So the acceleration, d2y/d2x, is constant. This means that this is a quadratic sequence of the form a(n)=an^2+bn+c. So we can set up a system of equations to solve for the values of a,b, and c. Using the first three points, (1,1), (2,2), and (3,4) we have:
9a+3b+c=4, 4a+2b+c=2, and a+b+c=1 getting the differences...
5a+b=2 and 3a+b=1 and getting this difference...
2a=1, so a=1/2 making 5a+b=2 become:
2.5+b=2, so b=-1/2, making a+b+c=1 become:
1/2-1/2+c=1, so c=1 so the rule is:
a(n)=0.5x^2-0.5x+1 or if you prefer to not have decimals
The correct answers are with side lengths 1 feet and 8 feet, the perimeter is 18 feet; and with side lengths 2 feet and 4 feet, the perimeter is 12 feet.
Step-by-step explanation:
The area of a rectangular banner is 8 square feet.
The side lengths of this rectangular banner are whole numbers.
Thus the possible pairs of side lengths that would give 8 when multiplied with each other are (1 , 8) ; (2 , 4).
So the possible side lengths are 1 feet and 8 feet or 2 feet and 4 feet.
The perimeter when the side lengths are 1 feet and 8 feet are 18 feet.
The perimeter when the side lengths are 2 feet and 4 feet are 12 feet.