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Solutions to the exercises

Exercise 1
a

-

b

At v = 8 on the v -axis go straight up until you reach the graph corresponding to D = 10 ; then read off the answer on the P -axis.

c

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d

P = 0 . 00013 25 2 20 3 = 650 kW.

Exercise 2
a

The heating costs when there are no sun-hours and the outside temperature is 20°C.

b

k = 800 - 60 3 . 5 - 50 ( - 4 ) = 790 , so € 790 per day.

c

When 60 u + 50 t = 800 , for example when there are 5 sun-hours and there is an outside temperature of 30°C, or 10 sun-hour with an outside temperature of 24°C.

d

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e

K = 340

f

The costs are highest when t = - 2 and u = 4 , i.e. € 660. The costs are lowest when t = 2 and u = 10 , i.e. € 100. Therefore, the cost can vary between € 100 and € 660.

Exercise 3
a

d = 0 . 5 v

b

The number 3.6 arrives from the conversion of v in km/h to m/s.

c

t = ( 14 . 4 + 1 . 8 v ) v

d

N = ( 60 v ) ( 14 . 4 + 1 . 8 v )

e

The speed should be 70 km/h.

Exercise 4
a

V = 50 , so a = 65 , b = 19 . 25 and c = 0 . 39 .
L = 1 , S = 2 and D = 40 gives B = 65 1 + 19 . 25 2 + 0 . 39 40 = 119 . 1 mL.
B ( s s ) = 19 . 25 2 = 38 . 5 mL, so 32.2%. B ( w a i t ) = 0 . 39 40 = 15 . 6 mL, so 13,1%.

b

Car 1 drives at 50 km/h = 13.9 m/s, so for 600 m the first car takes 43.2 s.
Car 2 drives at 70 km/h = 19.4 m/s, so for 600 m this car will take 30.9 s.
Therefore the second car must wait for 12.3 s.

c

Car 1: V = 50 , so a = 65 , b = 19 . 25 and c = 0 . 39 . L = 0 . 9 , S = 0 and D = 0 , so B = 58 . 5 mL.
Car 2: V = 70 , so a = 91 . 6 , b = 37 . 73 and c = 0 . 39 . L = 0 . 9 , S = 1 and D = 12 , so B = 124 . 85 mL.
Car 2 needs more than twice the amount of petrol.

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