FUNDAMENTAL CONCEPTS, FORMULA

Transcription

1 . Chge the subject of ech of the followig formule to the letter give gist them : As. (i) E (i) I ; r R + r (iii) m 4 ; b b + c (v) T r T πd ; d mv mu (vii) F ; u t I FUNDAMENTAL CONCEPTS, FORMULA AND EXPONENTS ; u f v u S d ; d (iv) + ( ) + b (vi) ; b (viii) π( ) E R + r I(R + r) E V R r h ; r IR + Ir E Ir E IR r E I IR f v u u v f f v u vf u vf f v Mth Clss VIII Questio Bk

2 (iii) m 4 b + c m 6 b + c Squrig both sides m (b + c) 6 m b + m c 6 m b 6 m c 6 m c b m (iv) S + ( ) d ( ) (v) S + ( ) d ( ) T T r πd S d r T π d T + d S S d d S ( ) T rt T r T π d πd T d π r T d πr T (vi) + b b + b Squrig both sides b b + b b + b ( ) b( + ) ( ) b( + ) Mth Clss VIII Questio Bk

3 b( + ) mv mu (vii) F Ft mv mu t mu mv Ft (viii) V π(r r ) h V R r πh V r R π h u mv Ft m V r R πh r πr h V πh. A dotio bo cotis cois of Rs ech, y cois of rupee ech, z cois of 50 pise ech d t cois of pise 5 ech. Fid the totl moey M (i rupees). As. Number of cois of Rs, the mout Rs Rs Number of cois of Re y, the mout Rs y Rs y Number of cois of 50 pise i.e. Rs Rs z Rs z z, the mout Number of cois of 5 pise i.e. Rs 5 t, the mout 00 Rs t 5 00 Rs t 4 Mth Clss VIII Questio Bk

4 Hece, totl moey M + y + z + t. 4. A m ers Rs 60 per dy d wom ers Rs 55 per dy. Fid the mothly erig of me d y wome, ssumig tht there re 6 workig dys i moth. As. Erig by m per dy Rs 60 Erig by me per dy Rs 60 Rs 60 Erig by me per moth Rs 60 6 Erig by wom per dy Rs 55 Erig by y wome per dy Rs 55 y Rs 55y Erig by y wome per moth Rs 55y 6 Hece, mothly erig by me d y wome E Rs Rs 55y 6 E Rs 6 (60 +55y) Where E is mothly erig i rupees. 4. I clss of 45 studets, the verge mrks of studets re 8 d the verge mrks of the remiig studets re 7. Fid formul for the verge mrks of ll the studets of the clss. As. Averge mrks of studets 8. Totl mrks of studets 8 Number of totl studets i clss 45 Remiig studets (45 ) Averge mrks of (45 ) studets 7 Totl mrks of (45 )studets 7 (45 ) Thus, totl mrks of 45 studets 8 + 7(45 ) Hece, frmig the formul for verge of 45 studets is PRT 5. If A P +, mke T the subject of the formul. Hece, fid T 00 whe A 575, P 500 d R 6. Mth Clss VIII 4 Questio Bk

5 As. P R T A P + (Give) 00 A P P R T P R T A P 00 P R T 00(A P) ( A P) T P R Substitutig the vlue of A 575, P 500 d R 6, we get ( ) T l 6. I the formul T π, mrke g s the subject of the formul. g Fid g whe 44 π, l 0 d T 7 49 l As. l T π π T g g l T g π l g T π g 4π 4π l g 4 l T T Substitutig the vlue of π, l 0 d 7 g T. We hve 49 Mth Clss VIII 5 Questio Bk

6 S d, mke d s the subject of the formul. Fid d whe S 55, 4 d 5 7. I the formul + ( ) S d S [ + ( )d] As. + ( ) As. S ( ) d + ( ) Mth Clss VIII 6 Questio Bk S d S S d d ( ) Substitutig the vlue of S 55, 4 d 5, we hve d ( ) d p 8. Mke s the subject of the formul y. + p Fid, whe y 0.5 d p p y + p y( + p) p y + py p y + p py y + p ( py) ( py) y + p Substitutig the vlue of y 0.5 d p, we hve y + p py

7 9. Mke s the subject of the formul l + ( ) d. Fid whe l 9, 5 d d. As. l + ( ) d As. l l ( ) d d l l l + d + d d d Substitutig the vlue of l 9, 5 d d If +, Fid the u i terms of v d f. Fid u, whe v f u v d f 4. + f u v u f v v f fv u. u fv v f Substitutig the vlue of v d f 4, we hve. Mke b, the subject i As. 4 4 u Squrig both sides b + b b + b. Mth Clss VIII 7 Questio Bk

