2u Mathematics Marathon v1.0 (1 Viewer)

[Jago]

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

I don't understand your diagram :s

anyway

Next Question

Solve ln(7x-12) = ln x

Spoiler

7x - 12 = x
x = 2

someone else do that wall/pole question.

 

[sunjet]

Spoiler

7x-12 = x ; 6x = 12 ; x = 2

 

[DeanM]

yea me either.... :s redraw the draw diagram..

 

[lie_stella]

how bout
ln(7x-12) = 2lnx

 

[karen88]

Spoiler

ln(7x-12) = ln x^2
x^2 = 7x-12
x^2 -7x+12=0
(x-4)(x-3)=0
therefore x=4 or x=3

A metal cube being heated has its edge length expanding at a constant rate of 0.01 mm/s. At what rate is its volume increasing when the side length is 60mm

 

[skyrockets1530]

how bout
ln(7x-12) = 2lnx

Spoiler

x² = 7x - 12
x² - 7x + 12
(x - 3)(x - 4)
x = 3,4

Next question
Find the area of the minor segment formed by an angle of 40^o subtended at the center of a circle with radius 2.82cm

 

[Kd14]

A metal cube being heated has its edge length expanding at a constant rate of 0.01 mm/s. At what rate is its volume increasing when the side length is 60mm

Just answerin this skipped question.

Spoiler

V(cube) = side * side * side = x^3
dV/ds = 3x^2
ds/dt = 0.01 mm/s

dV/dt = dV/ds * ds/dt
dV/dt = 3(60)^2 * 0.01
dV/dt = 108 mm^3/s

 

[word.]

yes i didn't read the question...

Spoiler

40 degrees = 2pi/9 radians
A = 1/2r²(@ - sin@)
A = 1/2(2.82)²(2pi/9 - sin(2pi/9)) = 0.22cm²

Question:
Find the sum of the first 100 multiples of 5.

 

[Daza]

I'm not sure how you do the spoiler thing but heres my answer anyways

A=0.5r^2(angle - sin angle)

=0.5*2.82 [ (40pi/180) -sin40 ]

= 55.49 [2dp] I think

 

[Daza]

Hey 'word.' isn't wat u just found the sector?

 

[word.]

no i found the length of the arc

 

[mcs]

Q188

S100 = n/2 (2a+(n-1)d)
= 100/2 (10+(99)5)
= 50 (10+495)
= 50 (505)
= 25250

 

[MarsBarz]

Find the sum of the first 100 multiples of 5.

Spoiler

5 + 10 + 15 + ...
Arithmetic serie with a = 5, d = 5
S₁₀₀ = (100/2)[2*5+99*5)
= 25250

Question #X:
20 cards, labelled 1 to 20, one card is chosen, find the probability that its number is composite or >12.

 

[chin music]

Spoiler

Sample space is 20, Event Space is 14 Therefore is 7/10

3*ln(2/3)=ln(8/x) Solve for x

 

[lie_stella]

Question #X:
20 cards, labelled 1 to 20, one card is chosen, find the probability that its number is composite or >12.

what is composite means?

Spoiler

I guess it is.. 7/20 ?

Next question

A fish farmer began business on 1 January 1998 with a stock of 100 000 fish. He contract to supply 15400 fish at price of $10 per fish to a retailer in December each year. In the period between January and the harvest in December each year, the number of fish incereases by 10%.

When will the farner have sold all his fish and what his total income will be?

 

[blue_eye_baby]

application of differentiation

a liquid is pumped from a 25000 litre tank such that the rate of changes in volume is given by dV/dt = -1.92t
i) if the tank is initailly full, show that V = 25000 - 0.96t^2

ii) how long before the tank is 40% full?

 

[lie_stella]

3*ln(2/3)=ln(8/x) Solve for x

Spoiler

ln (2/3)^3 = ln (8/x)
4/9 = 8/x
x = 18

 

[lie_stella]

application of differentiation

a liquid is pumped from a 25000 litre tank such that the rate of changes in volume is given by dV/dt = -1.92t
i) if the tank is initailly full, show that V = 25000 - 0.96t^2

ii) how long before the tank is 40% full?

Spoiler

integrating dV/dt = -1.92t
V = -0.96t^2+C
when t = 0 it is full V=25000
So 25000 = 0+C
Then V = 25000 - 0.96t^2

ii) 40% of full = 10000
10000 = 25000 - 0.96^t
t= 4.35, rounded to 5

 

[chin music]

what is composite means?

Next question

A fish farmer began business on 1 January 1998 with a stock of 100 000 fish. He contract to supply 15400 fish at price of $10 per fish to a retailer in December each year. In the period between January and the harvest in December each year, the number of fish incereases by 10%.

When will the farner have sold all his fish and what his total income will be?

Composite means something has factors. Ive seen this questin before.

Spoiler

So it starts at 100000
End of 1st year- 100000*(1.1)-15400
End of second year- (100000*(1.1)-15400)1.1-15400
= 100000(1.1)^2-15400(1.1)-15400
Third year=(100000(1.1)^2-15400(1.1)-15400)1.1-15400
=100000(1.1)^3 -15400(1.1)^2-15400(1.1)-15400
So.. An = amount left at time n years.
An=100000(1.1)^n-15400(1+(1.1)^2+(1.1)^3+...+(1.1)^(n-1))
Thats a GP with a=1 and r=1.1 which equals ((1.1)^n-1)/.1)
So it equals 100000(1.1)^n-(15400/.1)(1.1^n-1)
So when the farmers sold all his fish then An =0
So...... This happens when 100000(1.1)^n=154000((1.1)^n-1)
Simplifying this a lot.. (1/3)((1.1)^n)=1
(1.1)^n=3
log(1.1)3=n
=11.5 years!! and that was a bitch of a question. EDIT- crap didnt read the income part. um.. Someone else help me out on this one if no ones answered it by the time ive worked it out ill do my answer

Theres a few questions going now including one of mine so ill bar the question asking

 

[lie_stella]

Composite means something has factors. Ive seen this questin before.

Spoiler

So it starts at 100000
End of 1st year- 100000*(1.1)-15400
End of second year- (100000*(1.1)-15400)1.1-15400
= 100000(1.1)^2-15400(1.1)-15400
Third year=(100000(1.1)^2-15400(1.1)-15400)1.1-15400
=100000(1.1)^3 -15400(1.1)^2-15400(1.1)-15400
So.. An = amount left at time n years.
An=100000(1.1)^n-15400(1+(1.1)^2+(1.1)^3+...+(1.1)^(n-1))
Thats a GP with a=1 and r=1.1 which equals ((1.1)^n-1)/.1)
So it equals 100000(1.1)^n-(15400/.1)(1.1^n-1)
So when the farmers sold all his fish then An =0
So...... This happens when 100000(1.1)^n=154000((1.1)^n-1)
Simplifying this a lot.. (1/3)((1.1)^n)=1
(1.1)^n=3
log(1.1)3=n
=11.5 years!! and that was a bitch of a question.

Theres a few questions going now including one of mine so ill bar the question asking

and what is his total income?? hmm... ;P