5 pounds of apples cost $8.20. How much is it for 1 pound?
2 answers:
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Answer: Yes, she will have enough trim for all four sides of the square, because the perimeter of the square photo (30.98 inches) is less than 32 inches of trim she has.
Step-by-step explanation:
The formula for calculate the area of a square is:
Where "s" is the lenght of any side of the square.
The formula for calculate the perimeter of a square is:
Where "s" is the lenght of any side of the square.
We know that that the area of the photo is 60 square inches, therefore, we can solve for "s" from the formula and find its value:
Substituting the value of "s" into the formula , we get that the perimeter of the photo is:
Therefore, since Alicia has 32 inches of trim and , we can conclude that she will have enough trim for all four sides of the square.
A plausible guess might be that the sequence is formed by a degree-4* polynomial,
From the given known values of the sequence, we have
Solving the system yields coefficients
so that the n-th term in the sequence might be
Then the next few terms in the sequence could very well be
It would be much easier to confirm this had the given sequence provided just one more term...
* Why degree-4? This rests on the assumption that the higher-order forward differences of eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of
by
. Then
• 1st-order differences:
• 2nd-order differences:
• 3rd-order differences:
• 4th-order differences:
From here I made the assumption that is the constant sequence {15, 15, 15, …}. This implies
forms an arithmetic/linear sequence, which implies
forms a quadratic sequence, and so on up
forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.