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MisterBrainly

[tex]\\ \rm\dashrightarrow t=\sqrt{2x}{a}[/tex]

[tex]\\ \rm\dashrightarrow t^2=\dfrac{2x}{a}[/tex]

[tex]\\ \rm\dashrightarrow 2x=at^2[/tex]

[tex]\\ \rm\dashrightarrow x=\dfrac{at^2}{2}[/tex]

#b

  • Put a=4
  • t=90

[tex]\\ \rm\dashrightarrow x=\dfrac{4(90)^2}{2}[/tex]

[tex]\\ \rm\dashrightarrow x=2(8100)[/tex]

[tex]\\ \rm\dashrightarrow x=16200[/tex]

semsee45

Answer:

[tex]\textsf{A)} \quad x=\dfrac{t^2a}{2}[/tex]

[tex]\textsf{B)} \quad x=16200[/tex]

Explanation:

Given formula:

[tex]t=\sqrt{\dfrac{2x}{a}}[/tex]

Part A

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

[tex]\implies t^2=\left(\sqrt{\dfrac{2x}{a}}\right)^2[/tex]

[tex]\implies t^2=\dfrac{2x}{a}}[/tex]

Multiply both sides by a:

[tex]\implies t^2 \cdot a=\dfrac{2x\cdot a}{a}}[/tex]

[tex]\implies t^2a=2x[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{t^2a}{2}=\dfrac{2x}{2}[/tex]

[tex]\implies x=\dfrac{t^2a}{2}[/tex]

Part B

Given:

  • a = 4
  • t = 90

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

[tex]\begin{aligned}x & =\dfrac{t^2a}{2}\\\\\implies x & = \dfrac{90^2 \cdot 4}{2}\\\\& = \dfrac{8100 \cdot 4}{2}\\\\& = \dfrac{32400}{2}\\\\ \implies x & = 16200\end{aligned}[/tex]