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Page "Hyperbola" ¶ 13
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If and angle
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 a wedge-shaped coating of increasing thickness is removed from a substrate by an instrument like the Hesiometer with a knife of constant rake angle, a number of removal mechanisms are often observed which depend upon the thickness of the coating.
If the rake angle **yc of the knife is high enough and the friction angle **yt between the front of the knife and the back of the chip is low enough to give a positive value for Af, the resultant vector R will lie above the plane of the substrate.
If the polarity is correct, the platform will turn until the heading error angle is zero.
If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).
If the angle u1 is very small, O ' 1 is the Gaussian image ; and O ' 1 O ' 2 is termed the longitudinal aberration, and O ' 1R the lateral aberration of the pencils with aperture u2.
If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O ' 1 there is a circular disk of confusion of radius O ' 1R, and in a parallel plane at O ' 2 another one of radius O ' 2R2 ; between these two is situated the disk of least confusion.
If the index finger of the right hand is pointed forward, the middle finger bent inward at a right angle to it, and the thumb placed at a right angle to both, the three fingers indicate the relative directions of the x -, y -, and z-axes in a right-handed system.
If extension is executed properly the discus will be at the right angle to ride on the air current and thus be taken a farther distance.
Formulae connecting a tangential angle, the angle anchored at the ellipse's center ( called also the polar angle from the ellipse center ), and the parametric angle t < ref > If the ellipse is illustrated as a meridional one for the earth, the tangential angle is equal to geodetic latitude, the angle is the geocentric latitude, and parametric angle t is a parametric ( or reduced ) latitude of auxiliary circle </ ref > are:
If the angle between the plane and the axis is less than the angle between the line on the cone and the axis, or if the plane is parallel to the axis, then the conic is a hyperbola.
If the Earth were perfectly spherical and homogeneous, then longitude at a point would just be the angle between a vertical north-south plane through that point and the plane of the Greenwich meridian.
If the position angle of the body's Prime Meridian increases with time, the body has a direct ( or prograde ) rotation ; otherwise the rotation is said to be retrograde.
If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder which the approaching cylinder's center-of-mass cannot enter ( due to the hard-rod repulsion between the two idealized objects ).
If the lift coefficient for a wing at a specified angle of attack is known ( or estimated using a method such as thin airfoil theory ), then the lift produced for specific flow conditions can be determined using the following equation:

If and
If lines L < sub > 1 </ sub > and L < sub > 2 </ sub > make an angle θ with one another, then points P and P ′′ will make an angle around point O, the intersection of L < sub > 1 </ sub > and L < sub > 2 </ sub >.

If and between
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 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 we grasp this opportunity to build an age of productive partnership between the less fortunate nations and those that have already achieved a high state of economic advancement, we will make brighter the outlook for a world order based upon security and freedom.
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 the Af bond is linear then there are three reasonable positions for the hydrogen atoms: ( 1 ) The hydrogen atoms are centered and hence all lie on a sheet midway between the oxygen sheets ; ;
If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.
`` If there was collusion between an outside murderer and a member of the household it would be an elementary precaution to check on the door later.
`` If asked to choose between a terrible probability and a more terrible possibility, most men will choose the latter ''.
`` If Philip Toynbee is claiming that the choice lies between capitulation and the risk of nuclear war, I think he is right.
If there is a substantial difference between characters ' ranks, the conflict is generally over before the weaker character can react.
* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )
If antimatter-dominated regions of space existed, the gamma rays produced in annihilation reactions along the boundary between matter and antimatter regions would be detectable.
If a tile is placed between two hotel chains of the same size, the individual player who places the tile decides which hotel chain remains on the board and which is acquired.
If placing a tile causes three or four chains to merge, then the merger steps are handled between the largest and second-largest chain, then with the third-largest chain, and finally with the smallest chain.
If the daughter is an only child or her sisters are deceased and have no living issue, she ( or her heir ) is vested with the title ; otherwise, since a peerage cannot be shared nor divided, the dignity goes into abeyance between the sisters or their heirs, and is held by no one.
If a planet is found to rotate slower than expected, then astronomers suspect that the planet is accompanied by a satellite, because the total angular momentum is shared between the planet and its satellite in order to be conserved.
If not, the system may either be rejected or accepted on conditions previously agreed between the sponsor and the manufacturer.
If this special relationship does not exist then it not usually spoken of as " backward " compatibility but is instead just " compatible "— a consistent interface allowing interoperability between components and products that were each developed separately.
In the words of Geoffrey Crowther, then editor of The Economist, " If the economic relationships between nations are not, by one means or another, brought fairly close to balance, then there is no set of financial arrangements that can rescue the world from the impoverishing results of chaos.
If a stranger entered the circle, he had to do so to the woman's right so as not to come between her and her husband.
If rain arrives, it is usually between August and October.
If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.

