B2. Solve the problems:

(a) What is the value of the expression $(\sqrt{4+\sqrt{4}})^{4}$ ?

(b) What is $a$, if $\frac{a}{6}+\frac{6}{18}=1$ ?

(c) A five-digit number is composed of the digits 1, 3, 5, 7, and 9. The number is greater than 80000 and less than 92000. The units place is the digit 3. The hundreds and tens, in that order, form a two-digit number that is divisible by 5. What is the five-digit number?

(d) Six friends go to a canoeing event. Each canoe can seat two people. The friends will be randomly assigned to the canoes in pairs. In how many ways can they be arranged?

(e) A laser is shone from point $C$ to point $E$. The beam reflects at point $G$ and then at point $B$. The distance $\overline{D E}=\overline{E F}=1 \mathrm{~m}$. What is the distance $\overline{B D}$ ?

![](https://cdn.mathpix.com/cropped/2024_06_07_a04162d2cc6b04e5d61eg-04.jpg?height=494&width=332&top_left_y=952&top_left_x=248)
B2.

(a) The value of the expression $(\sqrt{4+\sqrt{4}})^{4}=36$.

(b) The value of $a=4$.

(c) Considering all the given properties of the number, we determine that the desired number is 91753.

(d) They can be arranged in $\frac{6 \cdot 5}{2} \cdot \frac{4 \cdot 3}{2} \cdot 1=90$ ways.
(e) From the diagram, we determine that the triangles $C D E, E F G$ and $B C G$ are isosceles. From this, it follows that $\overline{D E}=\overline{D C}=1 \mathrm{~m}$ and $\overline{C G}=\overline{C B}=2 \mathrm{~m}$. The distance $\overline{B D}=1 \mathrm{~m}+2 \mathrm{~m}=3 \mathrm{~m}$.

(a) The calculated value of the expression ${\sqrt{4+\sqrt{4}^{4}}}^{4}=36$. ....................................................

(b) The calculated value of $a=4$. .............................................................................................

(c) Determination of the desired number 91753. .....................................................................................

(d) Determination of the number of all possible arrangements: 90. .............................................. 2 t

![](https://cdn.mathpix.com/cropped/2024_06_07_a04162d2cc6b04e5d61eg-12.jpg?height=66&width=1734&top_left_y=795&top_left_x=178)