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If each mass point has the mass, the tension of the string is, the separation between the mass points is and are the offset of these points from their equilibrium points ( i. e. their position on a straight line between the two attachment points of the string ) the vertical component of the force towards point is
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If and each
If the Union conceded this to them, the same right must be conceded to each remaining state whenever it saw fit to secede: This would destroy the federal balance between it and the states, and in the end sacrifice to the sovereignty of the states all the liberty the citizens had gained by their Union.
If the railroads, for example, regularly slaughtered 25,000 passengers each year, the high priests of the cult would have cause to tremble for their personal safety, for such a holocaust would excite demands for the hanging of every railroad president in the United States.
If a branch extended out too far, each man held it back for the next, and if they met a low overhang, each warned the other.
If coffee is sold at the cafeteria, let a few workers in each department get it for the whole group.
If no specific organization plan exists limiting the number of scientists at each salary level, the result is a department top-heavy with high-level, high-salaried personnel ''.
If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.
If each text form is marked when matched with a dictionary form, the text forms not contained in the dictionary can be identified when all dictionary forms have been read.
If cell Af is an information cell, it and any information cells in the Y-region that have been linked to Af each contain an address in the W-region where a potentially matching form is stored.
If the bottom name in each column did not have a responsible executive identified, the next name above which identified such a responsible executive was substituted.
If the wedding party lasted late, and the travel schedule means there are only a few hours before resuming the trip or making an early start, the husband may forestall tensions and uncertainties by confiding to his bride that lying in each other's arms will be bliss enough for these few hours.
If he is not told which of four or five readings was meant for him, he can more readily assess each item in a larger frame: `` Does that statement really sound as if it were for me, significant in my particular life??
If laborers are merely commodities competing against each other in a market place like so many bags of wheat and corn ( unsupported, by the way, by any agricultural subsidy ), then they may be pardoned for reacting with complete antagonism to a system that imposes such status upon them.
If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.
If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.
If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles.
If the square mile is divided into quarters, each quarter has a side length of mile ( 880 yards ) and is square mile in area, or 160 acres.
If each node additionally records the size of its subtree ( including itself and its descendants ), then the nodes can be retrieved by index in O ( log n ) time as well.
If the domain of F is a disjoint union of two or more intervals, then a different constant of integration may be chosen for each of the intervals.
If a water absorbing swale for each yard is combined with permeable concrete streets, storm drains can be omitted from the neighbourhood.
If the candidate relies on sponsors, the celebrant asks them if they will raise the child in " the Christian faith and life " ( ECUSA BCP ), and will raise the child through " prayers and witness to grow into the full stature of Christ " to which the parents will state to each, " I will, with God's help.
If the dealer does not bust, each remaining bet wins if its hand is higher than the dealer's, and loses if it is lower.
If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.
If and mass
If we neglect higher than first order terms in the fluctuations, the mass balance equation becomes
* Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume.
If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.
If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have
If a small heater is available for the coldest nights, a slab or basement cistern can inexpensively provide the required thermal mass.
If the boat floats, the mass of the boat ( plus contents ) as a whole divided by the volume below the waterline is equal to the density of water ( 1 kg / l ).
If there are other stars orbiting a black hole, their orbit can be used to determine its mass and location.
If the air mass is colder than the ground below it, it is labeled k. If the air mass is warmer than the ground below it, it is labeled w. While air mass identification was originally used in weather forecasting during the 1950s, climatologists began to establish synoptic climatologies based on this idea in 1973.
If a main-sequence star is not too massive ( less than approximately 8 solar masses ), it will eventually shed enough mass to form a white dwarf having mass below the Chandrasekhar limit, which will consist of the former core of the star.
If is much smaller than, the mass ratio is almost identical to the mass fraction.
If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force.
If one item in a package or stack initiates, it will usually propagate to the other items, creating a mass fire.
If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid.
If the primary variable is mass fraction (, given, for example, in ), then the equation changes to:
If disk galaxies merge with another galaxy of comparable mass ( at least 15 percent of its mass ) the merger will likely destroy, or at a minimum greatly disrupt the disk, yet the resulting galaxy is not expected to be a disk galaxy.
If and point
If he had been `` liquidated '' in some way, he would have become a martyr, a rallying point for people who shared his ideas.
If we examine the three types of change from the point of view of their internal structure we find an additional profound difference between the third and the first two, one that accounts for the notable difference between the responses they evoke.
If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.
If their schedules were to synchronize, there was no point in wasting time.
If design head has a deep cavity, clay lid will be quite thick at this point ; ;
If the argument is accepted as essentially sound up to this point, it remains for us to consider whether the patient's difficulties in orienting himself spatially and in locating objects in space with the sense of touch can be explained by his defective visual condition.
If this attitude is seriously questioned in the Soviet Union, it does not necessarily follow that the majority of the society in which I live is too aware of the necessity for clarity on this ethical as well as aesthetic point of view.
If the Southerners were sufficiently aroused, they could very well cut the Kennedy legislative program to ribbons from their vantage point of committee chairmanships, leaving Sam Rayburn leading a truncated, unworkable party.
If it was, then it must have been God's intention to translate him at a certain point from time to eternity.
If one also removes the second postulate (" a line can be extended indefinitely ") then elliptic geometry arises, where there is no parallel through a point outside a line, and in which the interior angles of a triangle add up to more than 180 degrees.
If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.
If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence ; the sine condition then becomes sin u ' 1 / h1 = sin u ' 2 / h2.
If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.
If a system consists of several particles, the total angular momentum about a point can be obtained by adding ( or integrating ) all the angular momenta of the constituent particles.
If the net force on some body is directed always toward some fixed point, the center, then there is no torque on the body with respect to the center, and so the angular momentum of the body about the center is constant.
If the score reaches 20-all, then the game continues until one side gains a two point lead ( such as 24 – 22 ), up to a maximum of 30 points ( 30 – 29 is a winning score ).
If the filter shows amplitude ripple within the passband, the x dB point refers to the point where the gain is x dB below the nominal passband gain rather than x dB below the maximum gain.
If the player and dealer have the same point total, this is called a " push " and the player typically doesn't win or lose money on that hand.
If the heat of vaporization and the vapor pressure of a liquid at a certain temperature is known, the normal boiling point can be calculated by using the Clausius-Clapeyron equation thus:
If the large-scale Universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred ( or special ) observer or vantage point.
If a player is one point away from winning a match, that player's opponent will always want to double as early as possible in order to catch up.
If the holes are closed, the gas will only mix with ambient air at the point of combustion, that is, only after it has exited the tube at the top.
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