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Solve:(56.75)² - 3220

A sum of money invested at compound interest amounts to Rs. 1,000 in 3 years and 1,200 in 4 years. Find the rate of interest. 

A sum becomes Rs. 11,650 in 5 years and Rs. 12,076 in 6 years at simple interest. What is the sum? 

Given: \(\rm x+\frac{1}{x}=2\), find the value of \(\rm x^6+\frac{1}{x^6}-3\left(x^3-\frac{1}{x^3}\right)+5\left(x^2+\frac{1}{x^2}\right) \)

From the summit of a 90-meter-high building, the angles of depression to the top and bottom of a tower are measured at 30° and 60°, respectively. What is the height of the tower in meters?

If the space diagonal of a cuboid is 13 cm, and two of its edges are 3 cm and 4 cm, what is the third edge?

A solid metal sphere that has a radius of 12 centimeters is melted down and reshaped into smaller spheres, each with a radius of 2 centimeters. How many smaller spheres can be created from this material?

A solid metallic sphere of diameter 14 cm is melted and recast into smaller hemispheres each of diameter 7 cm. How many hemispheres can be made?

The proportions of the dimensions of a rectangular parallelepiped are 2 : 3 : 4. If its volume is 768 cm³ what is its smallest dimension?

A rectangular tank has a length of 1 meter, a width of 80 cm, and a height of 50 cm. If the tank needs to be covered completely with square tiles of side 20 cm, how many tiles will be required?