Bald-faced hornets have a hive that is approximately cone-shaped, as shown in the image. One such hive has a radius of 15 inches
1 answer:
Answer:
Volume of the hive is 4712.4 square inches.
Step-by-step explanation:
Since hive has the shape of a cone with radius = 15 inches and height = 20 inches
Therefore, volume of the given cone =
Area of the circular base = πr²
Area = π(15)²
= 225π
Volume of the cone =
= 1500π
= 4712.39
≈ 4712.4 square inches
Therefore, volume of the hive is 4712.4 square inches.
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Answer:
The answer is below
Step-by-step explanation:
Show that f(x) f(y) = f(x+y)
From trigonometric:
sin(x + y) = sinxcosy + cosxsiny
sin(x - y) = sinxcosy - cosxsiny
cos(x + y) = cosxcosy - sinxsiny
cos(x - y) = cosxcosy + sinxsiny
The Lagrangian for this function and the given constraints is
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
and 
, and at the same time we find only one critical point at 
.
Check the Hessian for
, given by
is positive definite, since 
for any vector 
, which means 
attains a minimum value of 
at 
. There is no maximum over the given constraints.
which has partial derivatives (set equal to 0) satisfying
This is a fairly standard linear system. Solving yields Lagrange multipliers of
Check the Hessian for