Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
The speed of a supersonic aircraft is usually represented by a Mach number, named after Austrian physicist Ernst Mach (1838–1916). A Mach number is the speed of the aircraft, in miles per hour, divided by the speed of sound, approximately 740 miles per hour. Thus, a plane flying at twice the speed of sound has a speed, M, of Mach 2. If an aircraft has a speed greater than Mach 1, a sonic boom is heard, created by sound waves that form a cone with a vertex angle θ,, shown in the given figure.
The relationship between the cone’s vertex angle, θ,, and the Mach speed, M, of an aircraft that is flying faster than the speed of sound is given by sin θ/2 = 1/M.
Solve, If θ = π/6, determine the Mach speed, M, of the aircraft. Express the speed as an exact value and as a decimal to the nearest tenth.
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