10.3 CHAPTER 10. MATHEMATICAL MODELS
(travelling time). Now deduce that the total cost, C, in Rands, for a 2 000 km trip is
given by:
C(x) =
256000
x
+ 40x
- During an experiment the temperature T (in degrees Celsius), varies with time t (in
hours), according to theformula:
T(t) = 30 + 4t−
1
2
t^2 t∈ [1;10]
(a) Determine an expression for the rate of change of temperature with time.
(b) During which time interval was the temperature dropping?
- In order to reduce thetemperature in a room from 28 ◦C, a cooling system is allowed
to operate for 10 minutes. The room temperature, T after t minutes is given in◦C
by the formula:
T = 28− 0 , 008 t^3 − 0 , 16 t where t∈ [0;10]
(a) At what rate (rounded off to two decimal places) is the temperature falling when
t = 4 minutes?
(b) Find the lowest roomtemperature reached during the 10 minutes for which the
cooling system operates, by drawing a graph.
- A washing powderbox has the shape of a rectangular prism as shown in the diagram
below. The box has a volume of 480 cm^3 , a breadth of 4 cm and a length of x cm.
Washing powder
Show that the total surface area of the box (in cm^2 ) is given by:
A = 8x + 960x−^1 + 240
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(1.) 010w (2.) 010x (3.) 010y (4.) 010z (5.) 0110 (6.) 0111
(7.) 0112 (8.) 0113 (9.) 0114 (10.) 0115
