Matematyka

Autorzy:Alina Przychoda, Zygmunt Łaszczyk

Wydawnictwo:WSiP

Rok wydania:2014

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`a)\ (1)/(f) = 1/p+1/q` 

`(1)/(f) = (q+p)/(pq)` 

`underline(underline(f=(pq)/(p+q)))` 

`f(p+q)=pq` 

`fp+fq=pq` 

`pq-fq=fp` 

`q(p-f)=fp`     

`underline(underline(q=(fp)/(p-f)))` 

 

`b)\ 1/R=1/r+1/s` 

 `1/r=1/R-1/s` 

`1/r=(s-R)/(Rs)` 

`underline(underline(r=(Rs)/(s-R)))`   

`r(s-R)=Rs`    

`rs-Rr=Rs` 

`rs-Rs=Rr` 

`s(r-R)=Rr` 

`underline(underline(s=(Rr)/(r-R)))` 

 

`c)\ R=(r_1r_2)/(r_1+r_2)` 

`R(r_1+r_2)=r_1r_2` 

`Rr_1+Rr_2=r_1r_2 ` 

`r_1r_2-Rr_1=Rr_2` 

`r_1(r_2-R)=Rr_2` 

`underline(underline(r_1=(Rr_2)/(r_2-R)))` 

`r_1r_2-Rr_1=Rr_2`

`r_1r_2-Rr_2=Rr_1` 

`r_2(r_1-R)=Rr_1` 

`underline(underline(r_2=(Rr_1)/(r_1-R)`

 

`d)\ t=(2dV)/(V^2-w^2)` 

`tV^2-tw^2=2dV` 

`tw^2=tV^2-2dV` 

`w^2=(tV^2-2dV)/t` 

`underline(underline(w=sqrt((tV^2-2dV)/t)))\ l u b\ underline(underline(w=-sqrt((tV^2-2dV)/t))`  

`tV^2-tw^2=2dV`

`tV^2-2dV-tw^2=0` 

`Delta=4d^2+4t^2w^2` 

`underline(underline(V=(2d-2sqrt(d^2+t^2w^2))/(2t)))\ l u b\ underline(underline(V=(2d+2sqrt(d^2+t^2w^2))/(2t))`