Suppose that two boats leave a dock at different times. One heads due north, the other due east. Find the rate at which the distance between the boats is changing when the first boat is 51 miles from the dock traveling at a speed of 56 miles per hour and the second boat is 26 miles from the dock traveling at a speed of 25 miles per hour. Answer:

7. \( 12,10^{-5} \)

37) \( \frac{7}{3},-\frac{2}{5}, 1 \frac{2}{3} \) या संख्या उतरत्या क्रमाने असणारा पर्याय कोणता? \( \begin{array}{ll}\text { 1) } \frac{-7}{3},-\frac{2}{5}, 1 \frac{2}{3} & \text { 2) } 1 \frac{2}{3},-\frac{2}{5}, \frac{-7}{3} \\ \text { 3i }-\frac{2}{5}, \frac{-7}{3}, 1 \frac{2}{3} & \text { 4) } \frac{-7}{3} 1 \frac{2}{3},-\frac{2}{5}\end{array} \)

Attempt 1:4 attempts remaining. A aircraft is climbing at a 30 degree angle to the horizontal. How fast is the aircraft gaining altitude if its speed is \( 200 \mathrm{mi} / \mathrm{h} \) ? Answer:

3. En deduire que pour tout entier \( n \) non nul: a) \( e^{\frac{1}{n}} \geq 1+\frac{1}{n} \quad \) et \( e^{\frac{-1}{n+1}} \geq 1-\frac{1}{n+1} \) b) En déduire que que pour tout entier \( n \) non nul: \( e^{\frac{1}{n+1}} \leq \frac{n+1}{n} \) 4. En remarquant que pour tout entier naturel \( k>0,\left(e^{\frac{1}{x}}\right)^{k}=e \), montrer que pour tout entier \( n \) non nul: \[ \left(1+\frac{1}{n}\right)^{n} \leq e \leq\left(1+\frac{1}{n}\right)^{n+1} \]

11. What is the LCM of: \( \begin{array}{ll}\text { a) } 24 \text { and } 180 & \text { b) } 18,27 \text { and } 36 \\ 360 & \text { [6] }\end{array} \)