log_5(1) = 0 because 5^0 = 1.

log_5(125) = log_5(5^3) = 3.

log_5(25) = 2, so log_5(25) + log_5(4) = 2 + log_5(4).

log_5(25) = 2 and log_5(5) = 1. Therefore, 2 - 1 = 1.

In the equation x^2 = 4py, we have 4p = 16, thus p = 4.

In the equation y^2 = 4px, we have 4p = 20, thus p = 5.

In the equation x^2 = 4py, we have 4p = 20, thus p = 20/4 = 5.

Setting the two pieces equal at x = 2: 3(2) + p = 2^2 - 4. Solving gives p = -2.

Substituting x = 1 into P(x) gives P(1) = 2(1)^2 + 3(1) - 5 = 0.

Substituting x = 1 into P(x) gives P(1) = 1^3 - 3(1^2) + 4 = 2.

Substituting x = 2 into P(x) gives P(2) = 2^3 - 3(2^2) + 4 = 8 - 12 + 4 = 0.

Planck's constant is approximately 6.626 x 10^-34 Joule seconds.

Setting the two pieces equal at x = 1: 5 - q = 3(1) + 2. Solving gives q = 0.

The ideal gas constant R is 0.0821 L·atm/(K·mol).

The value of R in L·atm/(K·mol) is 0.0821.

R can have different values depending on the units used, including 0.0821 L·atm/(K·mol), 8.314 J/(K·mol), and 62.36 L·mmHg/(K·mol).

The value of the ideal gas constant R in L·atm/(K·mol) is 0.0821.

The value of R in L·kPa/(K·mol) is 8.314.

sec(0°) = 1/cos(0°) = 1/1 = 1

sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3 = √3

sec(45°) = 1/cos(45°) = 1/(√2/2) = √2.

sec(60°) = 1/cos(60°) = 1/(1/2) = 2.

sec(sin^(-1)(1/2)) = 1/cos(π/6) = 2.

sec(sin^(-1)(3/5)) = √(34)/3

Using the triangle with opposite = 1 and adjacent = √3, hypotenuse = 2. Thus, sec(tan^(-1)(1/√3)) = 2.

sec(θ) = 1/cos(θ) = 1/(1/3) = 3.

sec(θ) = 1/cos(θ) = 1/(3/5) = 5/3.

sec^(-1)(2) = π/3, since sec(π/3) = 2.

The double angle formula states that sin 2θ = 2sin θ cos θ.

Using the identity, sin(180° - θ) = sin θ.