Answer:
the first box maybe
Step-by-step explanation:
I assume there are some plus signs that aren't rendering for some reason, so that the plane should be

.
You're minimizing

subject to the constraint

. Note that

and

attain their extrema at the same values of

, so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.
The Lagrangian is

Take your partial derivatives and set them equal to 0:

Adding the first three equations together yields

and plugging this into the first three equations, you find a critical point at

.
The squared distance is then

, which means the shortest distance must be

.
Answer:
8
Step-by-step explanation:
0) the basic formula is: L=v*t, where L - distance, v - speed/velocity; t - time;
1) if the person's speed in still water is 'v' and the speed of water is 5 (according to the condition), then the upstream speed is 'v-5' and the downstream speed is 'v+5';
2) according to the condition the upstream time and the downstream time are the same, it means t₁=t₂=t, where t₁=upstream time and t₂=downstream time;
3) according to the items above it is possible to make up the equation of the upstream travel: t(v-5)=3; ⇒ t=3/(v-5);
4) according to the items above it is possible to make up the equation of the downstream travel: t(v+5)=13; ⇒ t=13/(v+5);
5) if t=3/(v-5) and t=13/(v+5), then

Answer:6. 42 split 7 ways is 6
Step-by-step explanation:
Commenter jdoe said it right: solve for y and leave the rest on the other side.
-x + 3y = 6
3y = 6 + x add x on both sides
3y = x + 6 rearrange to get the x first
y = (x + 6) /3 divide both sides by 3
y = x/3 + 6/3 split the numerator (caution - never split denominators)
y = x/3 + 2 simplify 6/3
Thus the line in slope intercept form of y = mx + b is y = 