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.

Assuming the dialectical interpretation, it argues that Snow's concept of " two cultures " is not only off the mark, it is a damaging and short-sighted viewpoint ; and that it has perhaps led to decades of unnecessary fence-building.

* 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 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 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 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 air is incompressible, the rate of flow ( e. g. liters or gallons per minute ) must be constant within each streamtube since matter is not created or destroyed.

Assuming that a TNT explosion releases 1, 000 small ( thermochemical ) calories per gram ( 4. 2 kJ / g ), one tonne of TNT is equivalent to 4. 2 gigajoules.

Assuming an increase in output of during each year after the start of commercial production, RAND predicts the costs would decline to $ 35 – 48 per barrel ($ 220 – 300 / m < sup > 3 </ sup >) within 12 years.

Assuming a 12 % per year interest rate it follows

Assuming a modern PC could output 1 billion strings per second, it would take one billionth of 2 × 10 < sup > 96 </ sup > seconds, or 2 × 10 < sup > 87 </ sup > seconds to complete its task, which is about 6 × 10 < sup > 79 </ sup > years.

Assuming arrows are produced by labour only, with man-hours per arrow, we have:

Assuming a steady rate of discharge, this alone is sufficient to raise global sea levels by 0. 2 mm per year.

Assuming a hemoglobin concentration of 15g / dl and an oxygen saturation of 99 %, the oxygen concentration of arterial blood is approximately 200ml of O < sub > 2 </ sub > per litre.

Assuming the same per visitor spending at the park for 2007, the park attracted about 4. 2 million people.

Assuming no leakage of actinides to the waste stream during reprocessing, a 1GWe IFR-style reactor would consume about 1 ton of fertile material per year and produce about 1 ton of fission products.

Assuming that the employees of both parties are paid equally, Party B has an absolute advantage over Party A in producing widgets per hour.

Assuming a 60-year plant life and 5 % long-term cost of capital, the depreciation and capital costs not included in the previous marginal cost for Palo Verde are approximately another 1. 4 cents per kilowatt-hour.

Assuming that there is not one but N targets per unit volume, the reaction rate R per unit volume is:

Assuming 1. 0 as the density of water, 36 mL ( about 2. 5 tablespoons ) of water needs to be converted to oxygen per hour assuming 100 % efficiency.

Assuming each wire carries current I, and there are N wires per unit length, the magnetic field can be derived using Ampère's law: