Lagrangian:
where the function we want to minimize is actually
, but it's easy to see that
and
have critical points at the same vector
.
Derivatives of the Lagrangian set equal to zero:
Substituting the first three equations into the fourth gives
Solving for
, we get a single critical point at
, which in turn gives the least distance between the plane and (0, 2, 5) of
.
First, let's complete the angles in the triangle. Remember that the sum of the angles in a triangle is 180 degrees.
73 + 90 + x = 180
163 + x = 180
x = 17
So, the angle that completes the triangle is 17 degrees. If we look at that angle in the triangle and the one adjacent to it, we can see that those two angles form a linear pair (or are supplementary, both meaning that they add up to 180 degrees).
17 + x = 180
x = 163
So, 17's supplement is 163 degrees. The 163 degree angle corresponds with angle r, and corresponding angles are congruent.
Therefore, angle r is 163 degrees. The correct answer is option C.
Hope this helps!
Answer:
6
Step-by-step explanation:
This is basically 24 divided by 4 since he/she is dividing 24 into 4 equal groups.
24/4=6
Answer:
Ok
Step-by-step explanation:
Answer:
Upstream - 2 miles per hour
Downstream - 3 miles per hour
Step-by-step explanation:
For the speed upstream, the answer would be 2 miles per hour (mph), because 6÷3=2.
For the speed downstream, the answer would be 3 miles per hour (mph), because 6÷2=3.
Both answers come in similar methods. Hope this helps you!
If you don't mind, please mark my answer brainliest!
