ −12
−8 > −12 To keep the statement true, < must be reversed to >. To solve any inequality, find all the values of the variable that satisfies the inequality.
example: Solve 7 − 2x < 1 and graph its solution set. 7 − 2x < 1
−2x < −6 o Subtract 7...

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