Question

**Please Help. ASAP**

Rearrange the formula so the letter in parenthesis is the subject. Show your work as well.


1) v-u/a = t, (v)

2) y-x^2/x = 3z, (y)

3) x+xy = y, (x)

4) x+y = xy, (x)

5) x = y+xy, (x)

6) E = (1/2)mv^2-(1/2)mu^2, (u)

7) (x^2/a^2)-(y^2/b^2) = 1, (y)

8) ay^2 = x^3, (y)

Answer 1

The answer is below

Step-by-step explanation:

1)

`(v-u)/(a) =t\\\\Making \ v\ the \ subject\ of\ formula:\\\\First \ cross-multiply:\\\\v-u=at\\\\add\ u\ to \ both\ sides:\\\\v-u+u=at+u\\\\v=u+at`

2)

`(y-x^2)/(x)=3z\\ \\Making\ y\ the\ subject\ of\ formula:\\\\First \ cross \ multiply:\\\\y-x^2=3xz\\\\y=3xz+x^2\\\\y=x(x+3z)`

3)

`x+xy=y\\\\Making\ x\ the\ subject\ of\ formula:\\\\x(1+y)=y\\\\Divide\ through\ by\ 1+y\\\\(x(1+y))/(1+y) =(y)/(1+y) \\\\x=(y)/(1+y)`

4)

`x+y=xy\\\\Making\ x\ the\ subject\ of\ formula:\\\\Subtract\ x\ from \ both\ sides:\\\\x+y-x=xy-x\\\\y=xy-x\\\\y=x(y-1)\\\\Divide\ through\ by \ y-1\\\\(y)/(y-1) =(x(y-1))/(y-1)\\ \\x=(y)/(y-1)`

5)

`x=y+xy\\\\Making\ x\ the\ subject\ of\ formula:\\\\Subtract\ xy\ from \ both\ sides:\\\\x-xy=y+xy-xy\\\\x-xy=y\\\\x(1-y)=y\\\\Divide\ through\ by \ 1-y\\\\(x(1-y))/(1-y) =(y)/(1-y)\\ \\x=(y)/(1-y)`

6)

`E=(1)/(2)mv^2-(1)/(2)mu^2\\ \\Making\ u\ the\ subject \ of\ formula:\\\\Multiply \ through\ by \ 2\\\\2E=mv^2-mu^2\\\\mu^2=mv^2-2E\\\\Divide\ through\ by\ m:\\\\u^2=(mv^2-2E)/(m)\\ \\Take\ square\ root\ of \ both\ sides:\\\\u=\sqrt{(mv^2-2E)/(m)}`

7)

`(x^2)/(a^2)-(y^2)/(b^2)=1\\ \\Making\ y\ the\ subject \ of\ formula:\\\\(x^2)/(a^2)-1=(y^2)/(b^2)\\\\Multiply\ through\ by\ b^2\\\\b^2((x^2)/(a^2) -1)=y^2\\\\Take\ square\ root\ of\ both\ sides:\\\\y=\sqrt{b^2((x^2)/(a^2) -1)}`

8)

`ay^2=x^3\\\\Make\ y\ the\ subject\ of\ formula:\\\\Divide\ through\ by\ a:\\\\y^2=(x^3)/(a)\\ \\Take\ square\ root\ of\ both\ sides:\\\\y=\sqrt{(x^3)/(a)} \\`