8 b + b Applyig compoedo dividedo property + b + + b b b b + b, b + b + ( ) b ( + ) (By Ivertedo). Mke s the subject of formul. + y y Fid whe y. As. + y y y y y ( y ) ( ) y y y y ( ). y (y ) Substitutig the vlue of y, we hve ( ) 56. Fid the vlue of : (i) (7 5 ) (iii) 5 7 (iv) ( ) ( + ) Mth Clss VIII 8 Questio Bk

9 6 (v) (vi) (vii) (i) (viii) As. (i) (7 5 ) (7 5 ) [ b + b ] 7 (7) [ b b ] (7) [ 0 ] (iii) () ( ) () + () 4 8. (iv) ( ) ( 0 + ) Mth Clss VIII 9 Questio Bk

10 (v) (vi) (vii) ( ) ( 6) ( ) ( ) ( ) ( ) ( 8 9) Mth Clss VIII 0 Questio Bk ( 4) ( ) ( 5) 0 ( 6) ( 6) ( 5 4 ) ( ) ( 5)

11 (viii) ( ) 6 (5) ( ) ( ) ( ) ( ) ( ) ( ) (i) 5+ ( 6) + ( ) Simplify the followig : (i) 5 / Mth Clss VIII Questio Bk

12 As. (i) / / / / 5/ / ( 9 9) () 5 (9) / () 5 (9) ( ) 9 4 / / / (4) ( ) / 0 6 / / / / [ 0 ] Mth Clss VIII Questio Bk

13 5. Simplify : 4 6 ( ) + (i) ( ) ( ) ( ) b b b + c b c c + c y z As. (i) ( ) ( ) ( ) 5 y + b b b+ c b c c+ c ( + b)( b) ( b+ c)( b c) ( c+ )( c ) b b c c y z b + b c + c ( y z ) y / y z y. y +. z yz 4 b b c c b c 6. Show tht :.. b c y 4. y. z y Mth Clss VIII Questio Bk

14 b b c c b c As. LHS.. b c + b b b+ c b c c+ c ( ) ( ) ( ) ( + b)( b) ( b+ c)( b c) ( c+ )( c ) b b c c b + b c + c 0 RHS. 7. Evlute: (i) As. (i) ( ) ( ) (+ )( ) (4 ) + ( ) + (+ )( ) (4 ) + ( ) (+ )( ) (4 ) + ( ) ( + 6) Mth Clss VIII 4 Questio Bk Prove tht : (m + ) (m + ) (m) As. LHS (m + ) (m + )

15 9. Show tht : + m +. ( m) m + m m + m m RHS l m m l l m m l m l As. LHS l m 0. Show tht : m l l m l m [ ] [ ] [ ] ( m ) l ( l) m ( l m) ml l m lm l m ml l+ m lm + l m RHS. m + + l l + m m l m+ + l l+ m As. LHS m l ( ) m l + l + m m + + l m l m + + l m+ + l (m+ + l) m+ + l m l) 0 RHS Mth Clss VIII 5 Questio Bk 0

16 Hece, Proved.. Show tht As. LHS ( ) ( ) ( + b+ b b b + bc+ c c c + c+ ) b c ( ) ( ) ( + b+ b b b + bc+ c c c + c+ ) b c + b+ b b + bc+ c c + c+ ( b ) ( b c ) ( c ). Simplify : ( b)( + b+ b ) ( b c)( b + bc+ c ) b b c c ( c )( c + c+ ) b + b c + c (i) y z z y ( b) ( bc) ( c) 0 RHS + (+ )( + ). + (+ ) ( ). y z z y As. (i) ( b) ( bc) ( c) + (+ )( + ) + (+ ) ( ) y z b y z. b z. c z c y. y y z + y.b y z + z. c z + z.b y. c z y Mth Clss VIII 6 Questio Bk

17 ( ) Fid the vlue of whe : (i) As. (i) ( + 7+ ) ( ) 5 5 ( + 4) + 5 ( + ) 5 ( + 4) Thus, Mth Clss VIII 7 Questio Bk

18 5 5 Hece, 5 4 ( + ) ( )( )( ) 5 5 8( + ) 6( ) Hece, Mth Clss VIII 8 Questio Bk