The length , breadth and height is 32 cm, 16 cm and 8 cm. what is the maximum length of the string that can be used to measure the sides of a box exactly.

The maximum length of the string is 8 cm exactly

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the maximum length of the the string that can be used to

  measure the sides of a box exactly find the highest common factor

  of the dimensions of the box

- The length , breadth and height is 32 cm, 16 cm and 8 cm

∵ The length = 32 cm

∵ The breadth = 16 cm

∵ The height = 8 cm

- Lets find their factors

∵ 32 = 2 × 2 × 2 × 2 × 2

∵ 16 = 2 × 2 × 2 × 2

∵ 8 = 2 × 2 × 2

∴ The highest common factor = 2 × 2 × 2

∴ The highest common factor is 8

∴ The maximum length of the string that can be used to measure

   the sides of a box exactly is 8 cm

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.