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liq [111]
3 years ago
10

Let C be the boundary of the region bounded by x = y4 + 1 and x = 2, oriented in anticlockwise.

Mathematics
1 answer:
murzikaleks [220]3 years ago
4 0
Assuming the first term is \dfrac{e^y}x, we have by Green's theorem,

\displaystyle\int_C\left(\frac{e^y}x\,\mathrm dx+(e^y\ln x+2x)\,\mathrm dy\right)=\iint_R\left(\dfrac\partial{\partial x}\left(e^y\ln x+2x\right)-\dfrac\partial{\partial y}\left(\frac{e^y}x\right)\right)\,\mathrm dA
=\displaystyle\int_{y=-1}^{y=1}\int_{x=y^4+1}^{x=2}\left(\frac{e^y}x+2-\frac{e^y}x\right)\,\mathrm dx\,\mathrm dy
=\displaystyle2\int_{-1}^1\int_{y^4+1}^2\,\mathrm dx\,\mathrm dy
=\displaystyle2\int_{-1}^1(1-y^4)\,\mathrm dy
=\displaystyle4\int_0^1(1-y^4)\,\mathrm dy
=\dfrac{16}5
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avanturin [10]

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Hoochie [10]

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3 years ago
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ddd [48]

Answer:

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Step-by-step explanation:

To solve the first step is to change years to months because the time periods are in different units. There are 12 months in 1 year. This means that the company sells 48 tons over 12 months. 4 months is the equivalent of 1/3 of 12 months. This means that we can find the amount sold in 4 months by dividing 48 by 3. 48/3 is 16. Thus, the steel company sells 16 tons in 4 months.

Another way to find the answer is to find the unit rate. The unit rate is how many tons are sold in 1 month. Find this by dividing 48 by 12 because this represents the sales of 1 month. 48/12=4, this means that in 1 month, 4 tons of steel are sold. Next, multiply 4 times 4 to find the amount of steel sold in 4 months. 4 times 4 also gives you the same answer of 16.

6 0
3 years ago
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Viefleur [7K]

Answer:

A

Step-by-step explanation:

-3<-2

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