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Need help, URGENT maths question: (1 Viewer)

InteGrand

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Thanks so much InteGrand. Just another question, for one sided limits, when we're asked to find lim(x->a+) f(x) or lim(x-->a-) f(x), are we meant to just calculate f(a) in both cases if it is defined, or are we meant to find f(a) and f(-a) respectively?
 

1008

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Ok thanks! I'll post some more questions soon, BTW got 100% in the online calculus test thanks to you! But there is another algebra + calculus test coming up in two weeks...:(
 

1008

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Hey Everyone:

Here are a few additional questions I need help with, if anyone of you guys could help me that would be great:

1) A rower is rowing across a river. His rowing speed is 2km per hour and there is a current flowing in the river at 1km per hour. Find the direction that the rower must row to go directly across the river. If the river is 300m wide, how long will it take him to cross the river?

2) There are three ropes attached to a block of wood and a man is pulling on each rope. The first man is pulling with a force of 200N due north, the second is pulling with a force of 250N due east and the third is pulling with a force of 150N southwest. What is the net force on the block?

3) Town B is 18km N 18 degrees west from Town A. Town C is 25km N 36 degrees E from B. Town D is 20 km S 72 degrees E from C. Town F is 15km South 25 degrees west from D. What are the distance and bearing of Town F from Town A?

4) Find the parametric vector forms for the plane: 5x^(2) - 6x^(3) = 5 where x =((x(1)),(x(2)),(x(3))) in R3
 

davidgoes4wce

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Hey Everyone:

Here are a few additional questions I need help with, if anyone of you guys could help me that would be great:

1) A rower is rowing across a river. His rowing speed is 2km per hour and there is a current flowing in the river at 1km per hour. Find the direction that the rower must row to go directly across the river. If the river is 300m wide, how long will it take him to cross the river?

2) There are three ropes attached to a block of wood and a man is pulling on each rope. The first man is pulling with a force of 200N due north, the second is pulling with a force of 250N due east and the third is pulling with a force of 150N southwest. What is the net force on the block?

3) Town B is 18km N 18 degrees west from Town A. Town C is 25km N 36 degrees E from B. Town D is 20 km S 72 degrees E from C. Town F is 15km South 25 degrees west from D. What are the distance and bearing of Town F from Town A?

4) Find the parametric vector forms for the plane: 5x^(2) - 6x^(3) = 5 where x =((x(1)),(x(2)),(x(3))) in R3
Do you happen to have answers for them? Just want to compare my answers against the correct ones.
 

1008

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Do you happen to have answers for them? Just want to compare my answers against the correct ones.
Yep sure, here they are:
1) The rower must row 30 degrees upstream
2) 172 N 57 degrees E
3) Approximately 28 km N 51 degrees 9 minutes E from A
4) x = (0,1,0) + a(1,0,0) + b(0,6/5,1) for a,b in R

I think the answer in 4 could be different and still correct...
 

InteGrand

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Hey Everyone:

Here are a few additional questions I need help with, if anyone of you guys could help me that would be great:

1) A rower is rowing across a river. His rowing speed is 2km per hour and there is a current flowing in the river at 1km per hour. Find the direction that the rower must row to go directly across the river. If the river is 300m wide, how long will it take him to cross the river?

2) There are three ropes attached to a block of wood and a man is pulling on each rope. The first man is pulling with a force of 200N due north, the second is pulling with a force of 250N due east and the third is pulling with a force of 150N southwest. What is the net force on the block?

3) Town B is 18km N 18 degrees west from Town A. Town C is 25km N 36 degrees E from B. Town D is 20 km S 72 degrees E from C. Town F is 15km South 25 degrees west from D. What are the distance and bearing of Town F from Town A?

4) Find the parametric vector forms for the plane: 5x^(2) - 6x^(3) = 5 where x =((x(1)),(x(2)),(x(3))) in R3


























 
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davidgoes4wce

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With Question 1, I split up the velocities into horizontal components (current) and the applied force of the rower (diagonal) to work out the resultant velocity.

