Assuming these are in general position, i. e. four distinct intersections, we get another interpretation of the linear system as the conics passing through the four given points ( note that the codimension four here matches the dimension, one, in the five-dimensional space of conics ).

Assuming the French would dislike an English language interpretation of the Pagnol plays, Leslie Caron was hesitant to replace her, but she liked the script and accepted three weeks before principal photography began.

Assuming it was a kindly rejection, she was later surprised to be invited for a meal at Mr. Chow with Lloyd Webber and the lyricist Don Black to discuss the concept of a song cycle inspired by the story of a friend of the composer who had moved from London to the United States to begin a new life.

Assuming that these various words and uses should refer to a single underlying concept, St. Augustine renders it as clara notitia cum laude, " brilliant celebrity with praise ".

Assuming initially has value, two consecutive evaluations of the expression yield, respectively, and.

Assuming the gamma-ray explosion to be spherical, the energy output of GRB 080319B would be within a factor of two of the rest-mass energy of the Sun ( the energy which would be released were the Sun to be converted entirely into radiation ).

Assuming, the general second-order PDE in two independent variables has the form

Assuming that the second particle is at rest before the collision, the angles of deflection of the two particles, and, are related to the angle of deflection in the system of the center of mass by

Assuming the responsibility of mediator between the two sides, and with Erasmus ' willing participation ( the robot being left as the leader and controlling-force of the thinking machines ), Duncan does something similar to Bene-Gesserit Sharing with the robot ; possibly along with what seems to be a physical-bonding ( similar to what Leto II did with the sandtrout ) into something of a human-machine hybrid.

Assuming a fuel pump had failed, the pilots turned it off, since gravity would still feed fuel to the aircraft's two engines.

Assuming bus commuters do not care about the color of the bus, consumers are expected to choose between bus and car still with equal probability, so the probability of car is still 0. 5, while the probabilities of each of the two bus types is 0. 25.

Assuming both p and q are nonzero, neither of the groups O ( p, q ) or SO ( p, q ) are connected, having four and two components respectively.

Assuming that Jeconiah's reign ended on the day that the Babylonians captured Jerusalem the first time, 2 Adar ( 16 March ) 597 BC, and further assuming that the Jewish calendar in the sixth century BC had the same number of days in the two preceding months as in the modern Jewish calendar, Jehoiachin's reign of three months and ten days () would have started on 21 Heshvan ( 9 December ) 598 BC.

* By clock: Assuming that the dancer stands at the center of a clock with hands and faces 12, one may say, e. g., " take a step at two o ' clock ".

Assuming the crown, he passed Burgundy to his younger brother, Hugh the Black, after only two years as duke.

Assuming the spacing between two ions is a, the potential in the lattice will look something like this:

Assuming that the prophecy took place after Uzziah became sole regent in 768 / 767, Amos's prophecy can be dated to some time after that and some time before Jeroboam's death in 753 BC, with the earthquake two years after that.

Assuming geostrophic balance, the system is stationary and the first two equations become:

Assuming that two individuals share the same 32 ancestors of n =

Average growth approximation: Assuming that two stocks have the same earnings growth, the one with a lower P / E is a better value.

Assuming the hidden variable to be polarisation direction ( parallel on the two sides in real applications, not orthogonal ), equation ( 1 ) becomes:

Assuming two competitors per match, if there are competitors, there will be rounds required, or if there are rounds, there will be competitors.

Assuming the route was blocked, he returned to the two cargo ships on one of the expedition's small launches.

Assuming Sharchops still outnumber Ngalops some three to two, the total population is around 212, 500.

Assuming the radius of the first gear wheel is known as a function of z, and using the relationship, the above two equations can be combined to yield the differential equation:

Assuming Sharchops still outnumber Ngalops some three to two, the total Ngalop population is around 141, 700.

Assuming the right amount of current for the right time, this will weld the two pieces of metal together.

Assuming the plain black habit of the institution in 1828, she conducted the affairs of the home while Mother McAuley and two foundress companions were making their novitiate in the Presentation Convent of George's Hill preparatory to the founding of the new congregation.

Assuming the lower figure for the big blast and one shot estimated by the Japanese at 10 megatons, a conservative computation is that the 24 announced tests produced a total yield of at least 60 megatons.

Assuming the weather is halfway decent that day, hundreds of thousands of persons will mass along this thoroughfare as President John F. Kennedy and retiring President Dwight D. Eisenhower leave Capitol Hill following the oath-taking ceremonies and ride down this historic ceremonial route.

Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.

Assuming ZF is consistent, Paul Cohen employed the technique of forcing, developed for this purpose, to show that the axiom of choice itself is not a theorem of ZF by constructing a much more complex model which satisfies ZF ¬ C ( ZF with the negation of AC added as axiom ) and thus showing that ZF ¬ C is consistent.

Assuming that the pixel color is expressed using straight ( non-premultiplied ) RGBA tuples, a pixel value of ( 0. 0, 0. 5, 0. 0, 0. 5 ) implies a pixel which has 50 % of the maximum green intensity and 50 % opacity.

Assuming that the ion is accelerated during a very short interval, the ion can be assumed to be travelling at constant velocity.

Assuming that 10 – 15 % of bread is thrown away as stale, if it could be made to stay fresh another 5 – 7 days then perhaps 2 million tons of flour per year would be saved.

Assuming average population densities of 0. 25 animals per km² in regions where it is known to be common or abundant, and 0. 02 per km² elsewhere, and with a total area of occupancy of 327, 000 km², a total population estimate of approximately 28, 000 is suggested.

Assuming a fixed sample size, the technique gives more accurate results when most of the variation in the population is within the groups, not between them.

:< u > The Copenhagen Interpretation </ u >: Assuming wave functions are not real, wave-function collapse is interpreted subjectively.

Assuming the Axiom of choice, is regular for each α.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.

Assuming that the rule is known, one can derive the function that is used above in the classical heat calculation with respect to pressure.

Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices.

Assuming we can define at least one nonreal complex number, however, a complex number is definable if and only if both its real part and its imaginary part are definable.

Assuming that the visible material makes up only a small part of the cluster is the most straightforward way of accounting for this.