Math unit21 formulae
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Transcript of Math unit21 formulae
Unit 21Formula
Presentation 1 Using Formula
Presentation 2 Constructing Formulae
Presentation 3 Negative Numbers
Presentation 4 Temperature Differences
Presentation 5 Substitutions into Formulae
Presentation 6 More Complex Formulae
Presentation 7 Changing the Subject
Presentation 8 Pendulums
Unit 21Formula
21.1 Using Formula
Question
What are the perimeter length and area if and?
The perimeter length, P, and area, A, of a rectangle are given by the formulae
where l is the length and w the width of the rectangle.
Solution
(b)
l
w4cm
8 cm
Solution
(a)
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Unit 21Formula
21.2 Constructing Formula
When repairing air conditioning systems, an emergency engineer charges a basic fee of J$3000 plus J$1200 per hour.
QuestionFind a formula for calculating the engineer's charge for repair work which takes n hours.
SolutionLet C = ChargeSo C = fixed charge + hourly charge × no. of hours
C = J$3000 + J$1200 × nC = J$3000 + J$1200n
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QuestionWhat does the engineer charge in total if the repair takes 6 hours?
SolutionC = J$3000 + J$1200 × 6C = J$3000 + J$7200C = J$10200
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Unit 21Formula
21.3 Negative Numbers
Rules to remember
Calculate
- x - = +- x + = -+ x - = -+ x + = +
- ÷ - = +- ÷ + = -+ ÷ - = -+ ÷ + = +
4 + (−10) = −6 −6 + 8 = 2−4 − 5 = −9 −6 + (−7) = −13(−40) ÷ (5) = −8 (−24) ÷ (3) = −8(−40) ÷ (−5) = 8 (−6) × 7 = −42
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Unit 21Formula
21.4 Temperature Differences
Use information given on the above to answer these questions.What is the difference in temperature between
Kingston and Singapore 4 Kingston and London 25Kingston and Vancouver 29 London and New York 3London and Sydney 26 Lima and Kingston 0Oslo and Kingston 30 Moscow and Kingston 34
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Unit 21Formula
21.5 Substitution in Formula
l = (40 + 0.02T) cmThe length of a metal rod changes with temperature according to formula above; where T is the temperature in ˚CQuestionWhat is the length of the rod when
(a) T = 50˚C (b) T = −10˚C
(a) l = (40 + 0.02 x 50) cm = (40 + 1) cm = 41cm
Solution?
?(b) l = (40 + 0.02 x −10) cm
= (40 + −0.2) cm = 39.8cm
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Unit 21Formula
21.6 More Complex Formula
The formula gives the focallength f for a lensQuestion
What is the value of f, if u = 10cm and v = 8cm
Solution
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Hence ?
Unit 21Formula
21.7 Changing the Subject
The formula that connects ˚Celsius (C) and
˚Fahrenheit (F) is Question
Rewrite the formula in the form C = ......Solution
Take 32 from both sides of the formula
Multiply by 5throughout
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Divide by 9throughout
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So
Unit 21Formula
21.8 Pendulums
Problem
Make l the subject of this equation.?
The period of revolution, T, of a pendulum of length l is given by the formula when G is a constant.
Solution
Divide both sides by to give
Square both sides
Multiply both sides by G to give
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