I NEED HELP PLEASE !

Len [333]

(6x - 5y + 4) dy + (y - 2x - 1) dx = 0

(6x - 5y + 4) dy = (2x - y + 1) dx

dy/dx = (2x - y + 1) / (6x - 5y + 4)

Let X = x - a and Y = y - b. We want to find constants a and b such that

dY/dX = (a rational function)

where the numerator and denominator on the right side are free of constant terms. Substituting x and y in the equation, we have

dY/dX = (2 (X + a) - (Y + b) + 1) / (6 (X + a) - 5 (Y + b) + 4)

dY/dX = (2X - Y + 2a - b + 1) / (6X - 5Y + 6a - 5b + 4)

Then we solve for a and b in the system,

2a - b + 1 = 0

6a - 5b + 4 = 0

==> a = -1/4 and b = 1/2

With these constants, the equation reduces to

dY/dX = (2X - Y) / (6X - 5Y)

Now substitute Y = VX and dY/dX = X dV/dX + V :

X dV/dX + V = (2X - VX) / (6X - 5VX)

The equation becomes separable after some simplification:

X dV/dX + V = (2 - V) / (6 - 5V)

X dV/dX = (2 - V) / (6 - 5V) - V

X dV/dX = (2 - V - (6 - 5V)) / (6 - 5V)

X dV/dX = (4V - 4) / (6 - 5V)

- (5V - 6) / (4V - 4) dV = 1/X dX

Integrate both sides:

-5/4 V + 1/4 ln|4V - 4| = ln|X| + C

Extract a constant from the logarithm on the left:

-5/4 V + 1/4 (ln(4) + ln|V - 1|) = ln|X| + C

-5/4 V + 1/4 ln|V - 1| = ln|X| + C

-5V + ln|V - 1| = 4 ln|X| + C

Get this back in terms of Y :

-5Y/X + ln|Y/X - 1| = 4 ln|X| + C

Now get the solution in terms of y and x :

-5 (y - 1/2)/(x + 1/4) + ln|(y - 1/2)/(x + 1/4) - 1| = 4 ln|x + 1/4| + C

With some manipulation of constants and logarithms, and a bit of algebra, we can rewrite this solution as

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|x + 1/4| + 4 ln(4) + C

-5 (4y - 2)/(4x + 1) + ln|(4y - 4x - 3)/(4x + 1)| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| - ln|4x + 1| = 4 ln|4x + 1| + C

-5 (4y - 2)/(4x + 1) + ln|4y - 4x - 3| = 5 ln|4x + 1| + C

8 0

3 years ago

Certified checks are items that will be accepted even when your personal check will not. True False

erastovalidia [21]

The answer to your question is true

5 0

3 years ago

Read 2 more answers

A car has a windshield wiper on the driver's side that has total arm length of 10 inches. It rotates

son4ous [18]

Answer:

75.44 Square Inches

Step-by-step explanation:

The diagram of the problem is produced and attached.

To determine the area of the cleaned sector:

Let the radius of the larger sector be R

Let the radius of the smaller sector be r

Area of the larger sector $=\frac{\theta}{360}X\pi R^2$

Area of the smaller sector $=\frac{\theta}{360}X\pi r^2$

Area of shaded part =Area of the larger sector-Area of the smaller sector

$=\frac{\theta}{360}X\pi R^2-\frac{\theta}{360}X\pi r^2\\=\frac{\theta \pi}{360}X (R^2- r^2)$

From the diagram, R=10 Inch, r=10-7=3 Inch, $\theta=95^\circ$

Therefore, Area of the sector cleaned

$=\frac{95 \pi}{360}X (10^2- 3^2)\\=75.44$ Square Inches$

7 0

3 years ago

Harper works at an electronics store as a salesperson. Harper earns a 6% commission on the total dollar amount of all phone sale

agasfer [191]

Answer:

The system of equations are

x + y = 2600 …….equation (1)

and, 6x + 5y = 13700 ……equation (2)

Explanation:

Let x = amount of sales of phone;

y = amount of sales of computer

For phone, 6% of sales is 6% of x, or 6% * x = 0.06x.

Similarly for computer,

5% of y = 0.05y

Given the total sales; x + y = 2600

And commission; 0.06x + 0.05y = 137; or 6x + 5y = 13700

Therefore the system of equations are

x + y = 2600 …….equation (1)

6 x + 5 y = 13700 ……equation (2)

7 0

3 years ago

A cylinder has a radius of 10m and a 8m. What is the exact volume of the cylinder?

olasank [31]

The formula for the volume of a cylinder is πr^2*h. If you plug in the numbers of the radius and the height. π10^2*8=800π meters^3.

4 0

3 years ago