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3 years ago

Please help me to solve this ∫ 1/(x + √x) dx

Mathematics

1 answer:

skad [1K]3 years ago

6 0

Answer:

$\boxed{2ln (\sqrt{x} + 1 ) + c}$

Step-by-step explanation:

$\int\limits {\frac{1}{x + \sqrt{x} } } \, dx$

$= \int\limits {\frac{1}{\sqrt{x} (\sqrt{x} + 1 )} } \, dx$

$= \int\limits {\frac{2}{(\sqrt{x} + 1 )} } \, d(\sqrt{x} + 1 )$

$= 2ln (\sqrt{x} + 1 ) + c$

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3 years ago

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Answer:

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b) Attached

c) The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.

d) The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.

Step-by-step explanation:

a) The LP formulation for this problem is:

Objective function (minimize cost):

$C=0.50A+0.20B$

Restrictions

Proteins per pound: $16A+8B\leq 12$

Vitamins per pound: $4A+8B\leq 6$

Non-negative values: $A,B\geq0$

b) The feasible region is attached.

c) We have 3 corner points. In one of them lies the optimal solution.

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Corner A=0.5 B=0.5

$C=0.50*0.5+0.20*0.5=0.35$

Corner A=0.75 B=0

$C=0.50*0.75+0.20*0=0.375$

The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.

d) If the company requires only 5 units of vitamins per pound rather than 6, one of the restrictions change.

The feasible region changes two of its three corners:

Corner A=0 B=0.625

$C=0.50*0+0.20*0.625=0.125$

Corner A=0.583 B=0.333

$C=0.50*0.583+0.20*0.333=0.358$

Corner A=0.75 B=0

$C=0.50*0.75+0.20*0=0.375$

The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.

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Answer:

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Step-by-step explanation:

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