* Two cars started to move from C (118miles) and from D(256 miles), towards one another. The car that starts at point C moves twice as fast as the car that starts at point D. How far from Boston will these two cars meet?

They meet at 92 miles from C or 46 miles from D.

Step-by-step explanation:

Constant Speed Motion

An object is said to have constant speed if it travels the same distance at the same time. The ratio between the distance x and the time t is the speed and is given by

Solving for x

The car starting from C has double speed as the car starting from D. this means

When both cars meet, they travel these distances

The sum of both distances is x = 256 - 118 = 138 miles.

Or, equivalently

Using the relations of the speeds:

Solving for t

The distance traveled by the car from c is

The distance traveled by the car from d is

There is no reference of where Boston is located, thus we can only refer the distances respect to C or D, as shown above

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92