The Flow Lines (Or Streamlines) of a Vector Field Are $\mathbf { F } ( x , y ) = 8 x \mathbf { i } - 32 y \mathbf { j }$

question 50

Short Answer

The flow lines (or streamlines) of a vector field are the paths followed by a particle whose velocity field is the given vector field. Thus, the vectors in a vector field are tangent to the flow lines. The flow lines of the vector field $\mathbf { F } ( x , y ) = 8 x \mathbf { i } - 32 y \mathbf { j }$ satisfy the differential equations $\frac { d x } { d t } = 8 x$ and $\frac { d y } { d t } = - 32 y .$ Solve these differential equations to find the equations of the family of flow lines.

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Definitions:

Transitivity

Principle that says if a relation holds between a first object and a second object, and holds between the second object and a third object, then it holds between the first object and the third object. Piaget argued that an understanding of transitivity is characteristic of concrete operational thought.

Logical

Pertaining to the use of reason and systematic thinking to analyze and form judgments.

Seriation

The concrete operation that involves ordering stimuli along a quantitative dimension (such as length).

Horizontal Décalage

The observation that within Piaget’s stages of cognitive development, some abilities do not appear simultaneously but develop sequentially over time.