• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month
Page
  1. 1
    1
  2. 2
    2
  3. 3
    3
  4. 4
    4
  5. 5
    5
  6. 6
    6
  7. 7
    7
  8. 8
    8
  9. 9
    9
  10. 10
    10
  11. 11
    11
  12. 12
    12
  13. 13
    13
  14. 14
    14
  15. 15
    15

There are three snails; slippery, slimy and slidey. They enter a ten-metre race for food. Each snail runs according to the following rules. Slippery : d= 4.4 + 0.55t Slimy : d= 0.3t(t-7) Slidey : d= 0.3t(t-3.4)(t-9)

Extracts from this document...

Introduction

(Speedy Snails)

image00.png

INTRODUCTION

Mathematics can be used to solve the problem happened in our life such as finding distance or time. Now, we’ve got a problem here. We want to know following questions below. Let us solve the problem by using mathematical method.

There are three snails; slippery, slimy and slidey. They enter a ten-metre race for food. Each snail runs according to the following rules.

Slippery        :        d= 4.4 + 0.55t

Slimy                :        d= 0.3t(t-7)

Slidey                :        d= 0.3t(t-3.4)(t-9)

 The snails race from a designated starting point toward a designated finish line. The distance, d, is measured in metres, and the time, t, is measured in minutes.

QUESTIONS

1.        Find the distance of each snail from the start after:

image01.png

image11.png

image22.pngimage32.png

(An appropriate window and graph)

There are two ways to solve the question 1.

Firstly, we can substitute the time into each formula.

  1. 0 minutes

Slippery         :         d = 4.4 + 0.55t

                                   = 4.4 + 0.55(0)

                                      = 4.4 + 0

                                    = 4.4(m)

Slimy                 :         d = 0.3t(t-7)

                                   = 0.3(0)(0-7)

                                   = 0(-7)

                                   = 0(m)

Slidey                 :          d = 0.3t(t-3.4)(t-9)

                                   = 0.3(0)(0-3.4)(0-9)

                                   = 0(-3.4)(-9)

                                   = 0(m)

Name of snails

Slippery

Slimy

Slidey

Distance (m)

4.4

0

0

(A distance of each snail when the time is 0 min.)

  1. 2minutes

Slippery         :          d = 4.4 + 0.55t

                                   = 4.4 + 0.55(2)

                                   = 4.4 + 1.1

                                   = 5.5(m)

Slimy                 :          d = 0.3t(t-7)

                                   = 0.3(2)(2-7)

                                   = 0.3(-10)

                                   = -3(m) (This means Slimy is going backwards)

Slidey                 :          d = 0.3t(t-3.4)(t-9)

                                   = 0.3(2)(2-3.4)(2-9)

                                   = 0.3(19.6)

                                   = 5.88(m)

Name of snails

Slippery

Slimy

Slidey

Distance (m)

5.5

-3

5.88

...read more.

Middle

Distance (m)

7.15

-3

-9.6

(A distance of each snail when the time is 5min.)

State which snail is leading the race at each time

 According to the results above

@ Slippery         is leading the race at 0 min.

@ Slidey         is leading the race at 2 min.

@ Slippery _         is leading the race at 5 min.

Secondly, we can use a graphics calculator. If we use a graphics calculator we would know not only the distance of each snail at each time but also which snail is leading the race at each time very simply and easily by comparing 3 points on the graph.

      <Slippery>                   <Slimy>                  <Slidey>

image33.pngimage34.pngimage35.png

@(Slippery is leading the race at 0 min.)

     <Slippery>                     <Slimy>                           <Slidey>

image36.pngimage37.pngimage02.png

@(Slidey is leading the race at 2 min.)

       <Slippery>                      <Slimy>                         <Slidey>

image03.pngimage04.pngimage05.png

@(Slippery is leading the race at 5 min.)

Conclusion:

As you can see graphs above

@ Slippery is leading the race at 0 min.

@ Slidey is leading the race at 2 min.

@ Slippery is leading the race at 5 min.

  1. With the aid of your graphical calculator, sketch the path of each snail include each graph in your report.

image06.png

< y = 4.4 + 0.55t >

image07.png

            < y = 0.3t(t-7) >

image08.png

         < y = 0.3t(t-3.4)(t-9) >

3.        At what time(s) is each snail at the starting point.

...read more.

