Find the coordinates of the vertices of a triangle after a 90 degree rotation counterclockwise about the origin.
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<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>
Given that,
A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream
Therefore,
Upstream distance = 165 km
Upstream time = 3 hours
<h3><u>Find upstream speed:</u></h3>Thus upstream speed is 55 km per hour
Downstream distance = 510 km
Downstream time = 6 hours
<h3><u>Find downstream speed:</u></h3>Thus downstream speed is 85 km per hour
<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>
Speed downstream = u + v km/hr
Speed upstream = u - v km/hr
Therefore,
u + v = 85 ----- eqn 1
u - v = 55 ----- eqn 2
Solve both
Add them
u + v + u - v = 85 + 55
2u = 140
u = 70
<em><u>Substitute u = 70 in eqn 1</u></em>
70 + v = 85
v = 85 - 70
v = 15
Thus rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr
Step-by-step explanation:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
56 = 2 ×2 × 2 × 7
Now
Common factor = 2
Remaining factor = 2 × 3 × 2 × 3 × 7
LCM = RF × CF
= 504
hence the lCM of 12 , 18 and 56 is 504...