Question

myslalam ze tylko ja nie umiem zrobic tej matematyki .. ale widocznie nikt nie umie albo nikomu sie nie chce pomoc . dodaje zalaczniki moze jednak ktos sprobuje mi to rozwiazac. dziekuje z gory:)

Answer 1

z.3

ISC I = h

I AB I = 50

I BC I = x

Mamy

h / ( x + 50) = tg 45 st = 1

czyli   h   = x + 50

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oraz

h/x = tg 60 st = p(3)

h = x p(3)

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Mamy więc

x p(3) = x + 50

x p(3) - x = 50

x*( p(3) - 1) = 50

x - 50/[p(3) - 1]

===================

h = x* p(3) = [ 50 p(3)]/[ p(3) - 1] =  ... = 75 + 25 p(3)

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z.4

Trapez ABCD

I AB I =a = 16

I CDI = b = 12

I BC I = I AD I = c

x = [ a - b]/2 = [ 16 - 12 ]/2 = 4/2 = 2

h/x = tg 30 st = p(3)/3

h = x * p(3)/3  = 2 * p(3)/3 = (2/3) p(3 )

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x / c = cos 30 st

2/ c = p(3)/2

c = 4 /p(3) = (4/3) p(3)

====================

 

Pole trapezu

P = 0,5 [a + b]* h = 0,5 *[ 16 + 12 ]*(2/3) p(3) =14*(2/3) p(3) = (28/3) p(3)

P = (28/3) p(3)

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Obwód

L = a + b + 2 c = 16 + 12 * 2*(4/3) p(3) = 28 + (8/3) p(3)

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z.5

a)  L = 3a = 30 cm

to

a = 10 cm

============

P = a^2 p(3) / 4 = 10^2 p(3) / 4 = 25 p(3)

P = 25 p(3) cm^2

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b)

h = 3 p(3) cm

więc

h = a p(3)/2 = 3 p(3)

a/2 = 3

a = 2*3 = 6 cm

Pole

P = 6^2 p(3)/4 =9 p(3)

p = 9 p(3) cm^2

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z.6

a) sin alfa = 2/3

więc  y = 2, r = 3

x^2 + y^2 = r^2

x^2 = r^2 - y^2 = 3^2 - 2^2 = 9 - 4 = 5

x = p(5)

zatem

cos alfa = x/r = p(5)/3

tg alfa = y/x = 2/ p(5) = (2/5) p(5)

ctg alfa = 1 / tg alfa =p(50/2

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b)

ctg alfa = 5/6

więc  x = 5,  y = 6

r^2 = x^2 + y^2 = 5^2 + 6^2 = 25 + 36 = 61

r = p(61)

zatem

sin alfa = y/r = 6/p(61)

cos alfa = x/r = 5 /p(61)

tg alfa = 1 / ctg alfa = 6/5

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c)

cos alfa = 1/2

alfa = 60 st

więc

sin alfa = p(3)/2

tg alfa = p(3)

ctg alfa = p(3)/3

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z.1

a = 4, b = 2 p(2)

c^2 = 4^2 + ( 2 p(2))^2 = 16 + 8 = 24 = 4*6

c = 2 p(6)

===========

a = 3 p(2) , c = 3 p(5)

( 3 p(2))^2 + b^2 = ( 3 p(5))^2

18 + b^2 = 45

b^2 = 45 - 18 = 27 = 9*3

b = 3 p(3)

===========

b = 2 , c = 5/2 = 2,5

a^2 + 2^2 = 2,5^2

a^2 = 6,25 - 4 = 2,25

a = p(2,25) = 1,5

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z.2

a)  x^2 + x^2 = ( x +2)^2

2 x^2 = x^2 + 4x + 4

x^2 - 4x - 4 = 0

delta = (-4)^2 - 4*1*(-4) = 16 + 16 = 16*2

p (delty) = 4 p(2)

x > 0 więc

x = [ 4 + 4 p(2)]/2 = 2 +2 p(2)

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b)

6 /x = cos 30 st = p(3)/2

x p(3) = 6*2 = 12

x = 12 : p(3) = 4 p(3)

=======================

c)

( x + 1)/x = tg 60 st = p(3)

x + 1 = x p(3)

x p(3) - x  = 1

x*(p(3) - 1) = 1

x = 1 /[ p(3) - 1] = [ p(3) + 1]/2

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