An observer standing 300 m from a vertical cliff uses a surveying instrument to determine that the angle of elevation of the top of the cliff is \( 52^{\circ} \). Calculate the height of the cliff, to the nearest metre. Draw the suitable diagram to help answer the question.

Divide using the long division method. \( \frac{8 y^{3}-44 y+30}{2 y-4}=\square \)

Identify the false statement regarding the steps in constructing a bending diagram. A. project the lines from the space diagram downwards B. select the appropriate scale C. draw a vertical line from one point to another D. show that the bending moment is a point equal to zero

From a hang-glider 1 km from a beach, the angle of depression of the beach is estimated at \( 10^{\circ} \). What is its altitude? Draw the suitable diagram to help answer the question.

3. ( 1,0 punto) Calcular el valor de a para que la función siguiente sea continua: \( f(x)=\left\{\begin{array}{ll}x+1 & \text { si } x \leq 1 \\ 3-a x^{2} & \text { si } x>1\end{array}\right. \)

A line passes through the points \( \mathrm{V}(8,1) \) and \( \mathrm{W}(10,2) \). What is the gradient of a line: a parallel to VW ? b perpendicular to VW ?