Explanation

To find the fraction equivalent to 2/5%, first convert the percentage to a decimal:

2/5% = (2/5) × (1/100) = 2/500 = 1/250

Explanation

The given partial differential equation:

∂²U/∂x² + ∂²U/∂y² = f(x,y)

is known as the Poisson equation.

If f(x,y) = 0, it would reduce to the Laplace equation.

Explanation

Skew lines are non-coplanar, do not intersect, and are not parallel.

They exist in 3D geometry, not lying in the same plane.

Explanation

Explanation

The Maclaurin series expansion of cos(x) is derived from its Taylor series expansion around x = 0:

cos(x) = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

This series alternates signs and involves even powers of x, with factorials in the denominators.

The answer is cosx = 1 - x²/2! + x⁴/4! - x⁶/6! + ...

Explanation

The Pyrometer is used for measuring very high temperatures.

Pyrometers can measure temperatures without direct contact.

This making them ideal for extreme conditions.

Explanation

C.P. of 1 toy = 375/12 = Rs. 31.25

S.P of 1 toy = Rs. 33

Profit = 1.75/31.25 * 100 = 28/5 = 5.6%

Explanation

Explanation

The given inequalities define a region in the Cartesian plane:

a - δ ≤ x ≤ a + δ (horizontal bounds)

b - δ ≤ y ≤ b + δ (vertical bounds)

This region forms a square with:

Center at (a, b)

Side length of 2δ

The answer is A square.

Explanation

Given y = x²/(1 + x²),

∫y dx = ∫[x²/(1 + x²)] dx = ∫[1 - 1/(1 + x²)] dx = x - arctan(x) + C.

Given ∫y dx = C + f, f = x - arctan(x).

x - 1 + 1/(x + 1)