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:
Step-by-step explanation:
Hello,
Pls post the full question next time so that we can make sure what is expected.
I assume that you want to solve for (x,y)
(1) 2x + 3y = 7
(2) 3x + 2y = 8
2*(2)-3*(1) gives
2*3x + 2*2y - 3*2x - 3*3y = 2*8 - 3*7 = 16 - 21 = -5
6x - 6x + 4y -9y = -5
-5y=-5
y = 1
and we can replace in (1)
2x + 3*1 = 7
2x = 7 - 3 = 4
x = 2
hope this helps
4b²+20b+25=0
Divide everything by 4
b²+5b+ 6.25=0
use the quadratic formula
x= (-b+ or - √b²-4ac) /2a
x= (-5 + or - √5²-4*1*6.25) /2(1)
x= -5/2 so
in this case, b= -5/2
White chocolates
$4.50 x (2/3)
= $9/3
= $3
Gummy bears
$2.40 x (1/2)
= $2.40/2
= $1.20
Dark chocolates
$6.00 x (1 1/4)
= $6.00 6/4
= $7.50
$3.00 + $1.20 + $7.50
=$11.70
Therefore, Victor spent $11.70 on candy for the party.
:)
Answer:
Step-by-step explanat4+6uyyifigoomlion:4654565