MHB Solve 2000 = 4š¾^0.75 * L^0.25 - 5000(10/3)^.75

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The equation 2000 = 4K^0.75 * L^0.25 is analyzed, with K defined as K = 3/10 L. By substituting K into the equation and simplifying, it is determined that 500 = (3/10)^(3/4) * L. Further manipulation leads to the solution for L, which is L = 500 * (10/3)^(3/4). The correct answer confirms the relationship between L and K in the context of the given equation.
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can someone solve 2000 = 4š¾^0.75 * L^0.25 where k=3/10 L. i tryed to solve this by adding the powers 2000=4(3/10 L^1) however i get an answer of 5000/3 which is not the correct answer the correct answer is 5000(10/3)^.75
 
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Re: equation

We are given to solve for $L$:

$$2000=4K^{\frac{3}{4}}L^{\frac{1}{4}}$$

Divide through by 4:

$$500=K^{\frac{3}{4}}L^{\frac{1}{4}}$$

We are told:

$$K=\frac{3}{10}L$$:

$$500=\left(\frac{3}{10}L\right)^{\frac{3}{4}}L^{\frac{1}{4}}=\left(\frac{3}{10}\right)^{\frac{3}{4}}L$$

Hence:

$$L=500\left(\frac{10}{3}\right)^{\frac{3}{4}}$$
 
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