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Luden [163]
3 years ago
12

At the beginning of the year, a firm has current assets of $316 and current liabilities of $220. at the end of the year, the cur

rent assets are $469 and the current liabilities are $260. what is the change in net working capital?
Mathematics
1 answer:
Cerrena [4.2K]3 years ago
6 0
Net working capital is the sum of assets and liabilities.
Beginning of year, 
net working capital = 316-220=$96
At end of year,
net working capital = 469-220=$249
change in networking capital = new capital - old capital
=249-96
=$153
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37. Verify Green's theorem in the plane for f (3x2- 8y2) dx + (4y - 6xy) dy, where C is the boundary of the
Nastasia [14]

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy

and I assume <em>C</em> has a positive orientation in both cases

(a) It looks like the region has the curves <em>y</em> = <em>x</em> and <em>y</em> = <em>x</em> ² as its boundary***, so that the interior of <em>C</em> is the set <em>D</em> given by

D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}

• Compute the line integral directly by splitting up <em>C</em> into two component curves,

<em>C₁ </em>: <em>x</em> = <em>t</em> and <em>y</em> = <em>t</em> ² with 0 ≤ <em>t</em> ≤ 1

<em>C₂</em> : <em>x</em> = 1 - <em>t</em> and <em>y</em> = 1 - <em>t</em> with 0 ≤ <em>t</em> ≤ 1

Then

\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}

(b) <em>C</em> is the boundary of the region

D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}

• Compute the line integral directly, splitting up <em>C</em> into 3 components,

<em>C₁</em> : <em>x</em> = <em>t</em> and <em>y</em> = 0 with 0 ≤ <em>t</em> ≤ 1

<em>C₂</em> : <em>x</em> = 1 - <em>t</em> and <em>y</em> = <em>t</em> with 0 ≤ <em>t</em> ≤ 1

<em>C₃</em> : <em>x</em> = 0 and <em>y</em> = 1 - <em>t</em> with 0 ≤ <em>t</em> ≤ 1

Then

\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}

• Using Green's theorem:

\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}

4 0
3 years ago
Translate the sentence into an equation.
emmasim [6.3K]

Answer:

6x + 9 = 4

Step-by-step explanation:

6 0
1 year ago
HELP, it looks blurry sorryyy! 15 pointss
Step2247 [10]
The first and last one are true!
8 0
3 years ago
Two equivalent expressions have the same _____ even though they may be written in different ways.
Svetach [21]

Answer:

Value

Step-by-step explanation:

Value because order can be different and they can still be the same!

For example, 3x+2 = 2+3x different order but still are equivalent!

x = -2/3, so their values are equivalent!

Hope this helps!

Please mark brainliest if you think I helped! Would really appreciate!

3 0
3 years ago
Read 2 more answers
Which relationship has a zero slope
vesna_86 [32]

Answer:

The first table.

Step-by-step explanation:

A slope of 0 means that as x increases, y stays the same.  In the first table, all of our y-values are 2; this means that y stays constant.  

To prove it, we use our formula for slope:

m=\frac{y_2-y_1}{x_2-x_1}

The slope of the line between the first two points is

(2-2)/(-3--1) = 0/-2 = 0

The slope of the line between the second pair of points is

(2-2)/(-1-1) = 0/-2 = 0

The slope of the line between the next pair of points is

(2-2)/(1-3) = 0/-2 = 0

Since the slope between each pair of points is 0, the slope of the entire line is 0.

4 0
3 years ago
Read 2 more answers
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