Examination Papers for Science Schools and Classes |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 50
... hyperbola ? If any straight line Qq perpendicular to either axis of a hyperbola meet the asymptotes in Q , q , and the curve at P , prove that the rectangle QP . Pq is constant . R , R ' are points on an asymptote of a hyperbola , RQ ...
... hyperbola ? If any straight line Qq perpendicular to either axis of a hyperbola meet the asymptotes in Q , q , and the curve at P , prove that the rectangle QP . Pq is constant . R , R ' are points on an asymptote of a hyperbola , RQ ...
Σελίδα 51
... hyperbola . ( 40. ) 28. Show that the straight line x + ny + an2 = 0 touches the parabola y2 - 4 ax = 0 , and find the point of contact . Tangents are drawn to a parabola from a given ex- ternal point . Show that the line joining the ...
... hyperbola . ( 40. ) 28. Show that the straight line x + ny + an2 = 0 touches the parabola y2 - 4 ax = 0 , and find the point of contact . Tangents are drawn to a parabola from a given ex- ternal point . Show that the line joining the ...
Σελίδα 52
... hyperbola , and give the length of its latus - rectum . ( 40. ) 30. Find the constant relation existing among the direction- cosines of a line . If two of the direction - cosines of a line through the origin are known , show , by a ...
... hyperbola , and give the length of its latus - rectum . ( 40. ) 30. Find the constant relation existing among the direction- cosines of a line . If two of the direction - cosines of a line through the origin are known , show , by a ...
Σελίδα 162
... hyperbola , let the steam be dry before entering the cylinder at 120 lbs . per square inch absolute pressure , and temperature 348 ° F. , and let it expand down to 30 lbs . per square inch , and tem- perature 250 ° F. Find the heat ...
... hyperbola , let the steam be dry before entering the cylinder at 120 lbs . per square inch absolute pressure , and temperature 348 ° F. , and let it expand down to 30 lbs . per square inch , and tem- perature 250 ° F. Find the heat ...
Σελίδα 52
... hyperbola , and show that it consists of two infinite branches . Prove that the normal at any point of the curve bisects the exterior angle between the focal distances . Tangents to a hyperbola at P and Q meet on one directrix , and cut ...
... hyperbola , and show that it consists of two infinite branches . Prove that the normal at any point of the curve bisects the exterior angle between the focal distances . Tangents to a hyperbola at P and Q meet on one directrix , and cut ...
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Δημοφιλή αποσπάσματα
Σελίδα 34 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 36 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 34 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 126 - GENERAL INSTRUCTIONS. If the rules are not attended to, the paper will be cancelled. You may take the Elementary or the Advanced or the Honours paper, but you must confine yourself to one of them.
Σελίδα 46 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 36 - FG; then, upon the same base EF, and upon the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity: But this is impossible (i.
Σελίδα 36 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 197 - The value attached to each question is shown in brackets after the question. But a full and correct answer to an easy question will in all cases secure a larger number of marks than an incomplete or inexact answer to a more difficult one.
Σελίδα 37 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Σελίδα 57 - Put the number of the question before your answer. You are to confine your answers strictly to the questions proposed. Your name is not given to the Examiner, and you are forbidden to write to him about your answers.