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
To do these problems, plug in a couple of values into the equations, and see the general shape of the graph. To ensure you were right, check them on an online graphing calculator. I highly recommend Desmos Graphing Calculator. Cheers!
Answer:
The center of circle is 
Step-by-step explanation:
We need to find the center of the circle of the equation 
Since, the general equation of circle is 
Where (h,k) is center of circle and r is radius.
Re-write the circle equation is as,
Compare with
so, 
Hence, the center of circle is
Answer:
The answer is she sold 20 labradorite crytals and 3 galena crystals.
Step-by-step explanation:
First you times 20 x 20 and get 400 and then times 13 x 3 and get 39 and 400 plus 39 equals $439.
