Solve the equation: (x^4 - x + y)dx - xdy=0

1 answer:

5 0

Keeping in mind that "dx" is the delta x, or differential over the x-axis, whilst "dy" is the delta y or differential over the y-axis,

$\bf (x^4-x+y)dx-xdy=0\implies \stackrel{\textit{distributing dx}}{x^4dx-xdx+ydx}-xdy=0
\\\\\\
ydx=xdy-x^4dx+xdx\implies y=\cfrac{xdy-x^4dx+xdx}{dx}
\\\\\\
y=\stackrel{\textit{distributing the denominator}}{x\cfrac{dy}{dx}-x^4+x}$

You might be interested in

What does a persuasive visual designed to make an argument refer to a. visual rhetoric b. logos c. pathos

Mkey [24]

<span>a) Visual Rhetoric. Logos means creating a symbol for some fixed thing. Pathos is related to evoking pity or sadness. Both these are clearly can't be the answer. Visual Rhetoric means using visual images to communicate meaning. This includes using visual design to make an argument. So this should be the answer.</span>

6 0

2 years ago

Read 2 more answers

The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)2t. There are 25 bacteria prese

nordsb [41]

Answer: 1.67 hours.

Explanation:

1) Function that models the number of bacteria:

$B(t)=B_0(10)^{2t}$

2) Bo = 25, then the function is:

$B_0=25(10)^{2t}$

3) To know how many hours will elpase until the number of bactaria is 55,00, you equals B to 55,500 in the equation and solve for t, in this way:

i) start

$55000=25(10)^{2t)$

ii) division property

$2200=10^{2t}$

iii) antilogarithm property

$2t = log_{10}2200$

iv) division property

$t=\frac{log_{10}2200}{2}$

v) Due the operations:

t = 1.67 hours.

Note that the time is less than 2 hours. That sounds fine since after 1 hour there will be 10 times 25 (250 bacteria), and after 2 hours 100 times 25 (2500 bacteria).