a particle moves along the curve xy=10. if x=2 and dy/dt=3, what is the value of dx/dt.
i'm guessing this is something to do with parametric equations.
if x is 2, then y=5. but how do i get dx/dt.
you have to differentiate the equation with respect to t
so xy=10
x(dy/dt) + y(dx/dt) = 0
when x=2 y = 5 and dy/dt = 3
so 2(3) + 5(dx/dt) = 0
etc. solve for dx/dt
-6/5
Ah, the joy of parametric equations! Let me clown around and help you out.
We have the equation xy = 10, and we want to find the value of dx/dt. So, let's differentiate the equation with respect to t, as you correctly said:
x(dy/dt) + y(dx/dt) = 0
Now, we can substitute the given values: x = 2, y = 5, and dy/dt = 3:
2(3) + 5(dx/dt) = 0
6 + 5(dx/dt) = 0
To solve for dx/dt, we need to reverse those maths:
5(dx/dt) = -6
dx/dt = -6/5
So, the value of dx/dt is -6/5. Remember, with clown math, we always like to offer a unique twist!
To find the value of dx/dt, we need to differentiate the equation xy = 10 with respect to t.
Let's differentiate both sides of the equation using the product rule:
d/dt(xy) = d/dt(10)
Using the product rule, we get:
x(dy/dt) + y(dx/dt) = 0
Substituting the given values x = 2, y = 5, and dy/dt = 3, we can solve for dx/dt:
2(3) + 5(dx/dt) = 0
6 + 5(dx/dt) = 0
5(dx/dt) = -6
dx/dt = -6/5
Therefore, the value of dx/dt is -6/5.
To find the value of dx/dt, we need to differentiate the equation xy = 10 with respect to t. This can be done using the chain rule, which states that the derivative of a product of two functions is the first function times the derivative of the second function, plus the second function times the derivative of the first function.
Given that x = 2 and dy/dt = 3, we can substitute these values into the equation xy = 10:
2(3) + 5(dx/dt) = 0
Simplifying this equation gives us:
6 + 5(dx/dt) = 0
Next, we solve for dx/dt:
5(dx/dt) = -6
Dividing both sides of the equation by 5:
dx/dt = -6/5
Therefore, the value of dx/dt is -6/5.