Conclusion

2 + 9t +28)

image27.png

 Slippery will go 237(m) in 6 minutes.

We could also find the time taken by snail by using graphics calculator.

Example:

 How long will Slimy take to complete 17 metre race?

(But, Slimy runs according to the following rules. d= 0.8t+16)

image28.pngimage29.png

 Slimy will take 1.25 (min.) to complete 17 metre race.

Conclusion:

There are 2 methods that can always be used to predict the position of snail at any time and the time taken by each snail to reach any position.

 Substitute the time (the distance) in a function given.

 use a graphics calculator for accuracy and convenience

7.        Generalize your methods in question 6 to solve a function d(t) for any distance, d, or, time, t

I tried to take another kind of d(t) function to generalize my methods in question 6.

d(t) = (3/x)+5                       d(t) =e2t-2

d(t) = (3/x) + 5

By using first method.

1. Let us suppose t = 9(min.)

Substitute t = 9(min.) in function

d         = (3/9) + 5

d          = 5.33(2.d.p)

in this function, distance(d) = 5.33(2.d.p) when the time(t) = 9(min.)

2. Let us suppose d = 8(m)

Substitute d= 8(m) in function.

8         = (3/x) + 5        

8-5         = (3/x)

3        = 3/x

x         = 1

the time(t) = 1 when the distance(d) = 8(m)

 d(t) =e2t-2

By using second method (graphics calculator)

1. Let us suppose that time(t) = 2(min.)

image30.png

2. Let us suppose the distance(d) = 5.5(m)

image31.png

Conclusion:

I’ve generalized that my two methods ( substitute the time or (the distance) use a graphics calculator) can always be used to find any distance, d, or, time, t.

...read more.

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related AS and A Level Core & Pure Mathematics essays

  1. Marked by a teacher

    The Gradient Function

    5 star(s)

    -1 2 0.5 -0.25 3 0.333333 -0.111111111 4 0.25 -0.0625 I predict that the gradient function for when n=-1 = -x -2, in correspondence to the formula nx n-1. I can tell whether these data do in fact agree with this gradient function, but I shall binomially expand this to verify this is the case: 1 .

  2. Marked by a teacher

    Estimate a consumption function for the UK economy explaining the economic theory and statistical ...

    3 star(s)

    Take durable and non-durable goods for example, consumer will spend more on durable goods than non-durable goods. Thus, separate equation should be introduced. Moreover, there are more factors should be take into account. For instance, demographic change and changes in income distribution, and interest rate.

  1. Investigate the number of winning lines in the game of connect 4.

    is the equation for the number of connects in a Nx6 box. But since the first 2 heights didn't follow the pattern we didn't use them in the equation so this equation doesn't work for them. Connect 4 Hx4 Box Hx4 1 2 3 4 5 6 Connects 1 2

  2. Three ways of reading The Bloody Chamber.

    A third level understanding already knows that the elements of the story have mythic status. We are not understanding the story as a myth, but understanding that it presupposes that we already have mythic understanding which is the basis for a further interpretation.

  1. Portfolio - Stopping Distances

    First I will develop a quadratic model. Steps taken to develop quadratic model: 1. The value of is the y-intercept and since the car is at rest the speed is 0 and so is the braking distance. 2. To solve for , we can use a pair of coordinates and plug them into the equation P1 (64,0.024)

  2. Estimate a consumption function for the UK economy explaining the economic theory and statistical ...

    The simplest method of this is graphical although full statistical tests are included in the appendix. The top of figure 2 shows a very strong correlation between the actual consumption figures and the ones derived from our equation; however the bottom half still shows some large residual errors, especially in

  1. The open box problem

    To verify this I am going to draw another graph to show that this is correct. So we can see here the graph definitely shows that the largest volume possible is 16 and that the length of the square cutting for this would be 1.

  2. Estimate a consumption function for the UK economy explaining the statistical techniques you have ...

    Main body of the project The consumption function was introduced in Keynes (1936) " We shall therefore define what we shall call the propensity of consume as the functional relationship, between Y, a given level of income and C the expenditure on consumption out of that level of income...

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work