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Currently the subscription to a gym for a single member is R1 000 annually while family membership is R1 500. The gym is considering raising all memberships fees by the same amount. If this is done then the single membership will cost 5 7 of the family membership. Determine the proposed increase.

  1. Let the proposed increase be x .

    Now After increase
    Single 1 000 1 000+ x
    Family 1 500 1 500+ x
  2. 1 000 + x = 5 7 ( 1 500 + x )
  3. 7 000 + 7 x = 7 500 + 5 x 2 x = 500 x = 250
  4. Therefore the increase is R250.

End of chapter exercises

  1. When an object is dropped or thrown downward, the distance, d , that it falls in time, t , is described by the following equation:
    s = 5 t 2 + v 0 t
    In this equation, v 0 is the initial velocity, in m · s - 1 . Distance is measured in meters and time is measured in seconds. Use the equation to find how long it takes a tennis ball to reach the ground if it is thrown downward from a hot-air balloon that is 500 m high. The tennis ball is thrown at an initial velocity of 5 m · s - 1 .
  2. The table below lists the times that Sheila takes to walk the given distances.
    Time (minutes) 5 10 15 20 25 30
    Distance (km) 1 2 3 4 5 6
    Plot the points. If the relationship between the distances and times is linear, find the equation of the straight line, using any two points. Then use the equation to answer the following questions:
    1. How long will it take Sheila to walk 21 km?
    2. How far will Sheila walk in 7 minutes?
    If Sheila were to walk half as fast as she is currently walking, what would the graph of her distances and times look like?
  3. The power P (in watts) supplied to a circuit by a 12 volt battery is given by the formula P = 12 I - 0 , 5 I 2 where I is the current in amperes.
    1. Since both power and current must be greater than 0, find the limits of the current that can be drawn by the circuit.
    2. Draw a graph of P = 12 I - 0 , 5 I 2 and use your answer to the first question, to define the extent of the graph.
    3. What is the maximum current that can be drawn?
    4. From your graph, read off how much power is supplied to the circuit when the current is 10 amperes. Use the equation to confirm your answer.
    5. At what value of current will the power supplied be a maximum?
  4. You are in the lobby of a business building waiting for the lift. You are late for a meeting and wonder if it will be quicker to take the stairs. There is a fascinating relationship between the number of floors in the building, the number of people in the lift and how often it will stop: If N people get into a lift at the lobby and the number of floors in the building is F , then the lift can be expected to stop
    F - F F - 1 F N
    times.
    1. If the building has 16 floors and there are 9 people who get into the lift, how many times is the lift expected to stop?
    2. How many people would you expect in a lift, if it stopped 12 times and there are 17 floors?
  5. A wooden block is made as shown in the diagram. The ends are right-angled triangles having sides 3 x , 4 x and 5 x . The length of the block is y . The total surface area of the block is 3 600 cm 2 .
    Show that
    y = 300 - x 2 x
  6. A stone is thrown vertically upwards and its height (in metres)above the ground at time t (in seconds) is given by:
    h ( t ) = 35 - 5 t 2 + 30 t
    Find its initial height above the ground.
  7. After doing some research, a transport company has determined that the rate at which petrol is consumed by one of its large carriers, travelling at an average speed of x km per hour, is given by:
    P ( x ) = 55 2 x + x 200 litres per kilometre
    Assume that the petrol costs R4,00 per litre and the driver earns R18,00 per hour (travelling time). Now deduce that the total cost, C , in Rands, for a 2 000 km trip is given by:
    C ( x ) = 256000 x + 40 x
  8. During an experiment the temperature T (in degrees Celsius), varies with time t (in hours), according to the formula:
    T ( t ) = 30 + 4 t - 1 2 t 2 t [ 1 ; 10 ]
    1. Determine an expression for the rate of change of temperature with time.
    2. During which time interval was the temperature dropping?
  9. In order to reduce the temperature 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 ]
    1. At what rate (rounded off to TWO decimal places) is the temperature falling when t = 4 minutes?
    2. Find the lowest room temperature reached during the 10 minutes for which the cooling system operates, by drawing a graph.
  10. A washing powder box 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.
    Show that the total surface area of the box (in cm 2 ) is given by:
    A = 8 x + 960 x - 1 + 240

Simulations

A simulation is an attempt to model a real-life situation on a computer so that it can be studied to see how the system works.By changing variables, predictions may be made about the behaviour of the system.Simulation is used in many contexts, including the modeling of natural systems or human systems in order to gain insight into their functioning. Other contexts include simulation of technology for performance optimization, safety engineering, testing, training and education. Simulation can be used to show the eventual real effects of alternative conditions and courses of action.

Simulation in education Simulations in education are somewhat like training simulations. They focus on specific tasks. In the past, video has been used for teachers and education students to observe, problem solve and role play; however, a more recent use of simulations in education is that of animated narrative vignettes (ANV). ANVs are cartoon-like video narratives of hypothetical and reality-based stories involving classroom teaching and learning. ANVs have been used to assess knowledge, problem solving skills and dispositions of children and pre-service and in-service teachers.

Questions & Answers

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In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
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Source:  OpenStax, Siyavula textbooks: grade 11 maths. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11243/1.3
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