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
Answer: the diffrence is 2
Step-by-step explanation:
The first odd number is 1. The next is 2 more than the previous one.
It's an arithmetic sequence.
The general term of an arithmetic sequence:
a_n - n-th term
a_1 - first term
d - common difference.
We have
Substitute:
<h3>Answer: 137th odd number is equal 273.</h3>
Answer:
Ko-op is better
Step-by-step explanation:
1
£2.58/3= 86 p
2
£4.25/5= 85 p
3
£6.72/8= 84 p
Last one Ko-op is better