Question

Wyznacz ze wzoru wskazaną wielkość:
R=abc/4P (ułamek) ; P
v=at²/2 ; a

Z każdego z podanych niżej wzorów wyznacz x.
T= 1/abx (ułamek)
y=2t- 3x
y= x-1/ 2
y= 2/ x-1
P=1/3 (a²+2ax)

Answer 1

R = abc/4P /*P
RP = abc/4 /R
P = abc/4R

v=at²/2 /*2
2v = at² /t²
a = 2v/t²

T= 1/abx /*x
Tx = 1/ab /T
x = 1/abT

y=2t - 3x
3x = 2t-y /3
x = (2t-y)/3

y= x-1/2 /*2
2y = x-1
x = 2y+1

y= 2/x-1 /*(x-1)
y(x-1) = 2 /y
x-1 = 2/y
x = 2/y -1

P=1/3 (a²+2ax) /*3
3P = a(a+2x) /a
3P/a = a+2x
2x = 3P/a -a /2
x = 3P/2a -a/2

Answer 2

R=abc/4P (ułamek) ; P
4PR = abc
P = abc/4R
--------------------
v=at²/2 ; a
2v = at²
a = 2v/t²
----------------------------
T= 1/abx (ułamek)
Tabx = 1
x = 1/Tab
-----------------------
y=2t- 3x
3x = 2t - y
x = (2t - y)/3
-----------------------
y= x-1/ 2
2y = x - 1
x = 2y + 1
------------------
y= 2/ x-1
y(x - 1) = 2
xy - y = 2
xy = 2 + y
x = (2 + y)/y
---------------------
P=1/3 (a²+2ax)
3P(a² + 2ax) = 1
3Pa² + 6Pax = 1
6Pax = 1 - 3Pa²
x = (1 - 3Pa²)/6Pa

Answer 3

R=abc/4P --> P
R=abc/4P /*4P
4PR=abc /:4R
P=abc/4R

v=at²/2 ; a
v=at²/2 /*2
2v=at² /:t²
2v/t²=a
a=2v/t²

T= 1/abx --> x
T= 1/abx /*abx
Tabx=1 /:Tab
x=1/Tab

y=2t- 3x -->x
y=2t- 3x /-2t
y-2t=-3x /:-3
y-2t/-3=x
x=y-2t/-3

y= x-1/ 2 -->x
y= x-1/ 2 /*2
2y=x-1 /+1
2y+1=x
x=2y+1

y= 2/ x-1 -->x
y= 2/ x-1 /*x-1
y*x-1=2 /:y-1
x=2/y-1

P=1/3 (a²+2ax) --> x
P=1/3 a²+2/3ax /:1/3a²
P-1/3a²=2/3ax /:2/3a
x=P-1/3a² / 2/3a