Question

For the curve x² + y² = 25, dy/DX at the point (3,4) = ? .
Value of theta = ?.
tan theta = ?.
dy/dx at (3,4) = ?.



pls solve it..
​

Answer 1

Answer:

dy/dx at (3,4) is -3/4

Step-by-step explanation:

x² + y² = 25

y² = 25 - x²

Find dy/dx

2y dy/dx = -2x

dy/dx = -2x/2y

           = -x/y

At point (3,4)

            = -3/4

Answer 2

theta =$tan^(-1)(4/3)$ = 0.93 radians (approximately).

The values we have found are:

dy/dx at (3,4) = -3/4

theta = 0.93 radians

tan(theta) = 4/3

We can start by finding the derivatives of the equation x² + y² = 25 with respect to x and y.

Taking the derivative with respect to x, we get:

2x + 2y(dy/dx) = 0

Simplifying this, we get:

dy/dx = -x/y

We know that x = 3 and y = 4 at the position (3,4), so:

dy/dx = -3/4

To find the value of theta, we can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is y and the adjacent side is x, so:

tan(theta) = y/x = 4/3

Therefore, theta =$tan^(-1)(4/3)$ = 0.93 radians (approximately).

So, the values we have found are:

dy/dx at (3,4) = -3/4

theta = 0.93 radians

tan(theta) = 4/3

For such more questions on derivative,

https://brainly.in/question/55137449

#SPJ3