The pitch of a musical note is determined by frequency in He

The pitch of a musical note is determined by frequency in Hertz. The trigonometric function p(t)= a sin (2pift) approximates the sound of a note with volume a, frequency f, and a duration of t seconds. For the purposes of the following problems, we will assume all pitches are played are played volume where a=1. Within a major scale, the frequencies of the notes maintain ration to the first note of the scale. The first to the third note have a frequency ratio of 4.5 the first to fifth a ration of 2:3 the first to seventh a ratio of 8:15 and the octave (eighth) a ratio of 1:2. Below, you will see the graph of the standard pitch, A at 440Hz in black, alongside another in grey as well as the eight note of an octave of the major scale with their pitch names. Give the equation, p(t), for the function in grey and identify which pitch it is. The note is .and can be modeled by p(t)= Find the equation p(t), for C# and add its graph to the graph of A440 below.

Solution

a. the can produce 24 units of luxury, 48 units of mid size and 19 units of economy

profit= 24*22+48*16+19*11= 528+768+209= $1505,000

b. they can produce 24 units of luxury cars, 26 units of mid sized cars and 51 units of economy cars

profit= 24*22+26*16+51*11

= 528+416+ 561= $1,505,000

b. even in this case also,