2. The rate at which a phase transformation proceeds depends on the time t and the dt transformed volume fraction (quantity) y of the product, according to dy = 4kt° (1– y) dt where k is a constant. At the start of the phase transformation, the amount of transformed product is zero: y(0) =0. Determine the transformed fraction as a function y(t) of the time t.

Q: If y = 2x3 + 5x and dx = 2, find dt dy Y when x = 4. dt dy - dt

A:

Q: Consider a water tank that is being filled with rainfall at the top and is drained through a small…

A:

Q: bifurcation values

A:

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: The length, x, of the edge of a cube is increasing. (a) Write the chain rule fordV/dt, the time rate…

A: The length, x, of the edge of a cube is increasing. a). Consider the volume of a cube, V=x3…

Q: Find dy/dt.

A: Find dydt.

Q: Fluid runs through a drainage pipe with a 10-cm radius and a length of 10 m (1000 cm). The velocity…

A: Solution: From the given information,

Q: Verify that the function y increases at a maximum rate when y = L/2 .

A: Consider the function ⇒    where   Differentiating with respect to ‘x’

Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: Let X have the pdf 1 p(x) = T(1+ a2)' x E R. %3D Find the pdf of Y = X?.

A:

Q: ind and classify the equilibria for y'= (y- 1)(y – 2)y. The initial

A: