maths (1 Viewer)

luke567

New Member
Joined
Jun 18, 2016
Messages
12
Gender
Male
HSC
N/A
Hey All, can u guys please help me out?? having trouble solving these.
worked solutions will be great

1. Two families traveling on holiday drive along roads that intersect at right angles. One family is initially 230km from the intersection and drives towards the intersection at an average of 65kmh^(-1). The other family is initially 125km from the intersection and travels towards it at an average of 80kmh^(-1).
a) show that their distance apart is given by d^2= 10625t^2 -49000t=68525
b) hence find how long it will take them to reach their minimum distance apart.
c) find their minimum distance

please draw the diagram (it would help me a lot )

answer
b)2.3h
c)109.7km

2. A farmer want to fence a rectangular paddock and a square paddock with a combined area of 5000m^2. If the length of the rectangular paddock is to be 3 times the size of its breadth
a) find the dimensions of the paddocks that give the largest perimeter
b) calculate the cost of fencing the paddocks, at $19.95

answer
a)square 46.3m x 46.3m , rectangle 30.9m x 92.7 m
b) $8626.38

3. A chemical reaction causes the amount of hydrogen to be reduces at a rate proportional to the amount of hydrogen present at any one time. If the amount of hydrogen is given by the formula A= A0e^(-kt), and 800ml reduces to 650ml after 3 minutes, find
a) the amount of hydrogen after 1 hour
b) how long it will take for the hydrogen to reduce to 100ml

answer
a)12.6ml
b)30min
 

porcupinetree

not actually a porcupine
Joined
Dec 12, 2014
Messages
664
Gender
Male
HSC
2015
Hey All, can u guys please help me out?? having trouble solving these.
worked solutions will be great

1. Two families traveling on holiday drive along roads that intersect at right angles. One family is initially 230km from the intersection and drives towards the intersection at an average of 65kmh^(-1). The other family is initially 125km from the intersection and travels towards it at an average of 80kmh^(-1).
a) show that their distance apart is given by d^2= 10625t^2 -49000t=68525
b) hence find how long it will take them to reach their minimum distance apart.
c) find their minimum distance

please draw the diagram (it would help me a lot )

answer
b)2.3h
c)109.7km
For (a), use the fact that distance = speed*time to figure out the distance of each family from the intersection. Then use Pythagoras' Thm to calculate distance between the two families
For (b), differentiate the equation in (a) wrt t, and find the value of t which will give a turning point, i.e. the derivative = 0.
For (c), sub this time into the equation in (a).
 

Suu

Member
Joined
Jan 21, 2016
Messages
69
Gender
Undisclosed
HSC
N/A
I'm currently working on writing the working out for question 1, but it looks like there is a mistake in the calculations in the first question. It should be 10625t^2-49900t+68525, not -49000t. As such, the answers for question 1 b & c are slightly different then the ones given.
 
Last edited:

Suu

Member
Joined
Jan 21, 2016
Messages
69
Gender
Undisclosed
HSC
N/A




I have done questions 1&3, I couldn't do question 2. I hope this helps.
P.S. Sorry for the img. quality, it was done on my potato phone.
P.P.S. Im doing this in a LaTeX editor next time.
 

luke567

New Member
Joined
Jun 18, 2016
Messages
12
Gender
Male
HSC
N/A




I have done questions 1&3, I couldn't do question 2. I hope this helps.
P.S. Sorry for the img. quality, it was done on my potato phone.
P.P.S. Im doing this in a LaTeX editor next time.
thank you for your help!
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top