Answered By Majid B

a)

 $v=\left(-7\right)+8.2\times\sqrt{d}$v=‍(−7)+8.2×√d      =>         $\frac{\left(v+7\right)}{8.2}=\sqrt{d}$(v+7)8.2 =√d       =>        $d=\frac{\left(v+7\right)^2}{67.24}$‍d=(v+7)²67.24  

b)

 $v=90$v=90 km/h    =>        $d=\frac{\left(90+7\right)^2}{67.24}=\frac{97^2}{67.24}=140$d=(90+7)²67.24 =97²67.24 =140 m

c)

 $d=$d= 150 m    =>       $v=-7+8.2\times\sqrt{150}$v=−7+8.2×√150      =>      $v=93$v=93 km/h 

Answered By Sophia E

a) First, you want to manipulate the given formula so that you can find d by itself. You might have learned that when you manipulate formulas to get a different variable y itself, you need to consider BEDMAS going backwards (SAMDEB).

 $v=-7+8.2\sqrt{d}$v=−7+8.2√d

→  $v+7=8.2\sqrt{d}$v+7=8.2√d

→  $\frac{v+7}{8.2}=\sqrt{d}$v+78.2 =√d

→  $d=\frac{\left(v+7\right)^2}{67.24}$d=(v+7)²67.‍24  

b) Using the formula you mainpulated in part a), this part is straightforward as you plug in  $v=90$v=90 km/h.

→     $d=\frac{\left(90+7\right)^2}{67.24}=\frac{97^2}{67.24}=139.9315883\approx140$d=(90+7)²67.24 =97²67.24 =139.9315883≈140 m

Since  $d>0$d>0, then  $140>0$140>0, which saisfies the condition given in the question.

c) Going back to the original equation, let  $d=150$d=150.

 $v=-7+8.2\sqrt{150}$v=−7+8.2√150

→  $v=-7+8.2\left(12.2474487\right)$v=−7+8.2(12.2474487) 

→  $v=-7+100.42907945$v=−7+100.42907945

→   $v=93.429074945$v=93.429074945 km/h

→  $v\approx93$v≈93 km/h

Note: I would not suggest rounding these very long decimals that your calculator has until *after* you reach your fnal answer. If your teacher has mentioned this, then that's great!

Hope this helps!