Mathematical Exercises ...1867 |
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Page 12
... parallel sides a , b . Area of trapezium inscribed in circle = ✓ { ( s — a ) ( s — b ) ( s — c ) ( s — d ) } , s = na2 4 s = ( a + b + c + d ) . 180 ° Area of regular polygon = X cot n . ; n = number of sides each equal to a . Area of ...
... parallel sides a , b . Area of trapezium inscribed in circle = ✓ { ( s — a ) ( s — b ) ( s — c ) ( s — d ) } , s = na2 4 s = ( a + b + c + d ) . 180 ° Area of regular polygon = X cot n . ; n = number of sides each equal to a . Area of ...
Page 116
... parallel to the base , show that the section is a square . 9. In any plane triangle , if a and b are the sides opposite to the angles A and B , prove that— α ( 1 cos A ) ( 1 + cos A -cos B ) ( 1 + cOS B ) 10. A balloon ascends uniformly ...
... parallel to the base , show that the section is a square . 9. In any plane triangle , if a and b are the sides opposite to the angles A and B , prove that— α ( 1 cos A ) ( 1 + cos A -cos B ) ( 1 + cOS B ) 10. A balloon ascends uniformly ...
Page 117
... parallel ; these sides are 10 and 12 ft . respectively ; the perpendicular dis- tance between them is 4 feet . Find the area of the figure . 7. If two straight lines , AEB , CED , in a circle intersect in E , the angles subtended by AC ...
... parallel ; these sides are 10 and 12 ft . respectively ; the perpendicular dis- tance between them is 4 feet . Find the area of the figure . 7. If two straight lines , AEB , CED , in a circle intersect in E , the angles subtended by AC ...
Page 125
... another . 12. a , b , c , d , E are the angles of a regular pentagon taken in order ; join CA , CE ; then , ( 1 ) The angle BCD is trisected . ( 2 ) CA is parallel to DE . 13. The base and altitude of a right - angled PAPERS . 125.
... another . 12. a , b , c , d , E are the angles of a regular pentagon taken in order ; join CA , CE ; then , ( 1 ) The angle BCD is trisected . ( 2 ) CA is parallel to DE . 13. The base and altitude of a right - angled PAPERS . 125.
Page 129
... parallel to the tangent at P. 12. The sum of the alternate angles of any hexagon in- scribed in a circle is equal to four right angles . 13. Solve the equation sin 5x = 16 sin 3x . XCII . 1. What length of matting & yd . wide will be ...
... parallel to the tangent at P. 12. The sum of the alternate angles of any hexagon in- scribed in a circle is equal to four right angles . 13. Solve the equation sin 5x = 16 sin 3x . XCII . 1. What length of matting & yd . wide will be ...
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acres angle axis ball base binomial theorem bisected body CALC cent centre of gravity circle coefficient of friction compound interest cube cubic curve determine diameter Divide dwts ellipse equal equilibrium Express Extract the square feet Find the area Find the centre Find the distance Find the equation find the height Find the number Find the value fluid forces acting given horizontal plane inches inclined plane inscribed intersect latus rectum length logarithms lowest terms Multiply parabola parallel particle perpendicular plane triangle pressure Prove pulleys radius rectangular recurring decimal Reduce right-angled sides simple interest Simplify sin² sine smooth Solve the equations square root straight line string surface tangent tons tower TRIG velocity vertex vertical vulgar fractions weight yards
Popular passages
Page 12 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 113 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Page 283 - Find the distance of the centre of gravity of the remainder from the intersection of the diagonals.
Page 378 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 225 - A body is projected with a velocity v in a direction making an angle a with the horizon...
Page 229 - Hence the conditions of equilibrium of any system of forces, acting in one plane upon a rigid body, may be obtained as follows ; I.
Page 202 - A manufacturer having a capital of £5000 on which he can realise by hand labour 10 per cent. profit, buys a machine for £1000, by which his profit on the remainder of his capital is raised to 20 per cent. This machine lasts 5 years. Of how...
Page 88 - A number is divisible by 9 if the sum of its digits is divisible by 9.
Page 295 - Assuming the parallelogram of forces, prove that the algebraic sum of the moments of two forces about a point in the space between their directions is the same as the moment of their resultant.
Page 169 - One company guarantees to pay 5 per cent. on shares of £100 each; another guarantees at the rate of 4f per cent.