In the question they also mention the vertical distance 'directly' to the river , by using the formula speed=distance/time to work out the time required to cross the river





 

1008

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Got another question though:

5) You are an auditor for a company whose four executives make regular business trips on four routes and you suspect that at least one of the executives has been overstating her expenses. You don't know how much it costs to travel each route, but you know that it is the same for all the executives. You know the number of trips each executive made on each route in a certain period and you know the total expenses claimed by each executive for this period. If the numbers of trips are as shown in the table below, do you have sufficient information to be sure that someone is cheating? State your reasoning clearly
 

InteGrand

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Got another question though:

5) You are an auditor for a company whose four executives make regular business trips on four routes and you suspect that at least one of the executives has been overstating her expenses. You don't know how much it costs to travel each route, but you know that it is the same for all the executives. You know the number of trips each executive made on each route in a certain period and you know the total expenses claimed by each executive for this period. If the numbers of trips are as shown in the table below, do you have sufficient information to be sure that someone is cheating? State your reasoning clearly




 
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1008

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No, I'm afraid they don't give anything else with the question. I suppose they just want us to deduce if we would be able to find who was overstating their expenses supposing we knew the b values.

BTW how do you use LaTex in the reply form?
 

InteGrand

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No, I'm afraid they don't give anything else with the question. I suppose they just want us to deduce if we would be able to find who was overstating their expenses supposing we knew the b values.

BTW how do you use LaTex in the reply form?
To use LaTeX on this site, we enclose LaTeX code in tex tags. There's a Short Guide to LaTeX on this site here: http://community.boredofstudies.org/14/mathematics-extension-2/234259/short-guide-latex.html

e.g. To get , write [ tex] x^2 [ /tex] (without the spaces I put in the tex tags; I put the spaces in so that you can see the tags, as otherwise it'd get rendered as LaTeX).
 

1008

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Thanks! Also @InteGrand, Wouldn't this be correct, I just formed this augmented matrix:

Reducing it to row echelon form:



But I didn't know what to do next.

As only the b column is non-leading there is a unique solution, so the possibility of having no solution is ruled out. However, the answers at the back say "Perhaps if the costs are negative or very large then you can be sure that someone is cheating". I get the bit about costs being negative thanks to your explanation, but what of the costs being very large?
 
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1008

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Oh, excuse my LaTex code, I'm still learning!
 

Drongoski

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For (1):

Simply solve vector triangle (right -angled) with hypotenuse = 2 and shortest side 1. So resultant speed (2nd shortest side) = sqrt(3). The 2 other angles in said triangle are 30 deg and 60 deg resp. Hence must row 30 deg up river.

So time taken should be 0.3/sqrt(3) = 0.1732 . . . hr = 10.3923 . . . minutes.


ps
ha ha. Didn't see all the earlier-posted solutions, as I completely missed Page 2.
 
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InteGrand

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Thanks! Also @InteGrand, Wouldn't this be correct, I just formed this augmented matrix:

Reducing it to row echelon form:



But I didn't know what to do next.

As only the b column is non-leading there is a unique solution, so the possibility of having no solution is ruled out. However, the answers at the back say "Perhaps if the costs are negative or very large then you can be sure that someone is cheating". I get the bit about costs being negative thanks to your explanation, but what of the costs being very large?
Well if the costs (solutions for x1, x2, x3, x4 from my post) came out to be very large (say 1,000,000 or something), that'd be fishy, because clearly a trip wouldn't cost that much. Basically, if the costs came out to be anything "unreasonable", something must be up.
 

1008

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Well if the costs (solutions for x1, x2, x3, x4 from my post) came out to be very large (say 1,000,000 or something), that'd be fishy, because clearly a trip wouldn't cost that much. Basically, if the costs came out to be anything "unreasonable", something must be up.
Alright, thanks!
 

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