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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The total savings pattern is given by y = 800 + 250m, where m is the months. After 6 months, you have 2300 rupees. After 2 years (24 months), you have 6800 rupees.
Let the unknown number be x. The problem gives the linear equation 5/2 x + 2/3 = -7/12. Shifting 2/3 over gives 5/2 x = -15/12, which simplifies to the final number x = -1/2.
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.
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.