Answer:
A ) Not orthogonal to each other
B) 50i + 40j + 105k
C) The tensor product is attached below
D ) The value of X = F.X is attached below
Step-by-step explanation:
attached below is the detailed solution of the above problem
A) for the vectors ( u ) and ( v ) to be orthogonal to each other [ U.V has to be = 0 ] but in this scenario U.V = 4 hence they are not orthogonal to each other
b) The vector normal to plane is gotten by : U x V
= 50i + 40j + 105k
The expression will be x-3.
9-4=-5 would be the smallest answer
The answer is B. (Elite members earn 3 more points for every dollar spent and are awarded 100 more points per month than a regular memeber).
Volume
of a rectangular box = length x width x height<span>
From the problem statement,
length = 60 - 2x
width = 10 - 2x
height = x</span>
<span>
where x is the height of the box or the side of the equal squares from each
corner and turning up the sides
V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x
To maximize the volume, we differentiate the expression of the volume and
equate it to zero.
V = </span>4x^3 - 100x^2 + 600x<span>
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0</span>
<span>x^2 - 50/3x + 50 = 0
Solving for x,
x1 = 12.74 ; Volume = -315.56 (cannot be negative)
x2 = 3.92 ;
Volume = 1056.31So, the answer would be that the maximum volume would be 1056.31 cm^3.</span><span>
</span>
