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3 years ago

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0

Mathematics

1 answer:

dmitriy555 [2]3 years ago

8 0

Multiply the original DE by xy:

xy2(1+x2y4+1−−−−−−−√)dx+2x2ydy=0(1)

Let v=xy2, so that dv=y2dx+2xydy. Then (1) becomes

x(y2dx+2xydy)+xy2x2y4+1−−−−−−−√dxxdv+vv2+1−−−−−√dx=0=0

This final equation is easily recognized as separable:

dxxln|x|+CKxvKx2y2−1K2x4y4−2Kx2y2y2=−dvvv2+1−−−−−√=ln∣∣∣v2+1−−−−−√+1v∣∣∣=v2+1−−−−−√+1=x2y4+1−−−−−−−√=x2y4=2KK2x2−1integrate both sides

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It has been suggested that night shift-workers show more variability in their output levels than day workers (σ2N > σ2D). Bel

Murljashka [212]

Answer:

Calculated |t |= 7.72 > 2.1314 at 0.05 level of significance

Null hypothesis is rejected

The night shift-workers show more variability in their output levels are greater than day workers

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 9

Given mean of the first sample x₁⁻ = 520

Given sample variance of the first sample'S²₁' = = 38

Standard deviation of the first sample 'S₁' = √38 =6.16

Given second sample size n₂ = 8

Given mean of the second sample x₂⁻ = 540

Given sample variance of the second sample ( 'S²₂' = 20

Standard deviation of the second sample 'S₂' = √20 = 4.4712

Step(ii):-

Null hypothesis :H₀: σ²₁ =σ²₂

Alternative Hypothesis:H₁: σ²₁ > σ²₂

Test statistic

$t = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S^2_{1} }{n_{1} }+\frac{S^2_{2} }{n_{2} } } }$

$t = \frac{520 - 540 }{\sqrt{\frac{38 }{9 }+\frac{20 }{8 } } }$

t = - 7.72

|t| = |- 7.72| = 7.72

Degrees of freedom

ν = n₁ + n₂ -2 = 9 +8 -2 = 15

t₀.₀₅ = 2.1314

Final answer:-

Calculated |t |= 7.72 > 2.1314 at 0.05 level of significance

Null hypothesis is rejected

The night shift-workers show more variability in their output levels are greater than day workers

4 0

3 years ago

D. (3+5i) (6-i) = Show your work.

algol [13]

Answer:

4i + 9 < simplified version

Step-by-step explanation:

3 + 5i + 6 - i =

4i + 9

7 0

3 years ago

Read 2 more answers

GCF of 12x^2y^7 and 28x^3y^4

Firdavs [7]

Answer:

GCF of 12x^2y^7 and 28x^3y^4

5 0

3 years ago

Please I need help with this question asap.

kiruha [24]

Answer:

The table is:

x y

1 1

2 5

3 9

The graph B shows the relationship y=4x-3

Step-by-step explanation:

We need to fill the table using the rule:

To find y multiply x by 4 and then subtract 3.

Writing rule in mathematical form:

y=4x-3

Now for completing the table we need to put x=1,2 and 3 and find values of y

$For x=1//y=4x-3\\ y=4(1)-3\\ y=4-3\\ y=1\\$

$For \ x=2\\y=4x-3\\ y=4(2)-3\\ y=8-3\\ y=5$

$For \ x=3\\y=4x-3\\ y=4(3)-3\\ y=12-3\\ y=9$

So, the table is:

x y

1 1

2 5

3 9

The graph B shows the relationship y=4x-3

6 0

3 years ago

1. Ted found out that the rebate is not given until after he has

nadezda [96]

9514 1404 393

Answer:

maybe not

Step-by-step explanation:

Consider a couple of scenarios for a $20,000 car purchase and a $2000 rebate, with sales tax at 10%.

1) The rebate is applied directly to the purchase price.

Taxable amount: $20,000 -2,000 = $18,000.

Price with tax: $18,000 × 1.10 = $19,800

Amount financed: $19,800.

2) The rebate is given after the sale is complete.

Taxable amount: $20,000

Price with tax: $20,000 × 1.10 = $22,000

Amount financed: $22,000

Remaining loan balance if $2000 rebate is immediately applied to the loan: $22,000 -$2000 = $20,000

If the loan is for 5 years at 3%, the payments and total costs are ...

Scenario 1: Monthly payment $355.78;

total cost of loan: 60×355.78 = 21,346.80

Scenario 2: Monthly payment $395.31;

total cost of loan: 55×395.31 = $21,742.05 (note there are fewer payments because of the initial payment to principal of $2000)

Ted effectively has to finance an additional $200, equal to the sales tax on the rebate. So the delayed rebate costs him an extra $395.25 over the life of the loan.

_____

We have assumed certain tax and payment scenarios. If tax is not an issue, and if the loan terms are such that the rebate can be applied immediately to the loan amount, then there may be no difference in total cost, or the delayed rebate may result in a lower total cost due to the higher monthly payment.

7 0

3 years ago

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0​

Find the general solution of (2x² + y)dx + (x²y - x)dy = 0