Answer: $5,744.61
Step-by-step explanation:
year 1 = -2,277
year 2 = -2026.53
year 3 = -1803.61
year 4 = -1605.21
year 5 = -1428.64
year 6 = -1271.49
year 7 = -1131.62
year 8 = -1007.17
year 9 = -896.36
year 10 = -797.76
year 11 = -710
you are subtracting 11% from each year.
Answer:
80 minutes or 1 h 20 minutes
Step-by-step explanation:
15-13=2
2/0.025=80
So we can conclude that it takes 80 minutes till it reaches 13 feet.
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>
Answer:
The boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
The situation given in the question can be modeled as a triangle, please refer to the attached diagram.
A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.
The length of rope from bow to pulley is 13 feet that means y = 13 ft.
We know that Pythagorean theorem is given by
Differentiating the above equation with respect to time yields,
dx/dt = 0 since dock height doesn't change
The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s
First we need to find z
z² = (5)² + (13)²
z² = 194
z = √194
z = 13.93 ft
So,
Therefore, the boat is approaching the dock at rate of 2.14 ft/s
3 red shells equals $2.25 and 5 white shells equal 2.45. Add those together and you get $4.70.
So 3 red and 5 white shells would be the next guess.
