Solutions to the mathematical examination papers set for admission to the Royal military academy, Woolwich, and for the Royal military college [&c.] by D. Tierney and H. Sharratt1877 |
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Página 4
... whence easily x = 7 , ― 29 ; 2 = 4 , 49 . - 7. Form the equation whose roots are 5 + 6 ( -1 ) . If x2- px + q = 0 and x2 — p‚x + q , = 0 have a common - root , determine it ; and in that case shew that - - - ( q — q1 ) 2 = ( p − p1 ) ...
... whence easily x = 7 , ― 29 ; 2 = 4 , 49 . - 7. Form the equation whose roots are 5 + 6 ( -1 ) . If x2- px + q = 0 and x2 — p‚x + q , = 0 have a common - root , determine it ; and in that case shew that - - - ( q — q1 ) 2 = ( p − p1 ) ...
Página 48
... + 2c 3 . a Since ay = x2 + bx + c2 , dy_2x + b = dx a Now , because the tangent passes through the origin , we must have y_dy X dx ; = therefore Whence we find and x2 + bx + c2 48 PURE MATHEMATICS . Mathematics PAGE 8.
... + 2c 3 . a Since ay = x2 + bx + c2 , dy_2x + b = dx a Now , because the tangent passes through the origin , we must have y_dy X dx ; = therefore Whence we find and x2 + bx + c2 48 PURE MATHEMATICS . Mathematics PAGE 8.
Página 49
D. Tierney. therefore Whence we find and x2 + bx + c2 2x + b ах a x = ± c ; ( b + 2c y = ± α b + 2c = a therefore y Xx which are the equations to the two tangents through the origin . 10. If the logarithmic curve y = ae has contact of ...
D. Tierney. therefore Whence we find and x2 + bx + c2 2x + b ах a x = ± c ; ( b + 2c y = ± α b + 2c = a therefore y Xx which are the equations to the two tangents through the origin . 10. If the logarithmic curve y = ae has contact of ...
Página 74
... whence x2 — yz = 6 ( x − 1 ) , - x2 - 1 = - - 6 ( x − 1 ) , 5 + √ ( 21 ) x = or 1 ; 2 and from the symmetry of the equations with respect to x , y , and z , we see that the values of y and z will be the same as those of x , or 5 ...
... whence x2 — yz = 6 ( x − 1 ) , - x2 - 1 = - - 6 ( x − 1 ) , 5 + √ ( 21 ) x = or 1 ; 2 and from the symmetry of the equations with respect to x , y , and z , we see that the values of y and z will be the same as those of x , or 5 ...
Página 75
... whence 3.6N = 5.Nr ; x = 4 , 4 and amount of fee after reduction is therefore = 4d . 8. If a be positive and ( 62 — 4ac ) negative , shew that ax2 + bx + c will always be positive for all real values of x . If ( a ) , ( B ) are the ...
... whence 3.6N = 5.Nr ; x = 4 , 4 and amount of fee after reduction is therefore = 4d . 8. If a be positive and ( 62 — 4ac ) negative , shew that ax2 + bx + c will always be positive for all real values of x . If ( a ) , ( B ) are the ...
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Solutions to the Mathematical Examination Papers Set for Admission to the ... D. Tierney,Handell Sharratt Sin vista previa disponible - 2016 |
Solutions To The Mathematical Examination Papers Set For Admission To The ... D. Tierney,Handell Sharratt Sin vista previa disponible - 2023 |
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Pasajes populares
Página 55 - If two triangles have two sides of the one equal to two sides of the...
Página 71 - 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.
Página 11 - ... shall be equal to three given straight lines, but any two whatever of these must be greater than the third.
Página 12 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 13 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Página 15 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 13 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Página 62 - In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle.
Página 13 - PROP. X. THEOR. IF a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Página 70 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.