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marusya05 [52]
2 years ago
11

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

Mathematics
1 answer:
melomori [17]2 years ago
6 0

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

3y^3=28-4

3y^3=24

Divide both sides by 3.

y^3=8

Taking cube root on both sides.

y=2

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

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

-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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