A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone1845 |
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Seite 30
... determine the great- est and least . - 292. If ( x + y ) 3 — ( xy ) be greater or less than 1 , show that 4xy - 3 ( x2 — y2 ) 3 is greater or less than I respectively . 293. If m be greater than 3 , prove that 3m > m > m + 1 . 294 ...
... determine the great- est and least . - 292. If ( x + y ) 3 — ( xy ) be greater or less than 1 , show that 4xy - 3 ( x2 — y2 ) 3 is greater or less than I respectively . 293. If m be greater than 3 , prove that 3m > m > m + 1 . 294 ...
Seite 45
... Determine the proportion of gold to silver in each mix- ture ; the values of equal weights of gold and silver being as 13 to 1 . RATIO , PROPORTION , AND VARIATION . 617. Prove that a : b is a greater ratio than ax : bx + h ; and a less ...
... Determine the proportion of gold to silver in each mix- ture ; the values of equal weights of gold and silver being as 13 to 1 . RATIO , PROPORTION , AND VARIATION . 617. Prove that a : b is a greater ratio than ax : bx + h ; and a less ...
Seite 48
... Determine the relation which must exist between a , b and c , that they may be respectively the pth , qth and rth terms of an arithmetical series . 659. If P and Q denote the pth and qth terms respectively of an arithmetic series ; find ...
... Determine the relation which must exist between a , b and c , that they may be respectively the pth , qth and rth terms of an arithmetical series . 659. If P and Q denote the pth and qth terms respectively of an arithmetic series ; find ...
Seite 51
... determine which is greater , a2 + b2 + c2 or ( a − b + c ) 2 . 3.5.7 714. If S , = 1 + = + = + + .. to infinity , and 2 4 8 3,5 7 + + .. to infinity , 2 4 8 find the ratio S1 : S2 . 715. If a , b , c , d are in geometrical progression ...
... determine which is greater , a2 + b2 + c2 or ( a − b + c ) 2 . 3.5.7 714. If S , = 1 + = + = + + .. to infinity , and 2 4 8 3,5 7 + + .. to infinity , 2 4 8 find the ratio S1 : S2 . 715. If a , b , c , d are in geometrical progression ...
Seite 52
... determine which is greater , 262 or a2 + c2 . 731. Having given the mth and nth terms of an harmonical pro- gression , viz . M and N respectively , determine the ( m + n ) th term . 732. There are four numbers of which the first three ...
... determine which is greater , 262 or a2 + c2 . 731. Having given the mth and nth terms of an harmonical pro- gression , viz . M and N respectively , determine the ( m + n ) th term . 732. There are four numbers of which the first three ...
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A Collection of Examples in Pure and Mixed Mathematics, with Hints and ... Alfred Wrigley Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
angle of elevation arithmetic means arithmetic series arithmetical progression axes axis base bisecting Cape cent centre of gravity chord circumference coefficient cone conic section cos² curve described diameter direction Divide ellipse equal equilibrium Euclid expansion extremity find the angle Find the area Find the distance Find the equation find the inclination find the locus Find the ratio Find the value Formulæ fraction frustum geometrical progression given circle given point given straight line harmonic means horizontal plane hyperbola hypothenuse inches inclined plane infinity inscribed intersect latus rectum length lines be drawn middle point miles Multiply number of balls number of combinations parabola parallel pendulum perpendicular prob prove pulley radii radius respectively rest right angles right-angled triangle segments sides sin² Sum the series take moments tangent uniform beam vertex vertical angle weight yards
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Seite 69 - 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.
Seite 44 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.
Seite 45 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished 4 times as many men as there were companies in the regiment ; but these being found insufficient, each company furnished three more men, when their number was found to be increased in the proportion of 17 to 16.
Seite 67 - 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,. shall be equal to the square of the line which touches it.
Seite 93 - Wanting to know my distance from an inaccessible object 0, on the other side of a river; and having no instrument for taking angles, but only a chain or cord for measuring distances; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to...
Seite 48 - A and B set out to meet each other. A went 3 miles the first day, 5 the second, 7 the third, and so on. B went 4 miles the first day, 6 the second, 8 the third, and so on. In how many days did they meet?
Seite 89 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Seite 49 - Required the number. 9. A person employed 3 workmen, whose daily wages were in arithmetical progression. The number of days they worked was equal to the number of shillings that the second received per day. The whole amount of their wages was 7 guineas, and the best workman received 28 shillings more than the worst.
Seite 44 - A detachment of an army was marching in regular column, with 5 men more in depth than in front ; but upon the enemy coming in sight, the front was increased by 845 men ; and by this movement the detachment was drawn up in 5 lines. Required the number of men.
Seite 98 - If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from, the point of their intersection lines be drawn perpendicular to the sides which contain the opposite angle...