Respuesta :
Answer:
A(w) = 692 - 12w - (8000/w)
Step-by-step explanation:
Since it has a total area of 500 cm², it means that;
A = hw
Where;
A is area
h is height
w is width
Thus;
500 = hw
h = 500/w
We are told that There is a margin around the edges of 4 cm at the top and 8 cm on the bottom and sides where nothing is printed.
Thus;
We have height as; (h - 4 - 8) and width as; (w - 8 - 8)
Thus;
Area = (h - 4 - 8) × (w - 8 - 8)
Area = (h - 12) × (w - 16)
We know that h = 500/w
And we want to find the printed area in terms of the width(w)
Thus;
A(w) = ((500/w) - 12) × (w - 16)
A(w) = 500 - 12w - 8000/w + 192
A(w) = 692 - 12w - (8000/w)
Using the area formula, the appropriate expression for the area of the poster is A(w) = - 8000/w - 12w + 692
Total Area = 500 cm²
Area = Length × width
Entire area can be expressed thus :
- 500 = l × w
- l = 500 / w
Area with print can be expressed thus :
Length with print = (l - 8 - 4) = (l - 12) cm
Height with print = (w - 2(8)) = (w - 16) cm
Area = (l - 12)(w - 16)
Area = (500/w - 12)(w - 16)
Expressing in terms of width :
A(w) = 500 - 8000/w - 12w + 192
A(w) = - 8000/w - 12w + 692
Hence, the required expression is : A(w) = - 8000/w - 12w + 692