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ivanzaharov [21]
3 years ago
12

Solve the equation

7D%29%20dx%20%2B%20%282%20x%5E%7B6%7D-15x%20y%5E%7B6%7D%20%29dy%3D0%20%20" id="TexFormula1" title="(12 x^{5}y+12 x^{6}y-3 y^{5} -18x y^{5}) dx + (2 x^{6}-15x y^{6} )dy=0 " alt="(12 x^{5}y+12 x^{6}y-3 y^{5} -18x y^{5}) dx + (2 x^{6}-15x y^{6} )dy=0 " align="absmiddle" class="latex-formula"> leaving your answer in implicit form.
Mathematics
1 answer:
sweet-ann [11.9K]3 years ago
3 0
\underbrace{(12x^5y+12x^6y-3y^5-18xy^5)}_M\,\mathrm dx+\underbrace{(2x^6-15xy^4)}_N\,\mathrm dy=0

M_y=12x^5+12x^6-15y^4-90xy^4
N_x=12x^5-15y^4

-\dfrac{N_x-M_y}N=6\implies\mu(x)=\exp\left(\displaystyle\int6\,\mathrm dx\right)=e^{6x}

\underbrace{(12x^5y+12x^6y-3y^5-18xy^5)e^{6x}}_{\mu M}\,\mathrm dx+\underbrace{(2x^6-15xy^4)e^{6x}}_{\mu N}\,\mathrm dy=0

You can verify that the partial derivatives are equal.

F_x=\mu M
F=(2x^6y-3xy^5)e^{6x}+f(y)

F_y=\mu N
(2x^6-15xy^4)e^{6x}+f'(y)=(2x^6-15xy^4)e^{6x}
f'(y)=0
\implies f(y)=C

\implies F(x,y)=(2x^6y-3xy^5)e^{6x}=C
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A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all arou
Arisa [49]

Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

1) 2 1/2 feet

2) 3 feet

4) 5 feet

5) 8 1/2 feet

Answer:

2.5

Step-by-step explanation:

Solving for X in the perimeter equation :

2[(12+2x)+15+2x)]=74

Open the bracket

2[(12 + 2x + 15 + 2x)] = 74

2(27 + 4x) = 74

54 + 8x = 74

8x = 74 - 54

8x = 20

x = 20/8

x = 2.5

Hence, width fo border = 2.5

5 0
2 years ago
2. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected. a. Would you
ANEK [815]

Answer:

Step-by-step explanation:

a.

Size of the population, N = 4000

Size of the sample, n = 40

n/N = 40/4000 = 0.01

0.01 is less than 0.05 and hence we would not us the finite population correction factor in calculating the standard error of the mean.

b.

Population standard deviation is σ = 8.2

<u>So, the standard error of x’ using the finite population correction factor is give by</u>

σ(x’) = √[(N - n)/(N - 1)] x (sigma/√n)

σ(x’) = √[(4000 - 40)/(4000 - 1)] x (8.2/√40)

σ(x’) = 1.29

<u>Standard error of x’ without using the finite population correction factor is</u>

σ(x’) = σ/√n

σ(x’) = 8.2/√40 = 1.2965

<u>There is little difference between the two values of the standard error. So we can ignore the population correction factor.</u>

c.

Let the population mean be μ

Probability that the sample mean will be within =-2 of the population mean is

P(μ– 2 < x’ < μ + 2)

At x’ = μ – 2 , we have

z = (μ – 2 – μ)/1.2965

z = -1.54

at x’ = μ  + 2, we have

z = (μ + 2 – μ)/1.2965

z = 1.54

<u>So the required probability is </u>

P(μ – 2 < x’ < μ + 2) = p(-1.54< z < 1.54)

P(μ – 2 < x’ < μ + 2) = p(z < 1.54) – p(z < -1.54)

P(μ – 2 < x’ < μ + 2) = 0.9382 – 0.0618

P(μ – 2 < x’ < μ + 2) = 0.8764

7 0
3 years ago
Which equation illustrates the identity property of multiplication? (a + bi) × c = (ac + bci) (a + bi) × 0 = 0 (a + bi) × (c + d
labwork [276]

Answer:

(a + bi) \times 1 = (a + bi)

Step-by-step explanation:

The identity property means that whatever you put in is whatever comes out. Notice that if we multiply 1 with any number, we get that number back. So multiplying by 1 is the identity property of multiplication.

8 0
3 years ago
Read 2 more answers
Some one please help me with this geometry problem ASAP
Elden [556K]

Answer:

43.5

Step-by-step explanation:

Set it up like 3x-5+x+1=180. Combine the variables and the numbers without a letter next to it. 4x+6=180. Subtract 6 from 180. Divide that number by 4.

6 0
3 years ago
Kevin had six nickels and 4 dimes in his pocket. If he took out one coin and then a second coin without replacing the first coin
Umnica [9.8K]
Alright so A is 6/10 * 5/9 = 1/3
B is 4/10 * 7/9 = 2/15
C is 6/10 * 4/9 = 4/15

I hope this helps


4 0
3 years ago
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