Take note that the vine was 3.6 ft and now it is 2.1 times as long.
So since is it 2.1 times as long it will be multiplied by 3.6.
3.6(2.1)= 7.56
So it is 7.56 ft long, rounded it is 7.6 ft
Answer:
Ella's normal hourly pay is $12 per hour.
Step-by-step explanation:
Let us assume that the Ella's Normal hourly pay = $x per hour
Over hourly pay = 1.5 times ( Normal pay)
= 1.5 ( x) = $ 1.5 x
⇒Ella earns $1.5x in 1 hour of overtime.
So the amount she earns in 4 hour of overtime = 4 times (per hour pay)
= 4 ( $1.5x) = $ 6 x
The amount Ella earned in 4 hours of over time = $72.00
According to the question:
$ 6 x = $72.00
or, x = 72/6
=12
or , x = $12
Hence, Ella's normal hourly pay is $12 per hour.
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.
