j = # of jars
b = # of buckets
y = total # of rocks
2j + 3b = y (2 rocks per jar, 3 rocks per bucket)
Because Joy has 3 jars you can plug 3 in for "j", and because she has 4 buckets you can plug in 4 for "b"
2(3) + 3(4) = y
6 + 12 = y
18 = y
Step-by-step explanation:
Recall that
Therefore,
so
Step-by-step explanation
The orange machine, the very end of the shovel part. That line is a slope. The middle part of the scooper could also be a slope. The very beginng part of the scooper is also a slope. The bottom part of the scooper is also a slope. The bottom part at the end of the scooper could also be slope.
The cross product of the normal vectors of two planes result in a vector parallel to the line of intersection of the two planes.
Corresponding normal vectors of the planes are
<5,-1,-6> and <1,1,1>
We calculate the cross product as a determinant of (i,j,k) and the normal products
i j k
5 -1 -6
1 1 1
=(-1*1-(-6)*1)i -(5*1-(-6)1)j+(5*1-(-1*1))k
=5i-11j+6k
=<5,-11,6>
Check orthogonality with normal vectors using scalar products
(should equal zero if orthogonal)
<5,-11,6>.<5,-1,-6>=25+11-36=0
<5,-11,6>.<1,1,1>=5-11+6=0
Therefore <5,-11,6> is a vector parallel to the line of intersection of the two given planes.
You move the decimal point forward until it reaches the one so it looks like this:
1.4 x 10⁵
the exponent, 5, just tells you how many spaces the decimal point moved.
