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Thursday, June 08, 2006 

One steals on my hammer, the other one is skating

Hello all... Today I had the honor bestoded upon my of being the scribe... joy...
well its not like we did too much *rolls eyes* just finished two subjects, and got some closure on a couple questions, like the Ice Rink one, apparently people paint the ENTIRE surface of their ice rinks, hmmm...

First off
^2 = squared, ^3 = cubed... etc.

Sequences - If I Had A Hammer

Three nails, each 6 cm long, are hammered into a board until the head of the nail is flush with the surface of the board.

Note: To be flush, the head of the nail must not be more than 0.10 cm above the board's surface.

Nail 1 Moves 0.90 cm into the board with each hit of the hammer

Nail 2 Moves 0.90 cm into the board with the first hit of the hammer.
After each successive hit, the visible part of the nail is 80% of its previous

Nail 3 Moves 0.90 cm into the board wiht the first hit of the hammer.
After each successive hit, the nail moves 0.30 cm less than it moved

Task A.
How may hits of the hammer will it take to drive each nail into the board? Support your answer for each nail.

(My answer)
Nail 1: uMin = 1
u(nMin) = 6

7 Hits @ -0.3 cm

Nail 2: uMin = 1
u(nMin) = 5.1

19 Hits @ 0.09187 cm

Nail 3: Stops at the height of 4.2 cm

Task B
Which of these three situations is least likly to occur and why?

(My answer)
Nail 3 is least likely to occur

Task c
Create a new scenario where a 10 cm nail is hammered until it becomes flush with a board using from 19 to 21 hits (inclusively). The nail cannot move more than 1.5 cm on the first hit.
Support your answer.

(My answer)
nMin = 0
u(n) = u(n-1)-0.5 cm
u(uMin) = {10}

So that was that... lets move on....

Samantha's Ice Rink
Samantha wants to have an ice rink built in her backyard. In order to do this, she must:

  • Hire someone wiht landscaping equipment to level her back yard. This costs $2.50 per square metre.
  • Flood the ice with enough water to form ice to a depth of 12 centimeters. As water freezes, the volume of ice formes is about 1.1 times the volume of the water. The price of the water is $2.10 per 1000 liters. Note: 1 m^3 = 1000 liters
  • paint the ice with ice paint that costs $8.99 per litre. One litre covers eight square meters.
  • allow $65 for miscellaneous materials she need to buy.
  • pay PST and GST , both at 7 percent, for all materials, and only 7 percent GST for labour (having their yard landscaped).
  • pay her children for flooding the rink. Water flows through the garden hose at 20 litres per minute, and the children insist on receiving $3.50 per hour for flooding. Samantha pays no PST or GST on this expense.
Samantha has a budget of $400 to build this rink. Determine the maximum-size rink she can build for that amount. What would be a suitable shape of rink to design? What are the dimensions of the shape you suggest?

ok... that took forever, now the answers:
because everything can be split to fractions of the whole except for the paint, so we used the amount of area that the paint can can cover as the base number for the price quotes and then just divide the anoumt of money by the base price... you'll understand afer its all written down

Land scaping $2.50/m^2 + GST
Water $2.10/1000L = $2.10/m^3 + PST &GST
Paint $8.99/8m^2 + PST & GST
Misc $65 {assuming the taxes are included]
Flooding $3.50/h 1200L/h

For 8m^2
Landscaping 8 X 2.50 + Tx = $21.40
Water 0.8727 X 2.10 + Tx = $2.09
Paint $10.25
Misc $65
Flooding $2.55
Total..............$36.29 per unit

For water:
12 cm = 0.12 m
Vice = 8(0.12)
= 0.96m^3

Amount of water to make 12 cm of ice
1.1w = Vice
1.1w = 0.96
w = 0.96/1.1
w= 0.8727 m^3

How many liters is that?
1000L/1m^3 = XL/0.8727m^3
X = 272.7L

How many hours will that take to fill?
872.7/1200 = 0.72725 hr or 42 minutes and 36 seconds (I belive)

So all said and done how big can we go?
well $400 - $65 = $335
335/36.29 = 9.28

or 9.28 meters by 8 meters, but because we cant buy partial cans of paint, well have to go with 9m X 8m with this budget

Ok... the next question is from a while back, about 2 weeks I think

A water tank is a sphere with a diameter of 3.6m. Estimate the volume of water in the tank if the depth of the water is 24 cm.

Vcone is cone of water
Vcone = Pir^2L/3
= 0.2228m^3

Well thats it for today, and that on took forever :)
thanks for reading

Next Scribe is......... Andrew

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