Brodudedoodebrodude

Here's what I thought the answer was:

Here's the Exact process I followed to solve it in my head:

Split it up into 2 parts, 17*20 + 17* 4

First work out 17*4 in my head and remember it -> 10*4 + 7*4 = 40+28 = 68

Now 17*20 is 17*10*2 = 340.

Now I just add up these two numbers -> 340 + 68 = 408

If the method of Depreciation used is declining balance Melody then this is the correct answer, nothing suspect about it.

Here's the relationship between straight-line and declining balance depreciation:

As you can see the straight line method will depreciate the asset a fixed amount every year until the asset is worth its final(residual) value whilst Declining balance will constantly adjust the amount of depreciation each year based on its book value for that year. This means that once the book value gets low then the depreciation charge is also low so it will take a longer time to reach a book value that is a small fraction compared to its original value when compared to straight-line depreciation.

Whether to use straight-line or the Declining balance method is up to the person/company to decide - each have their own pro's and con's

I'm assuming we're using Straight-line depreciation here, then:

$$DepreciationPerAnnum = \frac{Cost - ResidualValue}{UsefulLife}$$

2015-2007 = 8 years and current Total Depreciation = (30,000 - 16,500) = $13,500 then

DepreciationPerAnnum = $13,500 total / 8 years = $1687.5 depreciation per annum

Therefore:

$$1687.5 = \frac{30,000 - 1000}{UsefulLife} \\ UsefulLife = \frac{29,000}{1687.5} = 17.19 Years$$

Year When Value is $1000 = 2007 + 17Years = Year 2024.

It'd be easier to multiply the first equation by 3 and the second by 2 then subtract the 2nd equation from the 1st to get one equation in terms of y, but since you said it had to be the substitution method here goes:

$$2x-\frac{y+2}{2} = 22 \\ 2x = 22+\frac{y+2}{2} \\ x=11+\frac{y+2}{4}$$

Now Substituting x into the other Equation:

$$3[11+\frac{y+2}{4}] + \frac{y+2}{3} = 7 \\ 99+\frac{9(y+2)}{4}+y+2 = 21 \\ 396+9y+18+4y+8=84\\13y=-338\\y=-26\\x=11+\frac{-26+2}{4}\\
x=5$$

The opposite sides of a rectangle have equal length. Since the width is 12cm, that means the two width sides added together give you a length of 24 cm.

Since the total length(perimeter) is 50cm, we subtract 24cm from 50cm to get 26 cm remaining for the last two sides. Remember these sides are equal length, so we can divide 26 by 2 to get the length of one side, that is 13cm.

Now area of a rectangle is width x height, so 12cm x 13cm = 156 cm squared.

1: Cos(30) = 1/r therefore r = 2/sqrt3 and r^2 = 4/3

2:Area of equil Triang = (1/2)*(2)*sqrt((2^2)-(1^2))=sqrt3 therefore Area of rectangle = xy = sqrt3

3 Draw lines to the opposite vertices of the rectangle then add the area of the 4 triangles you just made inside the rectangle = total area:

2*area Tri A= 2*[(1/2)(x)sqrt(4/3 - (x^2)/4)

2*area Tri B= 2*[(1/2)(y)(x/2)]

4, Solve simultaneous equation to get x and y:

xy = sqrt3

(x)sqrt(4/3 - (x^2)/4) + (1/2)xy = sqrt3

--> If doing manually you substitute the first equation into the second then solve for x, followed by y, but since I'm lazy I used Wolfram alpha to do this for me and got

x≈2.16662 and y≈0.799424

Thanks a lot Alan, cant thumbs up enough =)

Yeah it depends --> Sqrt(1.7) = ±1.3

Works for the negative version: -1.3 + 3 = 1.7

Falls apart for the positive version: 1.3 + 3 =4.3

You can always choose to take the negative version of the squareroot thats why I think x=1.70 is a suitable answer.

Maybe hard to learn, but definitely one of the easiest subjects once you have managed to learn it!