This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the extreme values of the function subject to the given constraint. f(x, y, z) = 8x + 8y + 4z; 4x2 + 4y2 + 4z2 = 36

The extreme max value is "" and min value is "".

According to the question,

let,

By using Lagrange multipliers,

→ ...(equation 1)

∴

then,

→

As we know,

→            

By substituting the values, we get

→

→                

→                                  

∴ x = 2, y = 2, z = 1

then,

→ (Extreme max value)

and,

∴ x = -2, y = -2, z = -1

then,

→ (min value)

Thus the above answer is correct.

Learn more about Lagrange multipliers here:

link

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}