Let the tens digit be x and units digit be x – 3. The number is 11x – 3. Interchanging digits gives 11x – 30. Adding them, 22x – 33 = 143, solving to x = 8. The numbers are ...
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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.
The remaining balance after x days is b(x) = 600 minus 15x. The balance becomes zero after 40 days. This represents linear decay because the balance decreases by the same 15 rupees every day.
A polynomial of degree 1 can be 3x plus 2. A polynomial of degree 2 can be x square plus 5x plus 1. A polynomial of degree 3 can be 2x cube minus x plus 4.