Question

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Oblicz.

A

a) 5⁻¹

b) (2¾)⁻¹

c) (-4,8)⁻¹

B

a) (-3)⁻⁴

b) (1⅖)⁻²

c) (2,5)⁻³

C

a) (-5)⁻⁴ : (-5)² · ((-5)⁻²)⁻³

b) (a³ ·a⁴ ·a ⁻⁵)⁻² : ( a⁷ : a⁹ · a ⁻⁴)⁻⁵

Oblicz wysokość trójkąta równobocznego jeśli a wynosi : √3, √6, √9, √10 , √12, √15

Answer 1

A 

 

a) 5⁻¹=(1/5)¹=1/5

b) (2¾)⁻¹=(11/4)⁻¹=(4/11)¹=4/11

c) (-4,8)⁻¹=(-24/5)⁻¹=(-5/24)¹=-5/24

 

B

 

a) (-3)⁻⁴=(-1/3)⁴=1/81

b) (1⅖)⁻²=(7/5)⁻²=(5/7)²=25/49

c) (2,5)⁻³=(5/2)⁻³=(2/5)³=8/125

 

C

 

a) (-5)⁻⁴ : (-5)² · ((-5)⁻²)⁻³=(-5)⁻⁴⁻² *(-5)⁶ = (-5)⁻⁶ *(-5)⁶ =(-5)°=1

b) (a³ ·a⁴ ·a ⁻⁵)⁻² : ( a⁷ : a⁹ · a ⁻⁴)⁻⁵= (a³⁺⁴⁻⁵)⁻²:(a⁷⁻⁹ ⁺ ⁻⁴)⁻⁵=(a²)⁻² : (a⁻⁶)⁻⁵=

                          =a ⁻⁴ : a ³⁰ = a ⁻⁴⁻³⁰=a ⁻³⁴

 

Oblicz wysokość trójkąta równobocznego jeśli a wynosi : √3, √6, √9, √10 , √12, √15 

 

h=a√3 /2

√3

h=√3*√3 /2=3/2

 

√6

h=√6*√3 /2 =√18/2=√(9*2)/2=3√2/2

 

 

 √9

h=√9*√3/2=3√3/2  

 

√10

h=√10*√3/2=√30/2  

 

√12

h=√12*√3/2=√36/2=6/2=3  

 

√15

h=√15*√3/2=√45/2=√(9*5)/2=3√5/2    

Answer 2

A.

a)   5^-1 = (1/5)^1 = 1/5

b)   (2 3/4)^-1 = (11/4)-1 = (4/11)^1 = 4/11

c)   (-4,8)^-1 = (-48/10)^-1 = (-24/45^-1 = (-5/24)^1  = -5/24

 

B.

a)   (-3)^-4 = (-1/3)^4 = 1/81

b)   (1 2/5)^-2 = (7/5)^-2 = (5/7)^2 = 25/49

c)   2,5^-3 = (25/10)^-3 = (5/2)^-3 = (2/5)^3 = 8/125

 

C. 

a)

(-5)^-4 : (-5)^2 *[(-5)^-2]^-3 = (-5)^-6 * (-5)^6 = (-5)^0 = 1

b)

  (a^3 * a^4 * a^-5)^-2 : (a^7 : a^9 * a*-4)^-5 =

= (a^2)^-2 : (a^-6)^-5 = a^-4 :a^30 = a^-34

 

h = a√3/4

 

dla a = √3

h = √3*√3/2 = 3/2 = 1,5

 

dla a = √6

h = √6*√3/2 = √18/2 = 3√2/2 = 1,5√2

 

dla a = √9  = 3

h = 3√3/2 = 1,5√3

 

dla a = √10

h = √10*√3/2 = √30/2

 

dla a = √12 = 2√3

h = 2√3*√3/2 = 3

 

dla a = √15

h = √15*√3/2 = √45/2 = 3√5/2 = 1,5√5