A standard cubic polynomial is written as ax3 + bx2 + cx + d. Setting the coefficient of the x2 term to -7 gives a valid polynomial of degree 3, such as x3 – 7×2 + x + 1.
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Using the relation C = aF + b, substitute the given conditions. From the melting point, 0 = 32a + b. From the boiling point, 100 = 212a + b. Solving this gives a = 5/9 and b = -160/9.
Form two equations from the gym data: 800 = 10a + b and 1100 = 15a + b. Subtracting them eliminates b to give 5a = 300, which means a = 60. Then, b equals 200.
Substitute the values into y = ax + b. For 10 modules, 400 = 10a + b. For 14 modules, 500 = 14a + b. Subtracting the equations gives 4a = 100, which results in a = 25 and b ...
The square root spiral starts with a base triangle of sides 1 and 1, giving a hypotenuse of root 2. Each successive triangle adds a side of 1, yielding hypotenuses of root 2, root 3, root 4, and continuing sequentially.