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MatroZZZ
1 month ago
7

For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v3. It is believ

ed that migrating fish try to minimize the total energy required to swim a fixed distance. If the fish are swimming against a current u (u < v), then the time required to swim a distance L is L/(v-u) and the total energy E required to swim the distance is given by the formula below, where a is the proportionality constant.E(v) = av^3 L/(v - u)1. Determine the value of v that minimizes E.
Mathematics
1 answer:
zzz [12.3K]1 month ago
5 0

Answer:

The value of v that minimizes E is v = 3u/2.

Step-by-step explanation:

The given function is;

E(v) = av³L/(v-u)

Applying the quotient rule yields;

dE/dv = [(v-u)•3av²L - av³L(1)]/(v - u)²

By expanding and setting it to zero, we obtain;

[3av³L - 3av²uL - av³L]/(v - u)² = 0

Resulting in;

(2av³L - 3av²uL)/(v-u)² = 0

Multiplying both sides by (v-u)² gives;

(2av³L - 3av²uL) = 0

This means that 2av³L = 3av²uL

Upon simplifying, we have;

2v = 3u.

Thus, v = 3u/2.

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A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each r
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Response:

The answer to the inquiry is 8 hours.

Step-by-step breakdown:

Information

Ladder length = 200 cm

Distance between rungs = 20 cm

Tide rise rate = 10 cm/h

Fifth rung =?

Procedure

1.- Determine the total height the tide must reach

Height = 20 cm x 4

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Response: The outcome is (x+7)(3x+1)=33x^2+22x+7.

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we need to finalize the subsequent sentence:

(x+7)(???)=???

We have the polynomial division algorithm as follows

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Using this principle in the current problem, it results in

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We understand that

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