Answer:
- P = 2x + 512/x
- 16cm by 16cm
Step-by-step explanation:
The formula for calculating the area of a rectangle = Length * width
Area = LW
256 = xy .... 1
y = 256/x
x is the length
y is the width
Perimeter of the rectangle = 2(x+y)
P = 2x + 2y
P = 2x + 2(256/x)
P = 2x + 512/x
Hence the perimeter as a function of x is P = 2x + 512/x
For the rectangle to have a least perimeter, this means dP/dx = 0
dP/dx = 2 - 512/x²
0 = 2 -512/x²
2 = 512/x²
2x² = 512
x² = 256
x = √256
x = 16
Since xy = 256
y = 256/16
y = 16
Hence the dimensions of the rectangle that has the least perimeter is 16cm by 16 cm
How To Find Inverses:
1. First, replace f(x) with y . ...
2. Replace every x with a y and replace every y with an x .
3. Solve the equation from Step 2 for y . ...
4. Replace y with f−1(x) f − 1 ( x ) . ...
5. Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
Step-by-step explanation:
The answers are A, D and E