Write an equation to match this graph. i will give brainlyest

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

Find the product (7m^2-3m-7)(m^2-7m-6)

earnstyle [38]

Answer:

7m^4-52m^3-28m^2+67m+42

Step-by-step explanation:

(7m^2-3m-7)(m^2-7m-6)

7m^4-3m^3-7m^2-49m^3+21m^2+49m-42m^2+18m+42

7m^4-3m^3-49m^3-7m^2+21m^2-42m^2+49m+18m+42

7m^4-52m^3-28m^2+67m+42

4 0

3 years ago

The cost of renting a boat for different

DIA [1.3K]

Answer:

Step-by-step explanation:

5 0

3 years ago

How to do this plastic help

liraira [26]

Answer:

39 degrees

Step-by-step explanation:

by seeing the diagram in the attachment, we can see that the angles UWV and VWX are on straight line or, their sum makes 180 degrees.

we also know that sum of the angles in a triangle is 180 degrees.

by using the first statement,

UWV + VWX = 180

UWV + 6x-3 = 180

UWV = 180+3-6x

= 183-6x

by using second statement,

UWV+WVU+VUW=180

substituting the values,

183-6x+2x+5+x+13=180

201-3x=180

substracting 180 from both sides,

21=3x

dividing both the sides by 3,

7=x

the angle VWX=6x-3

substituting 7=x,

VWX=6(7)-3= 39.

4 0

3 years ago

the hight, the feet, of a javelin t seconds afther it is moldeled by the function (t) =4t^2 + 24t + 6. Afther how many seconds d

ruslelena [56]

The max height will be reached after 3 seconds.

You have a typo in your equation. For this type of quadratic equation, it always starts out with a negative coefficient of the t squared term.

To find the x-coordinate of the vertex, we just need to use the expression: -b/2a.

Then, we have:

-24 / (2(-4))

-24 / -8

3

8 0

3 years ago