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An example of lateral earth pressure overturning a retaining wall. The lateral earth pressure is the pressure that soil exerts in the horizontal direction. It is important because it affects the consolidation behavior and strength of the soil and because it is considered in the design of geotechnical engineering structures such as retaining walls, basements, tunnels, deep foundations and ...
Scipione del Ferro was born in Bologna, in northern Italy, to Floriano and Filippa Ferro.His father, Floriano, worked in the paper industry, which owed its existence to the invention of the press in the 1450s and which probably allowed Scipione to access various works during the early stages of his life.
Sink: an endorheic depression generally containing a persistent or intermittent (seasonal) lake, a salt flat (playa) or dry lake, or an ephemeral lake. Panhole: a shallow depression or basin eroded into flat or gently sloping, cohesive rock. [2] Collapse-related: Sinkhole: a depression formed as a result of the collapse of rocks lying above a ...
If w 1, w 2 and w 3 are the three cube roots of W, then the roots of the original depressed cubic are w 1 − p / 3w 1 , w 2 − p / 3w 2 , and w 3 − p / 3w 3 . The other root of the quadratic equation is .
Soil pulled from the ground by the root ball of a linden tree that was blown over in a storm. A tree throw or tree hole is a bowl-shaped cavity or depression created in the subsoil by a tree . They are formed either by the long-term presence and growth of tree roots or when a large tree is blown over (as a windthrow ) or has its stump pulled ...
The polynomial P(x) has a rational root (this can be determined using the rational root theorem). The resolvent cubic R 3 (y) has a root of the form α 2, for some non-null rational number α (again, this can be determined using the rational root theorem). The number a 2 2 − 4a 0 is the square of a rational number and a 1 = 0. Indeed:
If the coefficients of the quartic equation are real then the nested depressed cubic equation also has real coefficients, thus it has at least one real root. Furthermore the cubic function C ( v ) = v 3 + P v + Q , {\displaystyle C(v)=v^{3}+Pv+Q,}
The above solution shows that a quartic polynomial with rational coefficients and a zero coefficient on the cubic term is factorable into quadratics with rational coefficients if and only if either the resolvent cubic has a non-zero root which is the square of a rational, or p 2 − 4r is the square of rational and q = 0; this can readily be ...