Can You Solve These Maths Problems?

Explanation
The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, the square root of 49 is 7 because 7 multiplied by itself equals 49.

Explanation
The diameter of a circle is twice the length of its radius. Therefore, if the radius is 50 yards, the diameter would be 100 yards.

Explanation
When you double the length of both sides of a rectangle, you are essentially increasing the dimensions of the rectangle. Since the area of a rectangle is calculated by multiplying its length and width, doubling both sides will result in quadrupling the area. Therefore, the correct answer is "Area is 4x".

Explanation
Calculate the volume of the cylindrical tank: Volume of a cylinder = π × r² × h Here, r = 4 meters and h = 10 meters Volume = π × 4² × 10 Volume = π × 16 × 10 Volume = 160π cubic meters
The volume of water needs to be transferred to the cuboidal tank. The volume remains the same. Volume of the cuboidal tank = base area × height Here, the base area = 32 square meters and the volume = 160π cubic meters.
Set up the equation to find the height of the cuboidal tank: 160π = 32 × height
Solve for the height: height = 160π / 32 height = 5π
The height of the water in the cuboidal tank: π cancels out, leaving: height = 5 meters
Therefore, the height of the water in the cuboidal tank is 10 meters.

Explanation
Each customer receives 5 CDs. This can be determined by dividing the total number of CDs (15) by the number of customers (3). 15 divided by 3 equals 5.

Explanation
The answer is correct because it accurately states the Pythagorean theorem, which is a fundamental principle in geometry. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship allows for the calculation of unknown side lengths in right-angled triangles and is widely used in various fields of mathematics and physics.

Explanation
The given expression sinθ/cosθ can be simplified using the trigonometric identity for tangent. The identity states that tanθ = sinθ/cosθ. Therefore, the expression sinθ/cosθ is equal to tanθ.

Explanation
The grocer sells 80 kg of jaggery at a 10% profit. This can be determined by setting up a system of equations. Let x represent the amount of jaggery sold at a 10% profit and y represent the amount sold at a 20% profit. We know that x + y = 100 (since the total amount sold is 100 kg) and that 0.10x + 0.20y = 0.12(100) (since the overall profit is 12% of the total outlay). By solving this system of equations, we find that x = 80 and y = 20. Therefore, the grocer sells 80 kg at a 10% profit.