The square root of thirty lies between the numbers 5 and 6.
Answer:
Step-by-step explanation:
Frt7v6c87buhinjomp,l.;
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Answer:
![AB=2\sqrt{ab}](https://tex.z-dn.net/?f=AB%3D2%5Csqrt%7Bab%7D)
Step-by-step explanation:
From figure,
![OA=a, \quad \quad O'B=b\\\Rightarrow OO'= (a+b) \quad \quad \text{and}\quad OD=(a-b)](https://tex.z-dn.net/?f=OA%3Da%2C%20%20%5Cquad%20%5Cquad%20O%27B%3Db%5C%5C%5CRightarrow%20OO%27%3D%20%28a%2Bb%29%20%5Cquad%20%5Cquad%20%5Ctext%7Band%7D%5Cquad%20OD%3D%28a-b%29)
In triangle ![OO'D](https://tex.z-dn.net/?f=OO%27D)
![(OO')^2=(OD)^2+(O' D)^2](https://tex.z-dn.net/?f=%28OO%27%29%5E2%3D%28OD%29%5E2%2B%28O%27%20D%29%5E2)
![\Rightarrow (a+b)^2=(a-b)^2+(O' D)^2\\\Rightarrow a^2+b^2+2ab-a^2-b^2+2ab=(O' D)^2\\\Rightarrow 4ab=(O' D)^2\\\Rightarrow O'D=2\sqrt{ab} \\\Rightarrow O' D=2\sqrt{ab}=AB \quad \quad [\because O' DAB\;\; \text{is a rectangle.}]](https://tex.z-dn.net/?f=%5CRightarrow%20%28a%2Bb%29%5E2%3D%28a-b%29%5E2%2B%28O%27%20D%29%5E2%5C%5C%5CRightarrow%20a%5E2%2Bb%5E2%2B2ab-a%5E2-b%5E2%2B2ab%3D%28O%27%20D%29%5E2%5C%5C%5CRightarrow%204ab%3D%28O%27%20D%29%5E2%5C%5C%5CRightarrow%20O%27D%3D2%5Csqrt%7Bab%7D%20%5C%5C%5CRightarrow%20O%27%20D%3D2%5Csqrt%7Bab%7D%3DAB%20%5Cquad%20%5Cquad%20%5B%5Cbecause%20O%27%20DAB%5C%3B%5C%3B%20%5Ctext%7Bis%20a%20rectangle.%7D%5D)
Hence, ![AB=2\sqrt{ab}](https://tex.z-dn.net/?f=AB%3D2%5Csqrt%7Bab%7D)
Answer:
7/11 = 0.6363...
Step-by-step explanation:
7 + 4 = 11
probability of winning: 7/11 = 0.6363...