Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The sum of the first 15 terms of an AP is 255, and the first term is 3. Find the common difference.
Solve the equations 3x + 2y = 5 and 4x – 3y = -2 using the elimination method.
If the polynomial f(x) = 2×3-5×2+ 3x-7 is divided by x — 1, find the remainder using the remainder theorem.
How much should a person invest today in a savings account that offers 5% annual interest, compounded annually, if they want the investment to grow to ₹1,00,000 in 10 years?
If the point (3,-4) is equidistant from points (x,1) and (1,x), find the value of “x”.
A rectangle is inscribed in a semicircle of radius 𝑟. Find the dimensions of the rectangle that maximize its area.
The population of a town grows at a rate proportional to its current population. If the population was 20,000 in 2010 and increased to 25,000 by 2015, find the projected population in 2025.
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