Suppose the population of a species of trout in a lake is given by a logistic model with intrinsic growth rate of k = 0.4 per year and carrying capacity of K = 10,000. In addition, suppose 500 fish are harvested from the lake each year. Which of the following differential equations describe the change in the population with respect to time? 

The first identifiable state in southern Africa was

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Compute the double integral \[\int\int_R \; \frac{x}{y} \; dA\]where R the region enclosed by the curves \(x=0\), \(y=e^x\), and \(y=e\).    

Suppose the population of a species of trout in a lake is given by a logistic model with intrinsic growth rate of k = 0.4 per year and carrying capacity of K = 10,000. In addition, suppose 500 fish are harvested from the lake each year. Which of the following differential equations describe the change in the population with respect to time? 

Solve the differential equation \[\frac{dy}{dx}=1-x+y-xy\] with initial condition \(y(0)=0\).

Let \[g(x,y) = xy + y^2 +3 \] where \(x = uv^2\) and \(y = u + v^2\). Use the chain rule to find the partial derivative \(\displaystyle\frac{\partial g}{\partial v}\) at the point \((u,v) = (1,2)\).

Solve the differential equation \[\frac{dy}{dx}=1-x+y-xy\] with initial condition \(y(0)=0\).

Create a labeled property graph model to store movie information. Entities and activities are described below. Use nodes, relationships, and properties. Use () for nodes. Use {} for properties. Use [] for relationships. Use for relationship directions.   A movie has an ID, title and release year. An actor has an ID and a name. A theater has an ID and a zip code. A movie plays in a theater for a certain number of days. An actor plays a role in movie(s). The role played by an actor in a movie could be lead or supporting.

As he traveled about India, the Chinese pilgrim Xuanzang was