• Best of luck to the class of 2024 for their HSC exams. You got this!
    Let us know your thoughts on the HSC exams here
  • YOU can help the next generation of students in the community!
    Share your trial papers and notes on our Notes & Resources page
MedVision ad

2u Mathematics Marathon v1.0 (1 Viewer)

skyrockets1530

Member++
Joined
Sep 10, 2004
Messages
184
Location
Sydney
Gender
Male
HSC
2005
DeanM said:
cant resist the simpsons...

sub x=2, 3, 4 into ln(x-1) to get the following...
1/3 { 0 + (4x0.6931) + 1.0986 }
~1.2904

someone else can post a question.. im off to bed.. for real this time..
Ok, i'll post a question

Serena invests 8000 at the begginning of each year into her supperannuation account which pays 10% pa compounded half-yearly, after 10 years, serena reduces her investment to 5000$, find the amount in the supper account after 20 years.
 

skepticality

Member
Joined
Feb 2, 2005
Messages
31
Location
Sydney
Gender
Male
HSC
2006
Question 85

There are two points on a wall of a building, A and B. The two points, A and B are 200meters apart. A pole has the perpendicular distance to the building 50m and point A is placed such that the line drawn from A to the pole is perpendicular to the wall. A person standing has the perpendicular distance to the building 80m and point B is placed such that the line drawn from B to the person is perpendicular to the wall. The two perpendicular lines drawn to the wall are 200m apart. The person is sqrt[40900] meters from the pole. The person is asked to reach the pole as fast as he can, ie with minimal distance. However he must touch the wall first. Find the point on the wall the person touches, by expressing it as the distance from B.

theres actually a dumbass(proper) way and a cheapass way
 
Last edited:

skyrockets1530

Member++
Joined
Sep 10, 2004
Messages
184
Location
Sydney
Gender
Male
HSC
2005
icycloud said:
Alright then DeanM, here goes:
Question 84
Find the equation of the tangent to the curve y = exln(x) at x = 2.
y = exln(x)
y' = exlnx + ex/x
m = e2ln2 + e2/2
y-(e2ln2) = (e2ln2 + e2/2)(x-2)
y = (e2ln2 + e2/2)(x-2) - e2ln2
xe2ln2 + xe2/2 - 2e2ln2 - e2 - y - e2ln2 = 0
thats too long
already posted a question
 
Last edited:

yabby

Member
Joined
Jul 25, 2005
Messages
46
Location
Screwed ville
Gender
Male
HSC
2005
icycloud said:
Alright then DeanM, here goes:
Question 84
Find the equation of the tangent to the curve y = exln(x) at x = 2.
y=e^xlnx
using product rule
dy/dx= e^x.1/x + e^x.lnx
sub x=2
dy/dx= e^2.1/2 +e^2.ln2

When x=2
y= e^2ln2

Sub into formula y-y1=m(x-x1)
y - (e^2.ln2) = (1/2.e^2+e^2.ln2)(x-2)
y= (1/2.e^2+e^2.ln2)(x-2) + (e^2.ln2)
Put that in the calc, and there u go

Umm there was 2 other questions..so i wont add one to make it even more confusing
 

skyrockets1530

Member++
Joined
Sep 10, 2004
Messages
184
Location
Sydney
Gender
Male
HSC
2005
yabby said:
lol sky,doh! u did it way fsater then me..anyways how do u do those square signs..?
haha, for those 2 things just do, sup in brackets and for the ones below, like 2 just do sub in brackets, and close the tags with the /, just click 'reply with quote' and you'll see em
 

skepticality

Member
Joined
Feb 2, 2005
Messages
31
Location
Sydney
Gender
Male
HSC
2006
skepticality said:
Question 85

There are two points on a wall of a building, A and B. The two points, A and B are 200meters apart. A pole has the perpendicular distance to the building 50m and point A is placed such that the line drawn from A to the pole is perpendicular to the wall. A person standing has the perpendicular distance to the building 80m and point B is placed such that the line drawn from B to the person is perpendicular to the wall. The two perpendicular lines drawn to the wall are 200m apart. The person is sqrt[40900] meters from the pole. The person is asked to reach the pole as fast as he can, ie with minimal distance. However he must touch the wall first. Find the point on the wall the person touches, by expressing it as the distance from B.

theres actually a dumbass(proper) way and a cheapass way
Answer is..
123
for those interested
 

skyrockets1530

Member++
Joined
Sep 10, 2004
Messages
184
Location
Sydney
Gender
Male
HSC
2005
I'll answer my own question...
Serena invests 8000 at the begginning of each year into her supperannuation account which pays 10% pa compounded half-yearly, after 10 years, serena reduces her investment to 5000$, find the amount in the supper account after 20 years.

