Plz help me solve this question?

1 answer:

4 0

The function is
b1 = 1200 (1.8)^t
The question is what does the value of 1000 represent but I think what you really mean to ask is what does the value of 1200 represent since there is a term in the function with that value.
The value 12000 represents the initial bacterial count or the colonies at t = 0.

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Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinat

dimaraw [331]

I assume the given plane has equation

x + 3y + 4z = d

for some constant d ≠ 0.

You want to maximize the function V(x, y, z) = xyz subject to the above constraint. The Lagrangian would be

L(x, y, z, λ) = xyz - λ (x + 3y + 4z - d)

Find its critical points:

∂L/∂x = yz - λ = 0

∂L/∂y = xz - 3λ = 0

∂L/∂z = xy - 4λ = 0

∂L/∂λ = x + 3y + 4z - d = 0

The first three equations tell you that λ = yz = xz/3 = xy/4. Then, for instance,

yz = xz/3 → 3yz - xz = z (3y - x) = 0 → z = 0 or 3y - x = 0

If z = 0, we get zero volume which is not useful. So 3y = x. Similarly, you would find x = 4z and 3y = 4z, so a critical point occurs when x = 3y = 4z.

In the fourth equation, we get upon substituting

x + 3y + 4z = 3x = d → x = d/3, y = d/9, z = d/12

Then the largest volume of this box would be

V(d/3, d/9, d/12) = d ³ / 324

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What is equivalent to (1/4 + y)^4

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Hope it will help you!!