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Page "Kinematics" ¶ 74

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Then and angle

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

Then we imagine the rays are parallel ( and given by two angles ), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point.

Then the changes of angle in seconds of arc per year are:

Then is already an angle variable, and the canonical momentum conjugate is L, the angular momentum.

Then the spinner overlaps a handful of fiber with the leader, holding both gently together with the left hand, and begins to slowly turn the drive wheel clockwise with the right hand, while simultaneously walking backward and drawing the fiber in the left hand away from the spindle at an angle.

In particular, let p define the coordinates of points in a reference frame M coincident with a fixed frame F. Then, when the origin of M is displaced by the translation vector d relative to the origin of F and rotated by the angle φ relative to the x-axis of F, the new coordinates in F of points in M are given by

Then, as it travelled, a mechanism possibly containing differential gears used the different rotational speeds of the two wheels to turn the pointer relative to the body of the chariot by the angle of turns made ( subject to available mechanical accuracy ), keeping the pointer aiming in its original direction, to the south.

Then measure the angle between them by counting grid lines along that meridian.

Then the angle of view is given by:

Then the degree of mapping is times the solid angle of the image S of with respect to the interior point of, O.

Then, a long, thick piece of kindling is driven into the ground at an angle, so that it overhangs the tinder pile.

Then angle APB is the arithmetic mean of the angles AOB and COD.

( 2. 2 ), Then, the lens passes-from the object plane over onto the image plane-only that portion of the radiated spherical wave which lies inside the edge angle of the lens.

Then, on command, the platoons of the columns turned left at Lobetinz, the whole Prussian army lay in line of battle at nearly a right angle to the left flank of the Austrian position.

Then the magnitude of the force is proportional to the angle of the bar.

Then cross out the 90 ° corner angle and replace all angles non-adjacent to it by their complement to 90 ° ( i. e. replace, say, B by 90 ° − B ).

Then Napier's Rules hold that the sine of the middle angle is equal to:

Then in the UEFA Champions League group stages he scored a goal from an extremely tight angle against Barcelona, at the Camp Nou, the match ended 2 – 2.

Then in the plane α ′ there is one and only one half-ray k ′ such that the angle ( h, k ), or ( k, h ), is congruent to the angle ( h ′, k ′) and at the same time all interior points of the angle ( h ′, k ′) lie upon the given side of a ′.

Then the vertex of this angle is X and traces out the pedal curve.

Then " Quickly, you find an angle from which everything appears to fit perfectly and take a snapshot, at a fast shutter speed before something else bulges out too noticeably.

Then the angle of the rotation is the angle between and.

Then and θ

: Then the estimated value of the weight θ 1 is

Then for a specific value x of X, the function L ( θ | x )

Then Y = u ( X 1 , X 2 , ..., X n ) is a sufficient statistic for θ if and only if, for some function H,

Then one faces the problem of expression sin ( θ ) and cos ( θ ) as functions of x.

Then the estimates of κ and θ are

Then P is a principal H-bundle on M, and the compatibility condition on the connection forms θ U implies that they lift to a g-valued 1-form η defined on P ( see below ).

Then the formula above would allow us to assess the likelihood of different values of θ.

Then E i is a Maurer – Cartan frame, and θ i is a Maurer – Cartan coframe.

Then, for a given set of parameters θ, the probability of attaining this particular set of data is given by

Then the endpoints are also given by re i θ ± ce i ψ .

Then and around

Then she turned the station wagon around and headed it back down the hill, with the village as her ostensible destination.

Then she took iced lemonade to Marsh's young aide where he sat in the cool of the big trees around the flower garden.

Then they had always been romping around him on these walks, yelping with delight, dashing off into the bushes on fruitless hunting expeditions, returning to jump up on him triumphantly with muddy paws.

Then, one after another, the villagers tied the waiting cotton strings around our wrists.

Then he put a rag around the dressing to keep it in place.

Then he backed out and swung around to the front drive.

Then it is to be plated entirely with gold, and a crown or molding of gold is to be put around it.

Then, following the battle, the Athenian army marched the 40 ( 25 miles ) or so kilometers back to Athens at a very high pace ( considering the quantity of armour, and the fatigue after the battle ), in order to head off the Persian force sailing around Cape Sounion.

Then he laughed, pulled a necklace of Spanish gold from around his neck and said " Our voyage is made, lads!

Then, ~ 150, 000 years later ( i. e. around 50, 000 years ago ), sub-groups of this population began to expand our species ' range to regions outside of, and ( later ) within, this continent ( Tishkoff, 1996 ).

Then he drank some hot chocolate and danced around the room, singing about his love for ice skating.

Then, around 1460 Mai Ali Dunamami defeated his rivals and began the consolidation of Bornu.

Then, spinning of the wheel ( around the wheelhub ) is added.

Then Patriot defensive coordinator ( and now head coach ) Bill Belichick is quoted as saying Parcells ' plans to leave for the Jets were a distraction, " Yeah, I'd say it was a little bit of a distraction all the way around.

Then the sum total of all the maintenance actions are bundled into maintenance intervals so that maintenance is not occurring around the clock, but rather, at regular intervals.

Then, at around 1960 a critical resurgence in interest occurred which has resulted in making general relativity central to physics and astronomy.

Then, completely confident in his own safety, the narrator comments on the sturdiness of the building and raps upon the wall he had built around his wife's body.

" Then he pointed to each person around him: " And so are you, and you, and you.

Then Congress never gets around to the task of reorganizing and renumbering all the sections in a title, which forces Congressional drafters to resort to awkward methods to shoehorn new laws into the existing section numbering of a title.

Then the groom marks the bride's forehead with vermilion ( sindoor ) and puts a gold necklace ( mangalsutra ) around her neck.

Then wrap the outer loop around the standing part and pull it through the hole of the inner loop.

Then she shows him a long, narrow case, which she tells him holds her only sacred treasure, but she cannot open it, because there are too many people around.

Then in 1918 Lytton Strachey published his critique of Victorianism in the shape of four ironic biographies in Eminent Victorians, which added to the arguments around Bloomsbury that continue to this day, and " brought him the triumph he had always longed for ...

Then wrap the free end of the rope around both spars about seven or eight times.

Then, wrap the free end of the rope around both poles parallel, and below, the clove hitch about seven or eight times.

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