29. In un triangolo la base ê lunga \( 2+4 x \) cm e l'altezza 20 om. Determina x in modo tale che il triangolo abbia area minore di quella del quadrato che ha per latol la meta dell'altezza.

\( \left. \begin{array} { l } { f ^ { \prime } ( x ) = ( \frac { 1 } { 2 \sqrt { x } } + x ^ { - 1 / 2 } ) ^ { 2 } - ( \frac { 1 } { 2 \sqrt { x } } - x ^ { - 1 / 2 } ) ^ { 2 } } \\ { f ^ { \prime } ( x ) = ( \frac { 1 } { 2 \sqrt { x } } + \frac { - 1 } { 2 } x ^ { - 3 / 2 } ) ^ { 2 } - ( \frac { 1 } { 2 \sqrt { x } } - - \frac { 1 } { 2 } x ^ { - 3 / 2 } ) ^ { 2 } } \end{array} \right. \)

1.) \( \sqrt{18}=4 \)

The area of a righe angled criangle is \( 6 \mathrm{~cm}^{2} \). The base is 4 cm long. What is the height? A triangle of 12 cm high has an area of \( 48 \mathrm{~cm}^{2} \). What is the length of its base? Calealare the area of cach of the following a. A rectangle with a leagth of 12.5 cm and a breadth of 15 mm b. A sequare with one side \( 13,5 \mathrm{~cm} \) fong c. A square with a perimeter measurement of 100 cm d. A recrangle with a perimeter of 16 m and one side 3 m long

Select all the true statements. If vertical angles are congruent, then two lines cut by a transversal are parallel. If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Points on a perpendicular bisector of a line segment are equidistant from the segment's endpoints. Points on a perpendicular bisector of a line segment are not equidistant from the segment's endpoints.

Find the derivative of the function using the definition of derivative. \( g(u)=\frac{u+1}{8 u-1} \) \( g^{\prime}(u)= \) State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)