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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