Answer:
7 hours
They worked together for 7 hours ($350 + $120)
The answer would be 14,000,000.00
The tangent to 
through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces 
and 
at that point.
Let 
. Then is the level curve 
. Recall that the gradient vector is perpendicular to level curves; we have
so that the gradient of 
at (1, 1, 1) is
For the surface , we have
so that 
. We can obtain a vector normal to by taking the cross product of the partial derivatives of 
, and evaluating that product for 
:
Now take the cross product of the two normal vectors to and :
The direction of vector (24, 8, -8) is the direction of the tangent line to at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by 
. Then adding (1, 1, 1) shifts this line to the point of tangency on . So the tangent line has equation
Any real number will work with the equation y=x
Answer:
square meters
Step-by-step explanation:
The area of a triangle can be calculated by multiplying its height and base, then dividing the result by 
. As an algebraic expression, that would be 
, where 
is the base and 
is the height. In this case, 
and 
. Therefore, the area of the triangle is:
Hope this helps!
