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# Two ships leave port at the same time. Ship A sails north at a speed of 30 mph while ship...

Two ships leave port at the same time. Ship A sails north at a speed of 30 mph while ship B sails east at a speed of 55 mph. (a) Find an expression in terms of the time t (in hours) giving the distance between two ships.

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xxxxxxxxxxxxxxxxxxxxxxx | a | ||||

Speed xx ship x | xx | mph | |||

Speed xx xxxx B | xx | mph | |||

30 | t | xx | |||

x | xx | t | x | ||

xxxxxxxxx | |||||

xx xxxxxxx speed = distance x time xxx | |||||

xxxxxxxxxx xxxxxxxx covered in north direction x 30t | |||||

xxx distance xxxxxxx in east direction = 55t | |||||

xx can xxxx the xxxxxxxx xxxxxxx point x xxx x by xxxxx pythagoras xxxxxx | |||||

xxxxxxxxxxxxxx = xxxxxxxx x perpendicular xxxx | |||||

xxxxxxxx xxxxxxx A and x = h2 | x xxxx + xxxx | ||||

h2= | xxx | t2 | + | xxxx | xx |

xx = | xxxx | / | xx | ||

x x | xxxxxxxxx / xxx |

# xxxxxx

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Two ships leave xxxx xx the xxxx time. xxxx x sails north at x xxxxx of xx xxx while ship B sails xxxx xx a xxxxx xx 55 mph. (a) xxxx xx expression xx terms xx xxx xxxx x xxx xxxxxx giving the xxxxxxxx between two xxxxxx

xxxxxxxxx (55mph)

xxxxxxxxx North 30 xxxx

In one xxxx x xxx xxxx xxxx will cover 55 xxxxx and xxx xxxxx xxxx will cover xx xxxx

This xx x xxxxx angled triangle xx

h2 = xx x l2

h x √ xxx x xxx

x = √ 900 x xxxxx √xxxx = 62.65 miles

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xxx xxxxx leave port xx the xxxx xxxxx Ship A sails xxxxx at a speed of xx mph while ship B xxxxx xxxx at x xxxxx of xx mph. (a) Find an xxxxxxxxxx xx xxxxx xx xxx xxxx t xxx hours) xxxxxx the distance xxxxxxx xxx ships.

N

Ship x

30 xxx x x sqrt (A^2 + B^2)

A

x E

xxxx B – xx xxx x

In time x xxxxxxx Ship x will cover the distance x = speed xx ship A x time = xxxx Miles

xxx xxxx x will the cover the xxxxxxxx xx time t . x x speed xx Ship x x xxxx x 55 x x Miles

As mentioned xxxxx xxxxxxxx A and distance B xxx xxx sides of triangle xxxx xxxxx 90 xxxxxx

This xxxxxxxx xxxxxxx xxxx xxxx be x

C^2 x A^2 x xxx x (30*t)^2 x (55*t)^2 x 30^2 * xxx x 55^2*t^2 = 900*t^2 + xx * t^2 = t^2* (900 x 3025) x t^2 x xxxx

x = Sqrt (t^2 x xxxxx = t x sqrt xxxxxx = t x xxxx xxx * 25 * xxx = 25 x t x xxxx xxx 25 * xxxx * x x xxxxx * x

xx After x xxxxxx distance between xxx xxxxx will xx 185.4 * x xxxxx

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## 62.649 * t mile. Where 't' is time in Hrs.

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