Place the following events in order of how they would occur to create sound according to the sequencing word. First the violin strings begin to vibrate Second, the vibrating violin strings cause air particles to vibrate. Third, the sound waves travel through the medium of air. Then, soundwaves are received by a listener's ear Finally, a violinist moves her bow across the strings of a violin.

in the problem you wrote said that the taxi charges $0.070 per mile(which would be 7 cents per mile), but then in your suggested equation you have it as $0.70 per mile (which is 70 cents per mile).

the latter seems more realistic, so i will assume that the taxi costs $5.00 and charges $0.70 per mile with tolls costing an additional $3.50. and it asks you to find how far you can travel on $36.50.

let x the number of miles traveled. since the taxi charges $0.70 per mile, multiplying this by the miles traveled (x) will yield the cost of the taxi ride as far as how far it took you. then adding this amount to the cost of the taxi ($5.00) and the additional cost for the tolls ($3.50) will give you the total cost of the taxi ride ($36.50)

that is,

            (0.70)x + 5.00 + 3.50 = 36.50

adding the like terms on the left-hand side of this equation, we arrive at the following:

            (0.70)x + 8.50 = 36.50

subtracting 8.50 from both sides of the equation, we get:

            (0.70)x = 28.00

to solve for x, divide both sides of the equation above by the coefficient of x (that being, 0.70):

            x = 40

thus, you can travel up to 40 miles on $36.50

vector v such that t( p) = p+ v