by \( x-3 \). Grouping. The number, \( N(x) \), of ways in which a delegation of three students can be formed from \( x \) students is given by \( N(x)=\frac{1}{6} x^{3}-\frac{1}{2} x^{2}+\frac{1}{3} x \). Find the value of \( x \) when \( \mathrm{N}(x)=35 \).

The sum of the first three terms of an arithmetic sequence is 15 and their product is 80. Determine the first threc terms.

The ratio between the sum of the fifth, sixth and seventh terms of a geometric series ind the sum of the first three terms of the same series is \( 81: 16 \). Determine the sum he first ten terms, if the first term is 1024 .

Show that If \( x^{2}-2 x<5 \) then \( x-1< \)

Make \( d \) the subject of the relation in \[ W=M \sqrt{\frac{\left(D^{2}+d^{2}\right)}{2 d^{2}}} \]

Make d the subject of the relation in \[ W=\sqrt{\frac{\left(\Delta^{2}+d^{2}\right)}{2 d^{2}}} \]