Explanation

Circumference is the total length around a circle.

It is calculated as 𝐶 = 2𝜋𝑟, where 𝑟 is the radius.

Explanation

To find the length of marks on dust when the wheel completes one rotation, we need to calculate the circumference of the wheel:

Circumference = π × diameter

= π × 35 cm

≈ 3.14 × 35 cm

≈ 109.9 cm

Rounding to the nearest whole number:

≈ 110 cm

Explanation

Parallel lines are lines in a plane that are always the same distance apart and never intersect, no matter how far they are extended.

They have the same slope in geometry and do not meet at any point.

Explanation

To find the distance from the tip of the pole to the tip of the shadow, use the Pythagorean theorem:

Distance² = Pole height² + Shadow length²

Given:

Pole height = 5 m

Shadow length = 3 m

Distance² = 5² + 3²

Distance² = 25 + 9

Distance² = 34

Distance = √34 ≈ 5.83 m

Explanation

To find the area of the road, we need to find the area of the garden and subtract the area of the inner garden (without the road).

Garden area = Length * Width

= 75 cm * 82 cm

= 6150 cm²

Inner garden dimensions:

Length = 75 cm - 2 * 5 cm = 65 cm

Width = 82 cm - 2 * 5 cm = 72 cm

Inner garden area = 65 cm * 72 cm

= 4680 cm²

Road area = Garden area - Inner garden area

= 6150 cm² - 4680 cm²

= 1470 cm²

Explanation

The triangle with vertices A(1,2), B(0,4), and C(3,5) has two sides of equal length.

This makes it an isosceles triangle, where at least two sides are equal.

Explanation

Area of carpeting part = (74 + 4) * (61 + 4) - 74 * 61

= 78 * 65 - 4514

= 5070 - 4514

= 556 cm²

Explanation

To convert numbers from decimal to binary

The given decimal number is divided repeatedly by 2 and the remainders are noted down till we get 0 as the final quotient.

Explanation

Given:

Height of the hill = 240 m

Angle of depression to the top of the minaret = 30°

Angle of depression to the bottom of the minaret = 60°

Let's denote the distance from the base of the hill to the minaret as x.

For the bottom of the minaret (60° angle):

tan(60°) = 240 / x

√3 = 240 / x

x = 240 / √3

For the top of the minaret (30° angle):

tan(30°) = (240 - h) / x

1/√3 = (240 - h) / (240 / √3)

Simplifying:

240 - h = 240 / 3

240 - h = 80

h = 160

Explanation

A kite is a four-sided shape with two pairs of adjacent sides equal — a type of quadrilateral.

It does not have six sides like a hexagon or qualify as a true diamond in geometry.