Answer:
What are the options?
Step-by-step explanation:
<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
Answer:
If you are simplifying it would be 4 for number 6 . 9 would be 1/81
Step-by-step explanation:
i can't see the whole piece of paper to see what you're actually doing , that would be more helpful .
We have that
<span>sin x=2/9
we know that
sin</span>² x+cos² x=1---------> cos² x=1-sin² x-----> cos² x=1-(2/9)²
cos² x=1-(4/81)------> (81-4)/81-----> 77/81
cos x=√(77/81)
Sin 2x = 2 sin x cos x-------> 2*(2/9)*(√(77/81))----> (4/81)*√77---> 0.43
Sin 2x=0.43
so
cos² 2x=1-sin² 2x---------> 1-[0.43]²-----> 1-[0.1878]----> 0.81
cos² 2x=0.81-----------> cos 2x=0.9
tan 2x=sin 2x/cos 2x--------> tan 2x=0.43/0.9---------> tan 2x=0.48
the answers are
sin 2x=0.43
cos 2x=0.9
tan 2x=0.48