Answer:
97.98
Step-by-step explanation:
The area of the parallelogram PQR is the magnitude of the cross product of any two adjacent sides. Using PQ and PS as the adjacent sides;
Area of the parallelogram = |PQ×PS|
PQ = Q-P and PS = S-P
Given P(0,0,0), Q(4,-5,3), R(4,-7,1), S(8,-12,4)
PQ = (4,-5,3) - (0,0,0)
PQ = (4,-5,3)
Also, PS = S-P
PS = (8,-12,4)-(0,0,0)
PS = (8,-12,4)
Taking the cross product of both vectors i.e PQ×PS
(4,5,-3)×(8,-12,4)
PQ×PS = (20-36)i - (16-(-24))j + (-48-40)k
PQ×PS = -16i - 40j -88k
|PQ×PS| = √(-16)²+(-40)²+(-88)²
|PQ×PS| = √256+1600+7744
|PQ×PS| = √9600
|PQ×PS| ≈ 97.98
Hence the area of the parallelogram is 97.98
Answer:
(-3, 13)
Step-by-step explanation:
Coordinate of A is (7,5)
4 units to the left means (7-4, 5) --> (3,5)
8 units up means (3, 5+8) --> (3,13)
Reflected across the y-axis means that the sign of whatever x coordinate you have now will be reversed.
So (-3,13)
Answer:

Step-by-step explanation:
Answer:
For each test run, the minimum time is 45 mins or <u>3/4 ____</u> hours
and the maximum time is 67.5 minutes or <u>1 hour 7.5 minutes.</u>
Step-by-step explanation:
If x is the number of hours the robot is performing a test run, the equation that can be used to find the minimum and maximum time (in hours) for a test run is <u>15 mins for 1 mile</u>
For 4 miles the time is 1 hour
For 1 miles the time will be 1/4 hour
For 3 miles the time will be 3/4 hours
and for 4.5 miles the time will be 4.5/4 hours
Now reversing
1 hour = 4miles
15 mins= 1 mile
45 mins = 3 miles
30 mins = 2 miles
67.5 min= 4.5 miles
For each test run, the minimum time is ____ hours
the minimum distance is 3 miles and time taken is 45 mins
and the maximum time is ____ hours.
The maximum distance is 3+ 1.5= 4.5 miles and time taken is 67.7 minutues or 1 hour 7.5 minutes.
15 is 360
16 the first one is 60 and the second is 120