500 meters to 3 kilometers.
500 divided by 3 = 166 with a remainder of 2
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. The range is the set of all valid y values.
Step-by-step explanation:
You divide it the inequalties and multiply the equations to get you answer
Original position: P1=(0,0)
<span>You drive 30 miles due east in a half hour: x=+30 miles, t1=1/2 hour=0.5 hours
</span><span>Then, you turn left and drive 30 miles north in 1 hour: y=+30 miles, t2=1 hour
Rectangular coordinates of final position: P2=(x,y)→P2=(30,30)
Total time: t=t1+t2=0.5 hours+1 hour→t=1.5 hours
Average speed: S ave=d/t
Total distance: d=x+y=30 miles+30 miles→d=60 miles
S ave = 60 miles / (1.5 hours)
S ave = 40 miles/hour
Velocity is a vector, the magnitude of this vector is the magnitude of the vector of change of position dividing by the total time t
The vector of change of position: s=P1-P2=(30,30)-(0,0)=(30-0,30-0)→
s=(30,30)
Magnitude of vector s=sqrt[30^2+30^2]=sqrt[30^2*2]=sqrt[30^2]*sqrt(2)
Magnitude of vector s=30*sqrt(2) miles
Magnitude of velocity vector = Magnitud of vector s / t
Magnitude of velocity vector = [30*sqrt(2) miles] / (1.5 hours)
Magnitude of velocity vector = 20*sqrt(2) miles / hour
Magnitude of velocity vector=20*1.4142 miles / hour
Magnitude of velocity vector=28.284 miles/hour
Polar coordinates of your position=(r, theta)
r=Magnitude of vector s=30*sqrt(2) miles
theta=tan^(-1) (y/x) = tan^(-1) [(30 miles) / (30 miles)]
theta=tan^(-1) (1)→theta=45°=Pi/4 (Pi=3.1416)
Polar coordinates of your position: ( 30*sqrt(2) miles, 45°)
Polar coordinate of your position: ( 30*sqrt(2) miles, Pi/4 )
Answers:
Average speed: 40 miles / hour
Velocity: 20*sqrt(2) miles / hour = 28.284 miles / hour
Rectangular coordinates of your position = (30,30)
Polar coordinates of your position=(30*sqrt(2) miles,45°)
Polar coordinates of your position=(30*sqrt(2) miles,Pi/4)</span>