First do the first ten years
deposit is made once a year and interest is paid twice yearly
A1 = 8000(1.05)
A2 = [8000(1.05)]1.05
= 8000(1.052)
A3 = 8000(1.053) + 8000(1.05)
A4 = 8000(1.054) + 8000(1.052)
A4 = 8000(1.054) + 8000(1.052)
An = 8000(1.05n + 1.05n-2 + 1.05n-4 + ....)
A20 = 8000(1.0520 + 1.0518 + 1.0516 + .... + 1.052)
A20 = 8000[(1.052(1.102510 - 1)) / .1025]
NOTE: the rate is 1.1025 as the series goes 1.052 + 1.054...
A20 = 142,264.2513
Now for the second 10 years
A21 = [142,264.2513 + 5000]1.05
A22 = 147,264.2513(1.052)
A23 = 147,264.2513(1.053) + 5000(1.05)
A24 = 147,264.2513(1.054) + 5000(1.052)
...
A40 = 147,264.2513(1.0520) + 5000[(1.052(1.10259 - 1)) / .1025]
Note the second series of interest only has 9 terms
A40 = $466,384.57 total value of super account
That should be all correct, please let me know if theres an error

Next question:
given that d/dx = ex2 = 2xex2 , evaluate the integral of xex2 between 1 and 0
 

rsingh

Member
Joined
Oct 2, 2004
Messages
186
Gender
Male
HSC
2005
Question: Find the integral of 1/x between 1 and 0.

Thanks.
 

skepticality

Member
Joined
Feb 2, 2005
Messages
31
Location
Sydney
Gender
Male
HSC
2006
skyrockets1530 said:
Next question:
given that d/dx = ex2 = 2xex2 , evaluate the integral of xex2 between 1 and 0
d/dx = ex2 = 2xex2
therefore 1/2 [integral] boundary 0..1 2xex2 = [ex2]10
=2[ex2]10
=2(e-1)

Next Question (do it guys..)

There are two points on a wall of a building, A and B. The two points, A and B are 200meters apart. A pole has the perpendicular distance to the building 50m and point A is placed such that the line drawn from A to the pole is perpendicular to the wall. A person standing has the perpendicular distance to the building 80m and point B is placed such that the line drawn from B to the person is perpendicular to the wall. The two perpendicular lines drawn to the wall are 200m apart. The person is sqrt[40900] meters from the pole. The person is asked to reach the pole as fast as he can, ie with minimal distance. However he must touch the wall first. Find the point on the wall the person touches, by expressing it as the distance from B.

theres actually a dumbass(proper) way and a cheapass way
 

rama_v

Active Member
Joined
Oct 22, 2004
Messages
1,151
Location
Western Sydney
Gender
Male
HSC
2005
d/dx (ex2) = 2x ex2
.: ∫xex2 dx
= (1/2) ex2
= (1/2)(e1 - e0)
= (1/2)(e - 1)

Next question:
A car, of initial value $15000 depreciates at a rate of 3% p.a.
Calculate the car's worth after five years.
 
Last edited:

Twiggyy

twiggy
Joined
Feb 20, 2005
Messages
65
Location
parra
Gender
Female
HSC
2005
question:
A car, of initial value $15000 depreciates at a rate of 3% p.a.
Calculate the car's worth after five years.

15000(1-0.97)^5 = $12881


next q -

What values of k are always positive?
x^2 - 2kx + 6k
 
I

icycloud

Guest
Twiggyy said:
What values of k are always positive?
x^2 - 2kx + 6k
Positive definite: a > 0 and Discriminant < 0

a = 1 > 0

Discriminant = (-2k)^2 - 4(6k)
= 4k^2 - 24k
< 0

4k^2 - 24k < 0
k^2-6k < 0
k(k-6) < 0

Therefore, 0 < k < 6 #

There's already an unanswered question above, post #174.
 

Kutay

University
Joined
Oct 20, 2004
Messages
600
Location
Castle Hill
Gender
Male
HSC
2005
lie_stella said:
Next Question

Solve ln(7x-12) = ln x
well because they got the same base they cancel out ---> log laws there for it becomes 7x - 12 = x and x = 2

Hope thats right, correct me if i am wrong

Next Question:

The point P(x,y) lies on the line y = 2x - 9 and is equidistant from A(0,1) and B(2,3) . Find the Equation of the Locus P

Answer:
ROOT {(x-0)2 + (y-1)2} = ROOT {(x-2)2 + (y-3)2}
Then jus square both sides and u you in up getting 4y +4x -12 = 0 by putting to one side
 
Last edited by a moderator:

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

Top