Meena sells apple pies at the farmers market. She charges $12 for each pie. It costs her $5 to make each pie and there is a $35
1 answer:
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The answer is 80 ft.
Based on the diagram we know that the tree triangle and the building triangle are similar triangles where the lengths of each are proportional to the other.
The lengths of the triangle the tree makes are half of the lengths of the building triangle. So this problem can be solved using ratio and proportion:
to solve for x, all you need to do is cross multiply then divide.
The answer is then 80ft.
Another way to solve this is just by using logic. If the lengths of the tree triangle is half of the building, simply divide the lengths of the building triangle by two.
160ft/2 = 80ft.
Based on the diagram we know that the tree triangle and the building triangle are similar triangles where the lengths of each are proportional to the other.
The lengths of the triangle the tree makes are half of the lengths of the building triangle. So this problem can be solved using ratio and proportion:
to solve for x, all you need to do is cross multiply then divide.
The answer is then 80ft.
Another way to solve this is just by using logic. If the lengths of the tree triangle is half of the building, simply divide the lengths of the building triangle by two.
160ft/2 = 80ft.
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 
.
where the function we want to minimize is actually
Derivatives of the Lagrangian set equal to zero:
Substituting the first three equations into the fourth gives
Solving for