Help ^_^ 2 Unit Questions. (1 Viewer)

[P!xel]

I need full working out Or else I'll end up not getting it again ><" Thanks!

1)Simplify

2) A country property increased in value by 12.5% to a new value of $36 000. What was the value of the property before the increase?

3)

4)

5)

6)

7)

8)

a)

b)

Please help D:

 

[jet]

1) First, 2^(3x) = (2^3)^x
=8^x
Hence, 2^(3x) x 8^(1-x) = (8^x) x 8^(1-x) = 8^(1 - x + x) =8
Hence Answer = 2

2)112.5% = 36000
Now, to get 100% we divide by 1.125
So original price = 32000

3)y=sqrt(x)(x-1)
dy/dx = sqrt(x)(1) + (x-1)[1/(2sqrt(x))]
=sqrt(x) + [(x-1)/2sqrt(x)]

4)dy/dx = (2x)(1) + (x-3)(2)
=2x + 2x -6
=4x -6

5)dy/dx = -[3((x-2)^2)(1)]/3 - [2(1 + 2x)(2)]/2
= -(x-2)^2 - 2 + 4x
=-(x^2 -4x + 4) -2 + 4x
=8x - x^2 -6

6)Using the quotient rule
First the derivative of (x + 1)(x - 2) = (x + 1) + (x - 2) = 2x - 1
Hence, dy/dx = [(x-1)(2x-1) - (x + 1)(x - 2)]/ (x-1)^2
= [x^2 - 3x + 1 -x^2 +x +2]/(x-1)^2
= [3-2x]/(x-1)^2

7)Solving the two equations
4 - x^2 = x^2 - 4x + 4
2x^2 - 4x = 0
x(2x - 4) = 0
x = 0 and x=2, y = 4 and y=0 respectively.

Now, dy/dx = -2x
Hence, at (0, 4), dy/dx = 0
y-4 = 0(x-0)
y=4

at (2, 0) dy/dx = -4
y=-4(x-2)
y = 8-4x

8)a) Firstly, PQT = TSR (alternate angles,PQ, SR parallel)
Similarly, QPT = TRS

Hence, ∆PQT is similar to ∆RST (equiangular)

b) Hence, PQ/RS = PT/RT (corresponding sides in similar triangles are in the same ratio)
PQ/36 = 5/15
PQ/36 = 1/3
PQ = 36/3 = 12cm.

 

[P!xel]

Thanks so much!

Now I get the proving thing a bit more :}

Edit: @ Franman: Yes, it's a part of my homework, I typed it up in MS Word 2007 to make it look neat ^_^.