If and asymptotes
If and are viewed as polynomials in with coefficients in, then the resultant of and is a polynomial in whose roots are the-coordinates of the intersection of the curves and of the common asymptotes parallel to the axis.

If and equals
If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).
# If equals are added to equals, then the wholes are equal.
# If equals are subtracted from equals, then the remainders are equal.
: If we have deprived or dispossessed any Welshmen of lands, liberties, or anything else in England or in Wales, without the lawful judgement of their equals, these are at once to be returned to them.
If the voltage to be sensed, E < sub > i </ sub >, is applied to op amp's (+) input, the result is a noninverting positive-level detector: when E < sub > i </ sub > is above V < sub > ref </ sub >, V < sub > O </ sub > equals + V < sub > sat </ sub >; when E < sub > i </ sub > is below V < sub > ref </ sub >, V < sub > O </ sub > equals − V < sub > sat </ sub >.
If E < sub > i </ sub > is applied to the inverting input, the circuit is an inverting positive-level detector: When E < sub > i </ sub > is above V < sub > ref </ sub >, V < sub > O </ sub > equals − V < sub > sat </ sub >.
If the firm decides to operate, the firm will continue to produce where marginal revenue equals marginal costs because these conditions insure not only profit maximization ( loss minimization ) but also maximum contribution.
If we want to retrieve every Invoice for a particular Order, we can query for all orders where < u > Order No </ u > in the Order relation equals the < u > Order No </ u > in OrderInvoice, and where < u > Invoice No </ u > in OrderInvoice equals the < u > Invoice No </ u > in Invoice.
If s is the length of the path traveled until time t, the speed equals the time derivative of s:
If scatterers are arranged symmetrically with a separation d, these spherical waves will be in sync ( add constructively ) only in directions where their path-length difference 2d sin θ equals an integer multiple of the wavelength λ.
If they are identical mirrors, their radius of curvature, R < sub > mirror </ sub >, equals L, where L is the distance between the mirrors.
If is rotated by radians with respect to and the x amplitude equals the y amplitude the wave is circularly polarized.
If a number equals the sum of its proper divisors, it is said to be a perfect number.
If f is a polynomial of degree less than or equal to d, then the Taylor polynomial of degree d equals f.
If it is not, then it can be completed: one can find an essentially unique complete topological ring S which contains R as a dense subring such that the given topology on R equals the subspace topology arising from S.
If you add up all the potential two-person groups, three-person groups, and so on that those members could form, the number of possible groups equals 2 < sup > n </ sup >.
If one considers the matrix as a linear transformation from R < sup > n </ sup > to R < sup > m </ sup >, then the column space of the matrix equals the image of this linear transformation.
If all elements to be sorted are distinct, the expected number of comparisons in the average case is asymptotically equivalent to, and the expected number of swaps in the average case equals.
If the trend rate of growth of money wages equals zero, then the case where U equals U * implies that gW equals expected inflation.

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