Solutions for Amath homework, specially by CHARLENE TAY!!! :) :) :)

Q1. y=(3x-2)^10 over 6

dy/dx = 10(3x-2)^9 (3) over 6

= 30 (3x-2)^9 over 6

When x=1/3,

30 (1-2)^9 over 6 = -5

dy/dx = dy/dx . dx/dt

dy/dx = -10 units/s

Q2.

(i) Clue-Write down all the information given first then start thinking.

dv/dt = dy/dx . dx/dt

60 = (0.03x^2 + 4.4x + 200) . dx/dt

When x = 10, 60 = (3+44+200) . dx/dt

60 = 247 . dx/dt

dx/dt = 60 over 247 cm/s

(ii) dx/dt = 0.2

60 = (0.03x^2 + 4.4x +200) . 0.2

0.03x^2 + 4.4x - 100 = 0

Use formula to solve for x.

Ans: x = 20cm

Q3. y = 3/4 ( x/12 - 1)^6

dy/dx = 3/4 [(6) (x/12 -1)^5 (1/12)]

= 3/8 (x/12 - 1)^5

dy/dt = 12 dx/dt

3/8 (x/12 -1)^5 = 12

(x/12 - 1)^5 = 32

x/12 - 1 = 2

x/12 = 3

x = 36

y = 3/4 ( 36/12 - 1 )^6

y = 48

As for Q5, we'll ask Math Guru tomorrow in class.

(cause I also don't know how to do , hahahas :p) but do try, if not she will scold! >:{

4N1, jia you! Study hard! Don't make our teachers DISAPPOINTED!