Explanation

• The trigonometric identity for cos(3a) is: cos(3a) = 4cos^3(a) - 3cos(a)
• This can be proved using the angle sum and difference formulas for cosine.

Explanation

The pattern of the sequence is adding 3 to the previous term, so:

1 + 3 = 4

4 + 3 = 7

7 + 3 = 10

10 + 3 = 13

...

(Adding 3 repeatedly 28 times)

...

88 + 3 = 91

Therefore, the 31st term of the sequence is 91.

Explanation

The idiom "talking through his hat" means to speak about something without having enough knowledge or information about it.

Explanation

Folic acid nutrient deficiency causes megaloblastic anaemia.

Explanation

In an intrinsic semiconductor, at thermal equilibrium, the number of free electrons is equal to the number of holes.

Explanation

• pH is a measure of the concentration of hydrogen ions (H+) in an aqueous solution.
• The term "pH" was coined by the Danish chemist Søren Sørensen in 1909, and it stands for "power of hydrogen". It is defined as the negative logarithm of the concentration of hydrogen ions in a solution: pH = -log[H+]
• A pH of 7 is neutral, while values below 7 are acidic and above 7 are basic.

Explanation

In Ruby, the syntax for defining a method is:

def method_name(parameters)

  # method body

end

The 'def' keyword is used to define a method, followed by the method name and parameters in parentheses.

The method body is indented and enclosed by the 'end' keyword.

Explanation

Variant Creutzfeldt-Jakob disease (vCJD) can be contracted only if an individual consumes nerve tissues (brain and spine) of cattle infected with Mad cow disease (bovine spongiform encephalopathy, BSE).

Explanation

• The line perpendicular to the tangent line at a point on a curve is called the normal line.
• It passes through the point of tangency and is perpendicular to the tangent line at that point.

Explanation

The partial fraction decomposition of (x+1)/(x² + 1) is: (x+1)/(x² + 1) = A/(x+1)-bx+c/(x²+1)