I am really sorry but I didn’t get the answe
Answer:
Lin needs 3 cups of flour and 6 cups of sugar. Noah needs 6 cups of sugar and 4 cups of flour.
Step-by-step explanation:
I want you to figure out how to do.
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
10.5 - 8.7 = 1.8
There is 1.8 feet of pipe left