Given the choice between nylon and gut, many luthiers prefer to use gut, as it conforms more readily to the sharp angle at the edge of the fingerboard.

Given two dual numbers p, and q, they determine the set of z such that the Galilean angle between the lines from z to p and q is constant.

Given two intersecting planes described by and, the dihedral angle between them is defined to be the angle between their normal directions:

Given: side a = 20, side c = 24, and angle C = 40 °

Given all of the above premises are true, the angle B may be acute or obtuse ; meaning, one of the following is true:

Given a unit vector n in R < sup > 3 </ sup > and an angle φ, let R ( φ, n ) represent a counterclockwise rotation about the axis through n ( with orientation determined by n ).

Given the above, for every point in this ball there is a rotation, with axis through the point and the origin, and rotation angle equal to the distance of the point from the origin.

Given the introduction of ligand concept, he was also able to further derive the idea of bite angle and other aspects of chelation.

Given a hill angle and launch angle as before, it can be shown that the range along the hill forms a ratio with the original range along the imaginary horizontal, such that:

: Given three points A, B and C on a circle with center O, the angle AOC is twice as large as the angle ABC.

Given the initial velocity of a particle launched from the ground, the downward ( i. e. gravitational ) acceleration, and the projectile's angle of projection θ ( measured relative to the horizontal ), then a simple rearrangement of the SUVAT equation

Given these approaches, the bowler can hope to both intimidate the batsman somewhat, and possibly have the ball deflect off the bat at an awkward angle and produce a catch for a nearby fielder.

Given his adept use of angle, depth, and pace, his opponents often have difficulty breaking down one particular side.

Given a unit vector u = ( u < sub > x </ sub >, u < sub > y </ sub >, u < sub > z </ sub >), where u < sub > x </ sub >< sup > 2 </ sup > + u < sub > y </ sub >< sup > 2 </ sup > + u < sub > z </ sub >< sup > 2 </ sup > = 1, the matrix for a rotation by an angle of θ about an axis in the direction of u is

Given the geometry of the array, the delays or phase differences can be used to estimate the incident angle.

* Trisecting the angle: Given any angle dividing it into three smaller angles all of the same size.

Given a fixed thickness of armour plate, a projectile striking at an angle must penetrate more armour than one impacting perpendicularly.

Given a point off of a line, if we drop a perpendicular to the line from the point, then a is the distance along this perpendicular segment, and φ is the least angle such that the line drawn through the point at that angle does not intersect the given line.

“ Given the high incidence of craniofacial injury, appropriate safety standards for taxicabs must be initiated, including the reevaluation of the utility of the safety divider ”

Given a point it is related to a line in projective twistor space where we can see the incidence relation as giving the linear embedding of

: Given any family of nonempty sets, their Cartesian product is a nonempty set.

Given the similarities in the two characters ' names, professions, written works and generally dark subject matter, it is likely that Lovecraft's Alhazred provided the main inspiration for al-Hazir.

Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

" Given that Thomas Aquinas died six years before Albertus Magnus ' death, this legend as stated is unlikely.

Given Ealdred's known support of Godwin's family, John of Worcester is probably correct.

* Given any Banach space X, the continuous linear operators A: X → X form a unitary associative algebra ( using composition of operators as multiplication ); this is a Banach algebra.

* Given an R-module M, the endomorphism ring of M, denoted End < sub > R </ sub >( M ) is an R-algebra by defining ( r · φ )( x ) = r · φ ( x ).

Given the other ZF axioms, the axiom of regularity is equivalent to the axiom of induction.

After Christians in Ephesus first wrote to their counterparts recommending Apollos to them, he went to Achaia where Paul names him as an apostle ( 1 Cor 4: 6, 9-13 ) Given that Paul only saw himself as an apostle ' untimely born ' ( 1 Cor 15: 8 ) it is certain that Apollos became an apostle in the regular way ( as a witness to the risen Lord and commissioned by Jesus-1 Cor 15: 5-9 ; 1 Cor 9: 1 ).< ref > So the Alexandrian recension ; the text in < sup > 38 </ sup > and Codex Bezae indicate that Apollos went to Corinth.

Given its " blue-water " bias, the navy is even less inclined to become involved in counterdrug operations than the army or air force.

Given any element x of X, there is a function f < sup > x </ sup >, or f ( x ,·), from Y to Z, given by f < sup > x </ sup >( y ) := f ( x, y ).

Given this, the bidding is said to start at the one-level when contracting for a total of seven tricks, at the two-level for eight tricks and so on to the seven-level to contract to take all thirteen tricks.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is

Given this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.

Given points P < sub > 0 </ sub > and P < sub > 1 </ sub >, a linear Bézier curve is simply a straight line between those two points.

Given the then GDP ($ 7. 095 bln ) of the country, military spending is roughly estimated to be about $ 300 million.

Given some encrypted data (" ciphertext "), the goal of the cryptanalyst is to gain as much information as possible about the original, unencrypted data (" plaintext ").

Given the federal nature of the holiday, celebrating Canada Day can be a cause of friction in the province of Quebec, where the holiday is overshadowed by Quebec's National Holiday, on June 24.

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given such a sweeping definition, it is apparent that cognition is involved in everything a human being might possibly do ; that every psychological phenomenon is a cognitive phenomenon.