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.
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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 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.
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.
Squaring x + y + z = 0 gives x2 + y2 + z2 + 2(xy + yz + zx) = 0. Since xy + yz + zx = 0, it simplifies to x2 + y2 + z2 = 0. ...