Answer:
[tex]\boxed{\sf r=33\sqrt{2}}[/tex]
Step-by-step explanation:
[tex]\sf \cfrac{\sqrt{2}}{3}\:r+1=23[/tex]
Subtract 1 from both sides:
[tex]\sf \cfrac{\sqrt{2}}{3}\: r+1-1=23-1[/tex]
Simplify 23 -1 =22
[tex]\sf \cfrac{\sqrt{2} }{3} \: r=22[/tex]
Now, Multiply both sides by 3:
[tex]\sf 3\times \cfrac{\sqrt{2r}}{3}=22\times \:3[/tex]
[tex]\sf \sqrt{2}\: r =22\times 3[/tex]
Simplify 22 * 3 =66
[tex]\sf \sqrt{2}r=66[/tex]
Now, Divide both sides by √(2):
[tex]\sf \cfrac{\sqrt{2}r}{\sqrt{2}}=\cfrac{66}{\sqrt{2}}[/tex]
[tex]\leadsto\sf \cfrac{\sqrt{2}r}{\sqrt{2}}=r[/tex]
[tex]\leadsto\sf \cfrac{66}{\sqrt{2}}= 33\sqrt{2}[/tex]
[tex]\sf r=33\sqrt{2}[/tex]
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