Volume = Width x Depth x Length. Increase in volume = Width x 2 m x 100 m. Assuming width = 1 m, Volume = 1 m x 2 m x 100 m = 200 m³.

Volume = Length × Width × Depth. If width is constant, Volume increase = 1000 m × Width × 2 m = 2000 m³.

If the derivative of a function is positive for all x, it indicates that the function is increasing throughout its domain.

Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.

The diagonal d of a square is related to the side length s by the formula d = s√2. Therefore, s = d/√2 = 10√2/√2 = 10 cm. The area is s² = 10² = 100 cm².

If the diagonals of a quadrilateral are equal and bisect each other, it can be classified as a rectangle.

A kite has diagonals that bisect each other at right angles.

If the diagonals of a quadrilateral bisect each other at right angles, it indicates that the quadrilateral is a rhombus.

If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.

A quadrilateral with diagonals that bisect each other is a parallelogram, but it can also be a rectangle or rhombus.

If the diagonals of a quadrilateral bisect each other, it is a property of parallelograms.

A quadrilateral with diagonals that bisect each other is a parallelogram.

Area = (d1 * d2) / 2 = (8 * 6) / 2 = 48 cm²

Area = π * (radius)² = π * (5)² = 25π cm²

Circumference = πd = π(12) = 12π cm.

The circumference of a circle is given by C = πd, where d is the diameter. Here, C = π * 14 cm ≈ 44 cm.

Circumference = πd; C = π * 20 ≈ 62.83 cm.

Circumference = πd = π(20) = 20π cm.

If diameter increases by 50%, radius increases by 25%. Area increases by (new area - old area)/old area = (1.25² - 1) × 100% = 56.25%.

Circumference = π * diameter = π * 10.0 cm ≈ 31.4 cm. Uncertainty in circumference = π * 0.1 cm ≈ 0.314 cm.

The volume of a sphere is given by V = (4/3)πr³. The radius r = diameter/2 = 5 cm. Thus, V = (4/3)π(5)³ = (4/3)π(125) = 500/3 π cm³.

Tensile strength is inversely proportional to the cross-sectional area. Halving the diameter reduces the area to a quarter, thus tensile strength quadruples.

The difference between CI and SI for 2 years is given by P * (r^2)/100^2. Setting this equal to $50 and solving gives P = $1500.

The difference between compound interest and simple interest for 2 years is given by SI * (r/100)^2. Setting this equal to $50 and solving gives Principal = $1200.

The difference SI and CI for 2 years is given by P * r^2 / 200. Setting this equal to 50 gives P = $1500.

The equation of a parabola with directrix y = -p is y^2 = -4px.

Image distance (v) = Object distance (u) + Distance between object and image = 30 cm + 70 cm = 40 cm.

Capacitance is inversely proportional to the distance between the plates. If the distance d is doubled, the capacitance C becomes C/2.

Capacitance is inversely proportional to the distance between the plates. If the distance is halved, the capacitance doubles.

If the distance d is halved, the capacitance C = εA/d will double.