Find the polynomial f(t) of degree 3 such that and , where is the derivative of . Graph this polynomial.
The graphical representation of the cubic polynomial is,
The equation is,
The derivative of the equation is,
Substitute the points in the above equation to form the equations.
Re-write the equations in terms of a matrix.
The matrix form is,
Consider the matrix.
Using row Echelon form to reduce the matrix.
The values are,
Therefore, the polynomial is,
The graphical representation of is, ss
If you sell two cows and five sheep and you buy pigs, you gain coins. If you sell three cows and three pigs and buy nine sheep, you break even. If you sell six sheep and eight pigs and you buy five cows, you lose coins. What is the price of a cow, a sheep, and a pig, respectively? (Nine Chapters, Chapter 8, Problem 8)
Make me a crown weighing 60 minae from a mixture of gold, bronze, tin, and wrought iron. Let the gold and bronze together form two-thirds of the weight, the gold and tin together three-fourths, and the gold and iron three-fifths. Tell me how much gold, tin, bronze, and iron you must use. (From the Greek Anthology by Metrodorus, century A.D.)
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