The final cache co-ordinates are located at:
S31 56.ABC E116 09.DEF
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A
Solve 0 = x2+ 1
This can be mathematically represented by a letter. How many times does this letter appear in the phrase, ”please i want to solve second order differential equations using Laplace Transforms”. Take 2 from this.
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B
Be careful what you wish for!
Solve the initial value problem y'' - 3y' + 2y= 4e2t, y(0) = -3, y’(0) = 5 using Laplace Transforms. Your final solution will be a function of y in terms of t.
At some stage you will have needed to use partial fraction decomposition to separate your Laplace function into separate fractions before being able to take the inverse laplace transform and find the solution. Multiply the final solution by the number of seperated fractions then substitute t = 0 and evaluate. Add 17 to this number.
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C
Something easier...
Maximise the function Z = 4x1 + x2 subject to the following conditions:
- 3x1 + x2 <= 6
- 10x1 + 6x2 <= 30
- x1 + x2 >= 4
- x1, x2 >= 0
With these conditions find the maximum value of the function, and the values of x1 and x2 that this occurs at. Multiply these 3 values together. Add 3 then divide by 4.
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D
Calculate the gradient vector of the two variable function f(x,y) = x2 – y2, then use this to find the greatest rate of increase at the point (x,y) = (-1,2), and also find the direction that this occurs in (as a UNIT vector). Calculate the dot product of this unit vector and the given point (-1,2), and then multiply this with the calculated greatest rate of increase. Divide your answer by -2.
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E
Solve the hyperbolic function sinh(2x + 1) = 2
Keep your real solution in exact form and add 1/2, you will now have a single fraction as an answer.
Now to the numerator ONLY take the inverse natural log (hint; think exponential function), then square each term separately before adding them together.
Now to the denominator ONLY divide it by the number of times that the exponential function appeared in the trigonometric identity that you used to solve the original function. You now have a new fraction which will simplify to a single number. Square this number then divide it by 3 before taking the cube root of it, then divide by 1.5.
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F
Last one! Something that is actually highschool level!
Michael has more money than Matthew. If Michael gave Matthew $20, they would have the same amount. While if Matthew gave Michael $22, Michael would then have twice as much as Matthew. Work out how much money each person has then add the two values together. Find the modulus from dividing this number by 42.
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Cache is located about a mile (1.6km) from the posted co-ordinates along 4WD tracks.
You can drive to North Ledge (nice spot for a picnic with fantastic views) with a 2WD but you'll need to walk the rest, or 4WD the whole way. If you go to the final co-ordinates directly from Atkins Rd, 2WD won't be a problem for most of the way as long as you have some common sense :-).