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

.
Based on the given problem above, this would appear that,
one pound of peanuts = 0.60*2 = $1.2
one pound of cashews = $2
Therefore, the cost of one pound of peanuts is $1.2.
The total cost of two pounds of peanuts and one pound of cashews would be this: 1.2 + 1.2 + 2 = $4.4
Hope this answers your question.
Answer: The HCF o two consecutive numbers is always one.
Step-by-step explanation: The reason behind this is that the two consecutive numbers do not have any common factor other than 1. Hence 1 becomes the highest common factor between two consecutive numbers
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Answer:
are the roots.
Step-by-step explanation:

Considering the expression

Solving





Solving

= 
![\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%5Cquad%20%5Csqrt%5Bn%5D%7Bab%7D%3D%5Csqrt%5Bn%5D%7Ba%7D%5Csqrt%5Bn%5D%7Bb%7D)
= 
![\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^m}=a^{\frac{m}{n}}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aradical%5C%3Arule%7D%3A%5Cquad%20%5Csqrt%5Bn%5D%7Ba%5Em%7D%3Da%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D)



So,

Similarly,

Therefore,
are the roots.
Keywords: roots, expression
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Answer:
a = 16 π cm² Exact answer
a = 50.24 cm² Decimal approximation
Step-by-step explanation:
Radius of the circle
16/2 = 8
Area of the circle
a = πr²
a = π4²
a = 16 π cm² Exact answer
a = 16 * 3.14
a = 50.24 cm² Decimal approximation