Question

Z podanych wzorów wyznacz wskazanie wielkości ( proszę o przekształcenia a nie samą odpowiedź)

1. Cp=(ms/(ms+mr) ) *100% >>mr, ms

2. m1*v1+m2*v2=(m1+m2)*v3 >>v1, v3, m1

3. V= (1/12)*a³ * √2 >>a

4. P= 2*(a*b+b*c+a*c) >> a

5. P= ((a+b+c)/2) *((a+b-c)/2) >>a, c (a,b,c >0)

Answer 1

1. Cp=(ms/(ms+mr) ) *100% >>mr, ms

100% = 1

Cp = ms/(ms + mr) |*(ms + mr)
Cp*(ms + mr) = ms
Cp*ms + Cp*mr = ms

Cp*mr = ms(1 - Cp) |:Cp
mr = ms(1 - Cp)/Cp = ms*(1/Cp - 1)

Cp*mr = ms(1 - Cp) |:(1 - Cp)
ms = Cp*mr/(1 - Cp)


2. m₁*v₁ + m₂*v₂ = (m₁ + m₂)*v₃ >>v1, v3, m1

m₁*v₁ + m₂*v₂ = (m₁ + m₂)*v₃ |- m₂*v₂
m₁*v₁ = (m₁ + m₂)*v₃ - m₂*v₂ |:m₁
v₁ = [m₁*v₃ + m₂*v₃ - m₂*v₂]/m₁
v₁ = v₃ + m₂(v₃ - v₂)/m₁

m₁*v₁ + m₂*v₂ = (m₁ + m₂)*v₃ |- m₂*v₂
m₁*v₁ = (m₁ + m₂)*v₃ - m₂*v₂ |:v₁
m₁ = [(m₁ + m₂)*v₃ - m₂*v₂]/v₁

m₁*v₁ + m₂*v₂ = (m₁ + m₂)*v₃ |:(m₁ + m₂)
v₃ = (m₁*v₁ + m₂*v₂)/(m₁ + m₂)


3. V= (1/12)*a³ * √2 >>a

V = (1/12)*a³ * √2 |*(12/√2)
a³ = 12V/√2
a³ = 12V*√2/√2*√2
a³ = 6√2V |∛
a = ∛(6√2V)

4. P= 2*(a*b+b*c+a*c) >> a

P = 2*(a*b + b*c + a*c) |:2
P/2 = a*b + b*c + a*c
P/2 = a*(b + c) + b*c | - b*c
P/2 - b*c = a*(b + c) |:(b + c)
a = (P/2 - b*c)/(b + c) = [(P - 2bc)/2]/(b + c) = (P - 2bc)/(b + c)

5. P= ((a+b+c)/2) *((a+b-c)/2) >>a, c (a,b,c >0)

P = ((a + b + c)/2)*((a + b - c)/2)
P = (([a + b] + c)*([a + b] - c)/4)

ze wzoru na iloczyn sumy i różnicy (a - b)(a + b) = a² - b²
P = ([a + b]² - c²)/4 |*4
4P = [a + b]² - c² | + c²
(a + b)² = 4P + c² |√
a + b = √(4P + c²) | - b
a = √(4P + c²) - b

4P = [a + b]² - c² | + c² - 4P
c² = (a + b)² - 4P | √
c = √[(a + b)² - 4P]

jak masz pytania pisz na pw

Answer 2

1. Cp=(ms/(ms+mr) ) *100%
Cp=(ms*100%)/(ms+mr) | *(ms+mr)
Cp (ms+mr)= ms*100% |:Cp
ms+mr = (ms*100%)/Cp |-mr
ms=[(ms*100%)/Cp]-mr

ms+mr = (ms*100%)/Cp |-ms
mr=[(ms*100%)/Cp]-ms



2. m1*v1+m2*v2=(m1+m2)*v3
(m1*v1)+(m2*v2)=(m1+m2)v3 |:(m1+m2)
[(m1*v1)+(m2*v2)]/(m1+m2)= v3

(m1*v1)+(m2*v2)=(m1+m2)v3 |-(m2*v2)
m1*v1=(m1+m2)v3 - (m2*v2) |:m1
v1= [(m1+m2)v3 - (m2*v2)]/m1

(m1*v1)+(m2*v2)=(m1+m2)v3 |-(m2*v2)
m1*v1=(m1+m2)v3 - (m2*v2)
m1*v1=m1*v3+m2*v3-m2*v2 |-m1*v3
m1*v1-m1*v3=m2*v3-m2*v2
m1(v1-v3)=m2(v3-v2) |:(v1-v3)
m1=[m2(v3-v2)]/(v1-v3)


3. V= (1/12)*a³ * √2 |:√2/12
12V/√2=a³
12√2V/2 =a³
6√2V=a³
a=³√(6√2V)


4. P= 2*(a*b+b*c+a*c)
P=2ab+2bc+2ac
P=2a(b+c)+2bc |-2bc
P-2bc=2a(b+c) |:2(b+c)
(P-2bc)/2(b+c)= a


5. P= ((a+b+c)/2) *((a+b-c)/2)
P=[(a+b+c)(a+b-c)]/4 |*4
4P=(a+b+c)(a+b-c)
4P=[(a+b)+c][(a+b)-c]
4P=(a+b)²-c² |+ c²
4P+c²=(a+b)² |-4P
c²=(a+b)²-4P

4P=(a+b)²-c² |+ c²
4P+c²=(a+b)²
√(4P+c²)=a+b |-b
a=√(4P+c²)-b