Answer:
Step-by-step explanation:
The given cylindrical equation is
Multiply both sides by r.
.... (1)
The required formulas are
Substitute in equation (1).
Add 1 on both sides.
It is the equation of a circle centered at (0,1) with radius 1.
Therefore, the equation in rectangular coordinates is .
Answer:
The distance between them after 30 minutes is 6.5 km.
Step-by-step explanation:
Speed =
Sarah's speed = 6 km/hr = 1.6667 m/s
Emily's speed = 10 km/hr = 2.7778 m/s
The measure of angle between their bearings =
After 30 minutes (1800 seconds);
distance = speed x time
Sarah would have covered a distance = 1.6667 x 1800
= 3000 m
= 3 km
Emily would have covered a distance = 2.7778 x 1800
= 5000 m
= 5 km
The distance between them, a, can be determined by applying the cosine rule;
=
+
- 2bcCos A
= +
-2(5000 x 3000) Cos 105
= +
-2(5000 x 3000) x (-0.2588)
= 2.5 x + 9 x
+ 7764000
= 41764000
a =
= 6462.5073
a = 6462.5 m
The distance between them after 30 minutes is 6.5 km.