What is the area of y?

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

7 0

Could you draw a better graph? I can't really see where y is at or what everything is.

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Solving separable differential equation DY over DX equals xy+3x-y-3/xy-2x+4y-8

Ivanshal [37]

It looks like the differential equation is

$\dfrac{dy}{dx} = \dfrac{xy + 3x - y - 3}{xy - 2x + 4y - 8}$

Factorize the right side by grouping.

$xy + 3x - y - 3 = x (y + 3) - (y + 3) = (x - 1) (y + 3)$

$xy - 2x + 4y - 8 = x (y - 2) + 4 (y - 2) = (x + 4) (y - 2)$

Now we can separate variables as

$\dfrac{dy}{dx} = \dfrac{(x-1)(y+3)}{(x+4)(y-2)} \implies \dfrac{y-2}{y+3} \, dy = \dfrac{x-1}{x+4} \, dx$

Integrate both sides.

$\displaystyle \int \frac{y-2}{y+3} \, dy = \int \frac{x-1}{x+4} \, dx$

$\displaystyle \int \left(1 - \frac5{y+3}\right) \, dy = \int \left(1 - \frac5{x + 4}\right) \, dx$

$\implies \boxed{y - 5 \ln|y + 3| = x - 5 \ln|x + 4| + C}$

You could go on to solve for $y$ explicitly as a function of $x$ , but that involves a special function called the "product logarithm" or "Lambert W" function, which is probably beyond your scope.

8 0

2 years ago

Functions f(x) and g(x) are shown below. f(x) = x2. . g(x) = x2 - 8x + 16. In which direction and by how many units should f(x)

Aliun [14]

The original function is given by:
$f (x) = x ^ 2
$
We apply the following transformation:
Horizontal displacements:
Suppose k> 0
To move the graph k units to the right, we must graph f (x-k)
Applying the transformation for k = 4 we have:
$g (x) = f (x-4)

g (x) = (x-4) ^ 2

g (x) = x ^ 2 - 8x + 16$
Answer:
B. Right by 4 units

3 0

3 years ago

Read 2 more answers

Will mark brainliest if correct

My name is Ann [436]

Answer:

identity

commutative

associative

distributive

Step-by-step explanation:

6 0