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3 years ago

Help pls I really need to turn this in !!!!!!!!!

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

3 0

Answer:

g > 8

Step-by-step explanation:

25g > 200, so divide 200 by 25, and you get 8. Since the original symbol was >, keep it.

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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 C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D 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 C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 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) C 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 C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 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

How do I solve -(x+7)-5=4(x+3)-6x

sasho [114]

Answer:

x = 24

Step-by-step explanation:

I checked and made sure the answer was correct.

Hope this helps!

Please Mark Brainliest!

4 0

3 years ago

M∠LONm, angle, L, O, N is a straight angle.

Ne4ueva [31]

Answer: 41

Step-by-step explanation:

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3 years ago

Lines f and g are perpendicular. The equation of line f is y = 1/4x + 2. What is

umka2103 [35]

Answer:

y = -4x + (any number)

Step-by-step explanation:

you want to use the negative reciprocal of the slope for line f

so m = -4, since you didn't say any points it has to go through then the

equation of the line is y = -4x + (any number)

8 0

3 years ago

What is 1/3 + 5/6 Help

gulaghasi [49]

7/6 is the right answer. First you had to add by the fractions. And it gave us, $\frac{2}{6}+ \frac{5}{6}$ . Since the denominators are equal, combine the fractions. And it gave us, $\frac{2+5}{6}$ . Finally, you had to add by the numbers, and it gave us the answer is 2+5=7, or 7/6 is the right answer. Hope this helps! And thank you for posting your question at here on brainly, and have a great day. -Charlie

5 0

2 years ago