another Maths question, done the question just need checking over please!

[Deep]

hey all, i was just hoping that you could help me with this question, i have done it but just need it checking over

Q 1. A ladder has to be manoeuvred around a T-junction in a mine between shafts of width v and w. Calculate a formula for the total length of the ladder l in terms of v, w, and theta, then Declare this as a function in Derive. For the specific shaft widths v=2.4 and w=3.1 produce a plot of the length l against a meaningful range of theta, before finding the maximum length of ladder which could be moved between the shafts. You may assume that the ladder is held horizontal at all times.

For this would you put
v=2.4 w=3.1
Then use this formula:
SIN(A)/a = SIN(B)/b = SIN(C)/c


sin90/b = sin(90 - theta)/w

w.SIN(90)/ SIN(90 - theta) = b

sin(theta)/v = sin(90)/a

a= v.sin(90)/sin(theta)

l=a+b

l = w.sin(90)/sin(90-theta) + v.sin(90)/sin(theta)

w/sin(90-theta) + v/sin(theta)

v/sin(theta) - w/sin(theta - 90)

w/cos(theta) + v/sin(theta)

l = 3.1/cos(theta) + 2.4/sin(theta)

when theta = 10

3.15 + 13.82

1697/100

16.97

when θ = 50

199/25

7.96

when θ =80

2029/100

20.29

Is this all correct? if not where have i gone wrong?

Thanks for the help

 

[Deep]

bump

 

[DaveF]

bump

This all looks more or less OK, but the only reason I can say that without having to spend hours on it is because I've seen a similar question before - what you have written is very hard to follow. You've plucked variables out of the air (what is a? what is b?), you've not said how any of your statements are related to each other (and in fact many of your "statements" aren't even statements), you've skipped out quite big steps in your calculations. [Sorry to be blunt, but one of the things you should be learning at this stage is how to set out your calculations so they are easy to understand].

Obviously evaluating the result for theta = 10, 50, 80 is not a meaningful range of theta, but I assume this is because you can't draw the plot here on the forum.

And you do realise you haven't actually given an answer to the question? (i.e. you haven't given a maximum length for the ladder).

 

[Deep]

This all looks more or less OK, but the only reason I can say that without having to spend hours on it is because I've seen a similar question before - what you have written is very hard to follow. You've plucked variables out of the air (what is a? what is b?), you've not said how any of your statements are related to each other (and in fact many of your "statements" aren't even statements), you've skipped out quite big steps in your calculations. [Sorry to be blunt, but one of the things you should be learning at this stage is how to set out your calculations so they are easy to understand].

Obviously evaluating the result for theta = 10, 50, 80 is not a meaningful range of theta, but I assume this is because you can't draw the plot here on the forum.

And you do realise you haven't actually given an answer to the question? (i.e. you haven't given a maximum length for the ladder).

ah my apologies i should have explained better.

i am using the mathematical program called derive so i have to present my answers and working on that. i have copied the info straight of derive which is why there is no working.

the max length of the ladder is 20.29.

i need to draw a diagram to explain what a and b are. so ill get to work on that and post it here

 

[DaveF]

ah my apologies i should have explained better.

i am using the mathematical program called derive so i have to present my answers and working on that. i have copied the info straight of derive which is why there is no working.

the max length of the ladder is 20.29.

This is wrong. It's actually wrong for two reasons. According to your reasoning, theta = 85 will give a longer ladder, so you haven't found a maximum. But note also that theta = 89 gives a longer one still, and theta = 89.99999 will give a very long ladder indeed. Which should give you a clue that your reasoning is flawed.

The point of the question is that for a ladder to fit round the junction, it has to fit for every value of theta. So you need to find the value of theta that minimizes the expression, not the one that maximises it.

Note that if I was examining, you'd be expected to do a heck of a lot better than saying f(10)=16.97, f(50)=7.96, f(80)=20.29, therefore the minimum is 7.96.

Edit: The actual minimum is about 7.7570963 by my calculations...

 

[Deep]

This is wrong. It's actually wrong for two reasons. According to your reasoning, theta = 85 will give a longer ladder, so you haven't found a maximum. But note also that theta = 89 gives a longer one still, and theta = 89.99999 will give a very long ladder indeed. Which should give you a clue that your reasoning is flawed.

The point of the question is that for a ladder to fit round the junction, it has to fit for every value of theta. So you need to find the value of theta that minimizes the expression, not the one that maximises it.

Note that if I was examining, you'd be expected to do a heck of a lot better than saying f(10)=16.97, f(50)=7.96, f(80)=20.29, therefore the minimum is 7.96.

Edit: The actual minimum is about 7.7570963 by my calculations...

hmm i see your point. how do you think would be best to show the minimum value?

 

[DaveF]

hmm i see your point. what do you think would be best to show the minimum value?

Well, you were specifically asked:

For the specific shaft widths v=2.4 and w=3.1 produce a plot of the length l against a meaningful range of theta,

so I think this is the approach you should take. (I don't think you're expected to get an answer as accurate as mine).

 

[Scarfacé]

Lets just see how clever you all are:


Does the gradient of the curve y = 3x^2 + 7x + 2, where x=2



= 19?

 

[Melm0]

Lets just see how clever you all are:


Does the gradient of the curve y = 3x^2 + 7x + 2, where x=2



= 19?

Yes In the words of Ms Showan: "BASIC! BASIC DIFFERENTIATION OF A QUADRATIC FUNCTION"