Military examinations. Mathematical examination papers, set for entrance to R.M.A., Woolwich, with answers, by W.F. Austin |
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Αποτελέσματα 1 - 5 από τα 27.
Σελίδα 4
... roots of a quadratic equation ? If ( a ) and ( 6 ) are the roots of the equation x2 − px + q roots of x2 and ( q ) . - - = 0 , and ( a ) ( B ) the Px + Q = 0 ; express P and Q in terms of ( p ) 10. Two workmen ( A ) and ( B ) ( 4 )
... roots of a quadratic equation ? If ( a ) and ( 6 ) are the roots of the equation x2 − px + q roots of x2 and ( q ) . - - = 0 , and ( a ) ( B ) the Px + Q = 0 ; express P and Q in terms of ( p ) 10. Two workmen ( A ) and ( B ) ( 4 )
Σελίδα 12
... roots . 3. If f ( x ) = 0 have equal roots , prove that the equations f ( x ) = 0 and f ' ( x ) = 0 must have a root in common ; Hence prove that the equation -1 + n . ( n - 2-2 - 1 ) . x2 - 2 + & c . + n . ( n − 1 ) ..... 2.1 = 0 ...
... roots . 3. If f ( x ) = 0 have equal roots , prove that the equations f ( x ) = 0 and f ' ( x ) = 0 must have a root in common ; Hence prove that the equation -1 + n . ( n - 2-2 - 1 ) . x2 - 2 + & c . + n . ( n − 1 ) ..... 2.1 = 0 ...
Σελίδα 20
... roots are 561 . = O and x2 - - P1x + q1 = 0 have a common If x2 - px + 9 : root , determine it , and in that case show that ( qq . ) 2 = ( p— p1 ) ( P1q — pq . ) . - · 8. A bill of £ 63 . 58. was paid in sovereigns and half crowns , and ...
... roots are 561 . = O and x2 - - P1x + q1 = 0 have a common If x2 - px + 9 : root , determine it , and in that case show that ( qq . ) 2 = ( p— p1 ) ( P1q — pq . ) . - · 8. A bill of £ 63 . 58. was paid in sovereigns and half crowns , and ...
Σελίδα 28
... roots of contrary signs . 2. Transform the equation x3 3 ceed by 2 - 3 - = 4 4 O into one whose roots ex- the corresponding roots of the given equation . 3. Prove that in any equation , complete or incomplete , the number of positive roots ...
... roots of contrary signs . 2. Transform the equation x3 3 ceed by 2 - 3 - = 4 4 O into one whose roots ex- the corresponding roots of the given equation . 3. Prove that in any equation , complete or incomplete , the number of positive roots ...
Σελίδα 29
... roots of the equation f ( x ) = 0 are all real and unequal , show how to integrate the expression 9x2 + 12x + 6 $ ( x ) dx . f ( x ) Integrate dx . 2x3 + 5x2 - X - 6 14. Find the length of the arc of a parabola from the vertex to the ...
... roots of the equation f ( x ) = 0 are all real and unequal , show how to integrate the expression 9x2 + 12x + 6 $ ( x ) dx . f ( x ) Integrate dx . 2x3 + 5x2 - X - 6 14. Find the length of the arc of a parabola from the vertex to the ...
Άλλες εκδόσεις - Προβολή όλων
Military Examinations. Mathematical Examination Papers, Set for Entrance to ... Woolwich Roy Military Acad Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD acceleration ALGEBRA arithmetic axes axis ball base binomial theorem bisected body centre of gravity chord circular measure cone continued fraction curve Define described diameter differential coefficient distance drawn elastic ellipse equiangular equilateral equilibrium feet per second Find an expression Find the equation Find the number Find the sum find the value find the velocity forces acting fraction geometrical given straight line harmonic mean horizontal plane hyperbola inclined plane inscribed intersect least common multiple length magnitude middle points number of combinations parabola parallel parallelogram particle pendulum perpendicular positive integer produced pulley PURE MATHEMATICS quadrilateral radius ratio rectangle contained rectangular right angles roots segments sliding smooth solid angle Solve the equation sphere square STATICS string tan-¹ tangent theorem things taken triangle ABC TRIGONOMETRY vertex weight
Δημοφιλή αποσπάσματα
Σελίδα 34 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle. Let...
Σελίδα 146 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 99 - IF a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Σελίδα 34 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 82 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, is equal to the square of the line which touches it.
Σελίδα 50 - 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 2 - 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 114 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...
Σελίδα 18 - If two straight lines cut one another within a circle, the rectangle contained by the segments of one of them, is equal to the rectangle contained by the segments of the other.
Σελίδα 130 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.