Question

A) Rearrange the equation to solve for x= square root of 2x/a

Answer 1

`\\ \rm\dashrightarrow t=√(2x){a}`

`\\ \rm\dashrightarrow t^2=(2x)/(a)`

`\\ \rm\dashrightarrow 2x=at^2`

`\\ \rm\dashrightarrow x=(at^2)/(2)`

#b

• Put a=4
• t=90

`\\ \rm\dashrightarrow x=(4(90)^2)/(2)`

`\\ \rm\dashrightarrow x=2(8100)`

`\\ \rm\dashrightarrow x=16200`

Answer 2

`\textsf{A)} \quad x=(t^2a)/(2)`

`\textsf{B)} \quad x=16200`

Step-by-step explanation:

Given formula:

`t=\sqrt{(2x)/(a)}`

Part A

To rearrange the equation to solve for x, square both sides:

`\implies t^2=\left(\sqrt{(2x)/(a)}\right)^2`

`\implies t^2=(2x)/(a)}`

Multiply both sides by a:

`\implies t^2 \cdot a=(2x\cdot a)/(a)}`

`\implies t^2a=2x`

Divide both sides by 2:

`\implies (t^2a)/(2)=(2x)/(2)`

`\implies x=(t^2a)/(2)`

Part B

Given:

• a = 4
• t = 90

Substitute the given values into the equation found in part A:

`\begin{aligned}x & =(t^2a)/(2)\\\\\implies x & = (90^2 \cdot 4)/(2)\\\\& = (8100 \cdot 4)/(2)\\\\& = (32400)/(2)\\\\ \implies x & = 16200\end{aligned}`