please solve it.......​

Answer:

dy/dx = - (y/x)^4

Step-by-step explanation:

We are given the equation:

[tex] \displaystyle \large{ \frac{1}{ {x}^{3} } + \frac{1}{ {y}^{3} } = {a}^{3} }[/tex]

Recall important differential formulas such as:

[tex] \displaystyle \large{ \frac{d}{dx} (f(x) + g(x)) = \frac{d}{dx} f(x) + \frac{d}{dx} g(x)} \\ \displaystyle \large{ \frac{d}{dx} k = 0 \: \: \tt(k \: \: is \: \: a \: \: constant.)}[/tex]

Above is a basic property of differential. Looking at the equation above, differentiate both sides with respect to x. (dy/dx)

[tex] \displaystyle \large{ \frac{d}{dx}( \frac{1}{ {x}^{3} } + \frac{1}{ {y}^{3} } )= \frac{d}{dx} {a}^{3} }[/tex]

Apply the distribution property in.

[tex] \displaystyle \large{ \frac{d}{dx} \frac{1}{ {x}^{3} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = \frac{d}{dx} {a}^{3} }[/tex]

We treat x^3 and y^3 as function to one another, this type of differential will be called implicit once another variable of function is involved f(x,y).

But we treat a^3 as a constant so we just put 0.

[tex] \displaystyle \large{ \frac{d}{dx} \frac{1}{ {x}^{3} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Recall the quotient rules for the numerator = 1.

[tex] \displaystyle \large{ \frac{d}{dx} (\frac{1}{f(x)}) = -\frac{ \frac{d}{dx} (f(x))}{ {(f(x))}^{2} } }[/tex]

Thus:

[tex] \displaystyle \large{ - \frac{ \frac{d}{dy} ( {x}^{3} )}{ ({x}^{3})^{2} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 } \\ \displaystyle \large{- \frac{ 3 {x}^{2} }{ {x}^{6} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Make sure to recall power rules for differential and exponent laws.

From 3x^2 / x^6.

[tex] \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } + \frac{d}{dx} \frac{1}{ {y}^{3} } = 0 }[/tex]

Now what do we do with 1/y^3? We just differentiate it normally but we multiply with dy/dx once we differentiate the y function.

[tex] \displaystyle \large{- \frac{ 3 }{ {x}^{4} } -\frac{ \frac{d}{dx}( {y}^{3}) }{ ({y}^{3})^{2} } = 0 } \\ \displaystyle \large{ -\frac{ 3 }{ {x}^{4} } - \frac{ 3 {y}^{2} }{ {y}^{6}} = 0 } \\ \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = 0 }[/tex]

Solve for dy/dx, add both sides by 3/x^4.

[tex] \displaystyle \large{ - \frac{ 3 }{ {x}^{4} } + \frac{3}{ {x}^{4} } - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = 0 + \frac{3}{ {x}^{4} } } \\ \displaystyle \large{ - \frac{ 3 }{ {y}^{4}} \frac{dy}{dx} = \frac{3}{ {x}^{4} } } \\ [/tex]

Divide both sides by - 3/y^4.

[tex] \displaystyle \large{ \frac{- \frac{3}{ {y}^{4} } \frac{dy}{dx} }{ - \frac{3}{ {y}^{4} } } = \frac{ \frac{3}{ {x}^{4} } }{ - \frac{3}{ {y}^{4} } } } \\ \displaystyle \large{ \frac{dy}{dx} = \frac{3}{ {x}^{4} } \times (-\frac{ {y}^{4} }{3} )} \\ \displaystyle \large{ \frac{dy}{dx} = \frac{1}{ {x}^{4} } \times (- \frac{ {y}^{4} }{1}) } \\ \displaystyle \large{ \frac{dy}{dx} = - \frac{ {y}^{4} }{ {x}^{4} } } \\ \displaystyle \large{ \frac{dy}{dx} = - ( { \frac{y}{x} })^{4}}[/tex]

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In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.

During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:



Finishing

Beginning work-in-process units

26,400

Units transferred in this period

74,800

Units completed & transferred out

79,200

Ending work-in-process units

22,000





Material costs added

$37,400

Conversion costs

$75,460

Transferred-in costs

$141,240



What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.
Moon Company produces baseball bats and cricket paddles. It has two departments that process all products – Cutting Department and Finishing Department.

In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.

During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:



Finishing

Beginning work-in-process units

26,400

Units transferred in this period

74,800

Units completed & transferred out

79,200

Ending work-in-process units

22,000





Material costs added

$37,400

Conversion costs

$75,460

Transferred-in costs

$141,240



What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.
Moon Company produces baseball bats and cricket paddles. It has two departments that process all products – Cutting Department and Finishing Department.

In Finishing Department, direct materials (DM) are added at the start of the process and conversion costs (CC) are added evenly during the process. Company is using Weighted Average method for the Finishing Department.

During July, beginning work in process in the Finishing Department was 80% complete as to conversion. Beginning inventories included $30,800 for transferred-in costs, $13,200 for direct materials, and $27,500 for conversion costs. Ending inventory was 30% complete as to CC. Additional information about the Finishing Department follows:



Finishing

Beginning work-in-process units

26,400

Units transferred in this period

74,800

Units completed & transferred out

79,200

Ending work-in-process units

22,000





Material costs added

$37,400

Conversion costs

$75,460

Transferred-in costs

$141,240



What is equivalent units for transferred-in cost, direct materials, and conversion cost, respectively? Separate with slash /.

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