amazingxin777

Hello... hope i didn't break into your conversation @gwenspooner85 

The formula for the sum in a infinite geometric sequence is \(\frac{{a}_{1}}{1-r}\) where a is the first term and r is the common ratio. We know that the sum equals 25 so \(\frac{{a}_{1}}{1-r}=25\). We also know the common ratio so \(\frac{{a}_{1}}{1+\frac{1}{3}}\Rightarrow\frac{{a}_{1}}{\frac{4}{3}}=25\). Solve for a and you get \(25\times\frac{4}{3}\Rightarrow\frac{100}{3}\) but it's asking for the second term (this is the first term) so we multiply \(\frac{100}{3}\) by \(-\frac{1}{3}\) (the common ratio) and you get \(-\boxed{\frac{100}{9}}\)

I created a graph (hopefully gives you a headstart) and maybe try trial-and-error

Write an equation where w is the width:

\(3w+6=100\)\(\Rightarrow3w=94\)

Try solving

hint: \(\sqrt{11}=11^{1/2}\)

You're welcome!!!!! 

135,135 

Someone check my answer! (I can't provide a solution now and hope to later )

So the total amount of days in three weeks is 21. Every 21 days, it rains 7 days. We can write out a ratio the same way for every 366 days.

\(\frac{7}{21}=\frac{n}{366}\) 

Now we solve for \(n\) (\(n \) being the number of days it rains in 366 days) by cross-multiplying. \(n=\frac{7\times366}{21}\Rightarrow \frac{366}{3}\Rightarrow 122\).

So our answer is \(\boxed{122}\)

14 is the answer because if Hannah is 7 yrs older than Tim was 2 yrs ago then she obviously still is now. If they are apart by 7 then Tim must be 7 and Hannah would be \(2\times7\) or 14. So the answer is \(\boxed{14}\)