The volume of a rectangular box is x³+16x²+83x+140cm³. The box is x +5 cm long and x+7 cm wide. How tall is the box?
To find the height of the box, we need to divide the volume of the box by the area of the base.
The volume of a rectangular box is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
In this case, the volume is x³ + 16x² + 83x + 140 cm³, the length is x + 5 cm, and the width is x + 7 cm.
So, we have the equation:
x³ + 16x² + 83x + 140 = (x + 5)(x + 7)h
Expanding the right side of the equation:
x³ + 16x² + 83x + 140 = x² + 12x + 35h
Now, we can simplify the equation:
x³ + 16x² + 83x + 140 = x² + 12x + 35h
x³ + 16x² + 83x + 140 = 12x + x² + 35h
x³ + 16x² + 83x + 140 = x² + 12x + 35h
x³ + 16x² + 83x + 140 = x² + 12x + 35h
x³ + 16x² + 83x + 140 = x² + 12x + 35h
Now, we need to solve for h:
h = (x³ + 16x² + 83x + 140) / (x² + 12x + 35)
Now, we substitute the given values of x + 5 for x and x + 7 for x in the equation above to find the height of the box:
h = ((x + 5)³ + 16(x + 5)² + 83(x + 5) + 140) / ((x + 5)² + 12(x + 5) + 35)
h = ((x + 5)³ + 16(x + 5)² + 83(x + 5) + 140) / ((x + 5)² + 12(x + 5) + 35)
h = ((x + 5)³ + 16(x + 5)² + 83(x + 5) + 140) / ((x + 5)² + 12(x + 5) + 35)
Solving for h will give us the height of the box.