Formulae 4
More Complex Formulae

Some formulae such as

= + and z2 = x2 + y2

arise in science or mathematics, but when used do not lead directly to values of f or z.

Here we show how to use the formula to calculate these values.

Worked Examples

1

Use the formula

= +

to find f if u = 10 and v = 8.

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Substituting into the formula gives

= +

First add together the two fractions using 40 as a common denominator:

= +
=

Now to find f, turn both fractions upside-down to give

=   or   f =

2

Find z using the formula

z2 = x2 + y2

if x = 3.6 and y = 4.8.

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Substituting these values into the formula gives

z2= 3.62 + 4.82
z2= 12.96 + 23.04
z2= 36

Now the square root can be taken of both sides to give

z= + or −
z= 6 or −6

Exercises

Use the formula

= +

to find f if:

(a)
v = 3 and u = 4 f =
(b)
v = 6 and u = −5 f =
(c)
v = 7 and u = −3 f =
(d)
v = 10 and u = −4 f =

Find z using the formula

z2 = x2 + y2

if:

Give your answer in the form e.g.: +−5 if there are two solutions.

(a)
x = 1.2 and y = 0.5 z =
(b)
x = 4.8 and y = 6.4 z =
(c)
x = 3 and y = 1.6 z =

Find the value of z as a fraction or mixed number in each case below.

(a)

= x = 4 and y = −10

z =
(b)

= + x = 3 and y = 4

z =
(c)

= + x = 4 and y = −5

z =
(d)

= x = −7 and y = −3

z =
(e)

= + x = 5 and y = −2

z =
(f)

= x = 2

z =
(g)

= x =

z =
(h)

= x = 4 and y =

z =
(i)

+ = x = 1 and y = 6

z =

When three resistors are connected in parallel the total resistance R is given by

= + +

where X, Y and Z are the resistances of each resistor.

Find R if:

(a)

X = 10, Y = 20 and Z = 30

R =
(b)

X = 1000, Y = 5000 and Z = 2000

R = (to 2 d.p.)
(c)

X = 1500, Y = 2200 and Z = 1600

R = (to 2 d.p.)

The formula f = is used in the study of light.

(a)

Calculate f when u = 14.9 and v = −10.2.

Give your answer correct to 3 significant figures.

f =
(b)

By rounding the values of u and v in part (a) to 2 significant figures, check whether your answer to part (a) is reasonable.

f ≈

Investigation

Find four integers, a, b, c and d such that a3 + b3 + c3 = d3.