A rigid body subjected to three forces acting at three points is known as a three-force member. These forces must have concurrent lines of action, except for parallel forces, where the lines of action are parallel.
For example, consider a dumpster connected to a pin support at point A and a pin attached to a hydraulic cylinder at point B.

Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors....

Cofunction identities are a key concept in trigonometry. They describe how trigonometric functions relate when their input angles are complementary — meaning the angles add up to 90°. On the unit circle, every angle θ— measured counterclockwise from the positive x-axis — corresponds to a point with coordinates (cos⁡ θ, sin ⁡θ). These values represent the horizontal and vertical components of the terminal side of the angle.If the same point on...

Human development is typically examined across three main domains: physical, cognitive, and socio-emotional. These domains represent the significant areas of change and continuity throughout the lifespan, from infancy to late adulthood.
Physical Development
Physical processes, also known as maturation, encompass the biological changes that occur across an individual's life. These changes begin with genetic inheritance and continue through various stages, including growth in height and weight,...

In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:

According to Newton’s second law of motion, the rate of change of the momentum of an object is the net external force acting on it. The total change in momentum between two timepoints thus depends on both the external force acting on it and the time over which it acts. Describing this mathematically, the total change of an object’s motion is proportional to the force vector and the time over which it is applied. This product is called impulse.
Additionally, it can be shown that the...