Answer:
Component Form: v = <-1,6>
Magnitude of v: ||v|| = √37
Direction of v: θv = 100° (to the nearest degree)
Step-by-step explanation:
Component Form: v = <(5-6),(3-(-3))> = <-1,6>
Magnitude of v: ||v|| = √[(-1)²+(6)²] = √(1+36) = √37
Direction of v: α = tan⁻¹|6/-1| = tan⁻¹|-6| = tan⁻¹(6) = 80.53° which is your reference angle, but to verify that the angle is in the second quadrant, you'll need to do θv = 180° - 80.53° = 99.47°, therefore your direction angle is θv=100° to the nearest degree.
Answer:
20 hours
Step-by-step explanation:
We can work easier if we think in terms of an hour
the first equation that we can write is
A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)
the second equation we can write is
A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)
the third equation that we can write is
B = 2C (its meaning is that in an hour B fill 2 times C the cistern)
now we can substitute the value of B in the first two equations
A + 2C = 1/4
A + C = 1/5
A = 1/5 - C
1/5 - C + 2C = 1/4
C = 1/4 -1/5
C = (5-4)/20
C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)
A = 1/5 - 1/20
A = (4-1)/20 = 3/20
B = 1/20 *2 = 1/10
Answer: The y intercepts would be: ( 0 , -2 ).
The x intercepts would be: ( 1 , 0 ).
Step-by-step explanation:
Using pi at 3.14 the answer is 1,017.36
