The slope of the line is 7/2. The slope of the perpendicular line is the negative reciprocal, which is -2/7.

f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.

f'(x) = 2x + 2. At x = 1, f'(1) = 2(1) + 2 = 4.

The integrating factor is e^(-2x). Solving gives y = Ce^(2x) + 3/2.

Using the integrating factor method, we find the general solution to be y = Ce^(5x) - (3/5).

Integrating both sides gives y = ∫3x^2 dx = x^3 + C.

Using an integrating factor, the solution is y = Ce^(4x) - 1/2.

Rearranging gives dy/(6 - 2y) = dx. Integrating both sides leads to y = 3 - Ce^(-2x).

This is a separable equation. Integrating gives y = Ce^(-kt).

This is a separable equation. Separating variables and integrating gives y = C/x.

This is a separable differential equation. The solution is y = Ce^(-5x), where C is a constant.

This is a separable equation. Integrating gives y = 1/(C - x).

This is a separable equation. The solution is y = Ce^(-2x).

This is a first-order linear differential equation. The solution is y = Ce^(-3x).

This is a first-order linear equation. The integrating factor is e^(3x), leading to the solution y = Ce^(3x) + 2.

The characteristic equation is r^2 + 4 = 0, giving complex roots. The general solution is y = C1 cos(2x) + C2 sin(2x).

For a monatomic ideal gas, the specific heat at constant volume (Cv) is 3R/2.

Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C.

Specific heat capacity (c) = Q / (m * ΔT) = 500 J / (2 kg * 5°C) = 50 J/kg°C

The specific heat capacity of water at constant pressure is approximately 4.18 J/g°C.

The specific heat capacity of water is defined as the amount of heat required to raise the temperature of 1 kg of water by 1°C, which is given as 4200 J/kg°C.

The specific heat capacity of water is approximately 4.18 J/g°C.

The speed of light in vacuum is approximately 3 x 10^8 m/s.

The modulus is √(1^2 + 2^2) = √(1 + 4) = √5. The square of the modulus is 5.

The modulus is √(1^2 + 1^2) = √2, and the square of the modulus is 2.

The square root of 64 is 8.

The standard electrode potential for Zn²⁺/Zn is -0.76 V.

The standard electrode potential of the hydrogen electrode is defined as 0 V.

A nucleotide consists of a sugar, a phosphate group, and a nitrogenous base.

The sum of the angles in a triangle is always 180 degrees.