If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.

If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for the formula above ; after some reworking, we get the following filter representation:

If one integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral – see proof of Cavalieri's quadrature formula for details.

If we allow both, the problem is called the quantified Boolean formula problem ( QBF ), which can be shown to be PSPACE-complete.

If the answer is " no ", the formula is unsatisfiable.

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,

If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.

Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like ( a + b )( a-b )= a²-b² it does not tell us how to think mathematically.

If empirical data reach significance under the appropriate statistical formula, the research hypothesis is supported.

If some specific deductive system of first-order logic is sound and complete, then is it " perfect " ( a formula is provable iff it is a semantic consequence of the axioms ), thus equivalent to any other deductive system with the same quality ( any proof in one system can be converted into the other ).

If every formula in R of degree k is either refutable or satisfiable, then so is every formula in R of degree k + 1.

" If I have learned a formula in gibberish which in any way jogs my memory so as to enable me in each single case to act as though I had a general idea, what possible utility is there in distinguishing between such a gibberish ... and an idea?

If the polygon can be drawn on an equally spaced grid such that all its vertices are grid points, Pick's theorem gives a simple formula for the polygon's area based on the numbers of interior and boundary grid points.

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

If ΔW is the amount of work performed during a period of time of duration Δt, the average power P < sub > avg </ sub > over that period is given by the formula

If G is a finite group and S and T are subgroups of G, then ST is a subset of G of size | ST | given by the product formula:

If the slope m of a line and a point ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) on the line are both known, then the equation of the line can be found using the point-slope formula:

If the respective impedances of the branches of the hybrid that are connected to the conjugate sides of the hybrid are known, hybrid balance may be computed by the formula for return loss.

If the observer is close to the surface of the earth, then it is valid to disregard h in the term, and the formula becomes

If h is significant with respect to R, as with most satellites, then the approximation made previously is no longer valid, and the exact formula is required:

* If 4a < sub > 0 </ sub > = −, the above formula yields ũ < sup > 2 </ sup > = 0.

* If 4a < sub > 0 </ sub > > −, the above formula yields ũ < sup > 2 </ sup > > 0.

If any official operation abroad begins to go wrong, we shall look to the ambassador to find out why and to get suggestions for remedial action.

`` If you saw the drama called Rhinoceros '', I said, `` think of the effect it would have on an audience of rhinos when the actor on stage suddenly begins turning into a rhinoceros.

If death receives more than its share of attention from the theologian and if sin receives less than its share, the gift of the life eternal through Christ begins to look like the divinely appointed means of rescue from temporal, i.e., created, existence.

If he begins to run too soon, the pitcher may throw to a base rather than to home — in this case, the runner is picked off, and will most likely be tagged out.

If a fighter is knocked down during the fight, determined by whether the boxer touches the canvas floor of the ring with any part of their body other than the feet as a result of the opponent's punch and not a slip, as determined by the referee, the referee begins counting until the fighter returns to his or her feet and can continue.

If the cord is twisted up tightly on itself and then the bucket is released, it begins to spin rapidly, not only with respect to the experimenter, but also in relation to the water it contains.

If more than one player remains after the first round, the " draw " phase begins.

If drain-to-source voltage is increased further, the pinch-off point of the channel begins to move away from the drain towards the source.

If a ship's hull classification symbol begins with " W ", it is a ship of the United States Coast Guard.

If a ship's hull classification symbol begins with " T -", it is part of the Military Sealift Command, has a primarily civilian crew, and is a United States Naval Ship ( USNS ) in non-commissioned service — as opposed to a commissioned United States Ship ( USS ).

If an appropriate form of written text is made available before formal schooling begins, reading should be learned inductively, emerge naturally, and with no significant negative consequences.

If an inability to sufficiently adjust to life circumstances begins within three months of a particular event or situation, and ends within six months after the stressor stops or is eliminated, it may instead be classed as an adjustment disorder.

If the carbonyl is at position 1 ( that is, n or m is zero ), the molecule begins with an formyl group H ( C = O )-, and is technically an aldehyde.

If the nation state begins to disappear, it may well be the direct or indirect result of globalization and internationalism.

" If he replies with the word " Accepto ", his reign begins at that instant, not at the inauguration ceremony several days afterward.

If met with ideal conditions on a new planet's surfaces, the bacteria become active and the process of evolution begins.

If the opponent in the hold begins to tap out at the same time a referee counts to three for pinning the opponent delivering the hold, both opponents have legally achieved scoring conditions simultaneously.

If a burial occurs on Chol HaMoed, shiva begins before is completed.

If they become plugged by debris, water begins flowing over the outside, depositing more calcite and creating the more familiar cone-shaped stalactite.

If the wedding is part of a religious service, then technically the service begins after the arrival of the participants, commonly with a prayer, blessing, or ritual greeting.

# If the word begins with ' KN ', ' GN ', ' PN ', ' AE ', ' WR ', drop the first letter.

If a photon rocket begins its journey in low earth orbit, then one year of thrusting may be required to achieve an earth escape velocity of 11. 2 km / s if the vehicle is already in orbit at a velocity of 9, 100 m / s, and 400 m / s additional velocity is obtained from the east to west rotation of the earth.

If any contestants are visually impaired, the host will read the question and four choices all at once, then repeat the choices after the music begins.

; Loop-invariant code motion: If a quantity is computed inside a loop during every iteration, and its value is the same for each iteration, it can vastly improve efficiency to hoist it outside the loop and compute its value just once before the loop begins.

If a small external magnetic field is applied to the superconducting loop, a screening current,, begins circulating in the loop that generates a magnetic field canceling the applied external flux.