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gibbenergy

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Everything posted by gibbenergy

  1. I don't know how to solve this one. Can anyone help me? A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks from the pole with a speed of 5ft/s along the straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?
  2. It can be solved quickly if you know derevative. I can post my sols quickly. Let [math]f(x)=(x+27)^{\frac{1}{3}} - 3[/math] so [math]f(0)=0[/math] then [math]f'(0)=\lim_{x\to0} \frac{(x+27)^{\frac{1}{3}} - 3}{x-0}[/math] So you know how to do next?
  3. Sorry but I don't think it is nice. Because, in order to prove that ,you use Fermar's last theorem which is too strong. In fact, we can prove it very simple by number theory . For example: Suppose it is rational then we can write it as [imath] a^n= 2b^n[/imath] so [imath] a^n [/imath] must be even so [imath] a [/imath] must be even .Put [imath] a=2k[/imath] then we get [imath] (2k)^n=2b^n[/imath] [imath]2^{n-1}k^n=b^n [/imath] so [imath]b [/imath] must be even.Then [imath]b=2k1 [/imath] .... And we can countinue it .So it is only ended when [imath] a=b=0[/imath] with is never happen. So [imath] \sqrt[n]{2} [/imath] can't be rational:D
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