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Drupady [299]
4 years ago
15

How do you rearrange the equation (2x) /(4pi) +((1-x) /2) =0 to solve for x?

Mathematics
1 answer:
USPshnik [31]4 years ago
3 0
\frac{2x}{4 \pi } + \frac{1-x}{2} =0 \\ 
 \frac{x}{2 \pi } + \frac{1-x}{2} = 0
Then we will multiply both sides of the equation by 2 π :
x + π ( 1 - x ) = 0
x + π - π x = 0
x ( 1 - π ) = - π    / · ( - 1 )
x ( π - 1 ) = π
x = π / ( π - 1 )
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assume x and y are both differentiable functions of t. find dx/dt given x=-1 and dy/dt=8 for the relation: 4x^2+3y^3=28
melomori [17]

Given:

x and y are both differentiable functions of t.

4x^2+3y^3=28

x=-1\text{ and }\dfrac{dy}{dt}=8

To find:

The value of \dfrac{dx}{dt}.

Solution:

We have,

4x^2+3y^3=28       ...(i)

At x=-1,

4(-1)^2+3y^3=28

4+3y^3=28

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3y^3=24

Divide both sides by 3.

y^3=8

Taking cube root on both sides.

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So, y=2 at x=-1.

Differentiate (i) with respect to t.

4(2x\dfrac{dx}{dt})+3(3y^2\dfrac{dy}{dt})=0

Putting x=-1, y=2 and \dfrac{dy}{dt}=8, we get

4(2(-1)\dfrac{dx}{dt})+3(3(2)^28)=0

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-8(\dfrac{dx}{dt}-9(4))=0

Divide both sides by -8.

\dfrac{dx}{dt}-36=0

\dfrac{dx}{dt}=36

Therefore, the value of 4x^2+3y^3=28 is 36.

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3 years ago
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