A rectangle has sides of length x cm and 2x - 4cm and the length x cm at time t

seconds is given by x = 2 + 3t, (t >=0) . Show that the area, Acm2 , the rectangle, in
terms of t is A =12t + 18t^2 . Hence find the rate of change of the area at the instant when
t = 2.....

Please solve it........i can't understand this question properly.

2 answers

L = Length = x

W = Width = 2 x - 4

x = 2 + 3 t

L = x

L = 2 + 3 t

W = 2 x - 4 =

W = 2 ( 2 + 3 t ) - 4 =

W = 2 * 2 + 2 * 3 t - 4 =

W = 4 + 6 t - 4 =

W = 6 t

W = 6 t

L = 2 + 3 t

A = W * L =

A = 6 t * ( 2 + 3 t ) =

A = 6 t * 2 + 6 t * 3 t =

A = 12 t + 18 t ^ 2

t = 2

A = 12 t + 18 t ^ 2

A = 12 * 2 + 18 * 2 ^ 2

A = 24 + 18 * 4

A = 24 + 72

A = 96 cm ^ 2
Picking up the equation found by Bosnian at
A = 12t + 18t^2
dA/dt = 12 + 36t ---> the instantaneous rate of change for any t

when t = 2
dA/dt = 12 + 36(2) = 84 cm^2/second
Similar Questions
    1. answers icon 5 answers
  1. Which shape is always a rhombus?my answer is **** A square because it has 4 sides that are the same length.**** A rectangle
    1. answers icon 1 answer
  2. Which shape is always a rhombus?A square because it has 4 sides that are the same length.(my answer) A rectangle because it has
    1. answers icon 2 answers
  3. Which shape is always a rhombus?am i right A square because it has 4 sides that are the same length.(my answer) A rectangle
    1. answers icon 1 answer
more similar questions