5th grade math written practice math lesson 16

Ex.16. Evaluate * I. f j 6X + $ (I.S.C.) 2. (I.S.C.) y]6 + x - 2x ' Sol. 1. Let 6x + 5 = A (6 + x - 2x 2 ) + B - A (1 - 4x) + B Equating coeffts. of x and constants, we obt..

Prove that 2 2 2 xyz y 2 ** ^-.yXK-zHz-xXxy+yz + zx). (NMOC1994) x, y 2 2 2 xyz Sol. Let A = yz zx xy xyz. 3 3 3 i x y z = - xyz xyz xyz , multiplying C,, C 2 and C 3 by x, y and z respectively. xyz 2 2 2 xyz ..

.1 2 -3 The d.c's of the normal are 2 3 1 The d.c.'s of the line are vl4 V14 vl4 Let 6 be the angle between the normal and the given line. Then cos 9 = 1 2.2 3 3 1 "Vm V^~7i4'VT7 (Vz+^+'W 2,6 3 5 0 -1 / 5 \ . = .14 14 ~ 14 = 14 0=COS lu)- 90 - 0 is the angle ..

= 0, x = n and the x-axis. . < . \ [Hint " lJ * ' 5 - H Jk ' 3ft \ . 6 4 1 3 .2 3 4 . 6 . 71 1 V3 -J_ I n 1..

= 5x intersect at the point P (a, p) where a > 0. (a) Calculate the value of a and p. (b) Calculate the area bounded by the curve and the line segment OP, where O is the origin. (I.S.C.) 21. (0 Find the area enclosed by the curve y = - x 2 and the straight line x + y + 2 = 0.' (it) If ..

y 2 = 12x and its latus rectum. [Hint Eqn. of latus rectum is x = 3] . 3. Draw the rough sketch of the curve y = V3x + 4 and find the area under the curve, above the x-axis and between x = 0 and x = 4. 4. Sketch the graph y = I jc + 11. Evaluate J I x + 11 dx. ..

1. Find the magnitude and direction of the resultant of two forces of magnitudes V2N and 3 N, if they are inclined to each other at an angle of 45. [Ans. 4.123 N making an angle of 3058' with V2~ N] 2. The resultant of two forces of magnitudes 3 N and 4 N has a ma..

I [x ] dx, where [xj is the greatest integer < x, is given by '"' * v (a) 72-1 (6) \- yfl (c) . ( d ) 2(72-1) (v/7) The area bounded' by the curves y = x 4 and y = 2 | x | is equal to (a) 4/3 (b) 8/3 " ' '(c)' 2/3 (d) 1/3 (v7) If A is the area between the curv..

Introduction In mathematics, especially in elementary arithmetic, division is the arithmetic operation one among 4 arithmetic operations and it is the inverse of multiplication. a divided by b equals c, written: a/b=c Its dented by () or / Where: a is called ..

[1 x - 31] dx is : (a) 1 (.b) 2 (c) 4 (d) 8 (REE (Q) 1999) f > dx (Hi) --:-= < J 1 - cos x - sin x . (a) log 1 + cot ^ + c (b) log 1 - tan ~ + c (c) log I 1 - cot ^ + c (d) log 1 + tan - + c (EAMCET 2001) 1 I 2 ^ 2 5. Evaluate: ->':>._. t x/2 _ ~ x/2 ..