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Rudiy27
4 years ago
9

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

Mathematics
1 answer:
algol [13]4 years ago
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}
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The volume of a cube depends on the length of its sides.This can be written in function as v(s).What is the best interpretation
Natasha_Volkova [10]

Answer:


Step-by-step explanation:

We know that,

Volume of cube = (side)^3

Fro side length s , we can write:

V(s) = s^3  , where volume is the function of s.

Now ,

We have given :  v(4) = 64

If we compare this with v(s) = s^3

Then we get s =4 , i.e side length of cube is 4

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8 0
3 years ago
What is 18x-(8x-7)=67
dimaraw [331]

Answer:

6

Step-by-step explanation:

18x−(8x−7)=67

Step 1: Simplify both sides of the equation.

18x−(8x−7)=67

18x+−1(8x−7)=67(Distribute the Negative Sign)

18x+−1(8x)+(−1)(−7)=67

18x+−8x+7=67

(18x+−8x)+(7)=67(Combine Like Terms)

10x+7=67

10x+7=67

Step 2: Subtract 7 from both sides.

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7 0
4 years ago
Solve the system by substitution.<br> [-2.5x+y = 13.5<br> 12.25x - y=-12.25
IrinaK [193]

Answer:

x = 5/39 , y = 539/39

Step-by-step explanation:

Solve the following system:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

In the first equation, look to solve for y:

{y - 2.5 x = 13.5

12.25 x - y = -12.25

y - 2.5 x = y - (5 x)/2 and 13.5 = 27/2:

y - (5 x)/2 = 27/2

Add (5 x)/2 to both sides:

{y = 1/2 (5 x + 27)

12.25 x - y = -12.25

Substitute y = 1/2 (5 x + 27) into the second equation:

{y = 1/2 (5 x + 27)

1/2 (-5 x - 27) + 12.25 x = -12.25

(-5 x - 27)/2 + 12.25 x = 12.25 x + (-(5 x)/2 - 27/2) = 9.75 x - 27/2:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

In the second equation, look to solve for x:

{y = 1/2 (5 x + 27)

9.75 x - 27/2 = -12.25

9.75 x - 27/2 = (39 x)/4 - 27/2 and -12.25 = -49/4:

(39 x)/4 - 27/2 = -49/4

Add 27/2 to both sides:

{y = 1/2 (5 x + 27)

(39 x)/4 = 5/4

Multiply both sides by 4/39:

{y = 1/2 (5 x + 27)

x = 5/39

Substitute x = 5/39 into the first equation:

{y = 539/39

x = 5/39

Collect results in alphabetical order:

Answer: {x = 5/39 , y = 539/39

5 0
3 years ago
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