Odpowiedzi

2010-02-17T18:11:37+01:00
Zad 1
a) d=V/m |*m
V=dm

V=dm |:d
m=V/d

b) F=ma |:a
m=F/a

c) pV=nRT |:V
p=nRT/V

pV=nRT |:nR
T=pV/nR

Zad 2
a) x=x_0+vt
x_0=x-vt

b) x=x_0+vt
x-x_0=vt |:v
(x-x_0)/v=t

c) C_p=m_s/(m_s+m_r)*100%
C_p*(m_s+m_r)=m_s*100%
C_p*m_s+C_p*m_r=m_s*100%
C_p*m_r=m_s(100%-C_p)
m_r=m_s(100%-C_p)/C_p

m_s=(C_p*m_r)/(100%-C_p)

d) m_1v_1+m_2v_2=(m_1+m_2)v_3
v_3=(m_1v_1+m_2v_2)/(m_1+m_2)

m_1v_1=(m_1+m_2)v_3-m_2v_2
v_1=((m_1+m_2)v_3-m_2v_2)/m_1

m_1v_1=m_1v_3+m_2v_3-m_2v_2
m_1v_1-m_1v_3=m_2v_3-m_2v_2
m_1(v_1-v_3)=m_2v_3-m_2v_2
m_1=(m_2v_3-m_2v_2)/(v_1-v_3)

Zad 3
a) P=d_1d_2/2
2P=d_1d_2
d_1=2P/d_2

b) P=(a^2*√3)/4
4P=a^2*√3
a^2=4P/√3
a=√(4P/√3)

c) R=a√6/4
4R=a√6
a=4R/√6

d) V=1/12a^3*√2
a^3=V/(1/12*√2)
a=³√(V/(1/12*√2))

Zad 4
a) P=((c+d)/2)*h
h=P/((c+d)/2)

P/h=(c+d)/2
2P/h=c+d
c=2P/h-d

b) P=2πr(r+h)
P/2πr=r+h
h=(P/2πr)-r

c) P=2(ab+bc+ac)
P/2=ab+bc+ac
P/2-bc=a(b+c)
a=(P/2-bc)/(b+c)

d) P=(a+b+c)/2*(a+b-c)/2
4P=(a+b+c)(a+b-c)
4P=(a+b)^2-c^2
4P=a^2+2ab+b^2-c^2
c^2=-4P/(a^2+2ab+b^2)
c=√(-4P/(a^2+2ab+b^2))

a^2+2ab=b^2-c^2-4P
a(a+2b)=b^2-c^2-4P
a=(b^2-c^2-4P)/(a+2b)
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