The mass of a particular eagle is twice that of a hunted pigeon. Suppose the pigeon is flying north at \( v_{i, 2}=18.1 \mathrm{~m} / \mathrm{s} \) when the eagle swoops down, grabs the pigeon, and flies off. At the instant right before the attack, the eagle is flying toward the pigeon at an angle \( \theta=58.7^{\circ} \) below the horizontal and a speed of \( v_{i, 1}=39.5 \mathrm{~m} / \mathrm{s} \). What is the speed \( v_{\mathrm{f}} \) of the eagle immediately after it catches its prey?

Найдите наибольшее значение функции \( y=\frac{x^{2}+25}{x} \) на отрезке \( [-10 ;-1] \).

The basic trigonometric identities (1) \( \cos ^{2} \theta+\sin ^{2} \theta=1 \) (2) \( 1+\tan ^{2} \theta=\sec ^{2} \theta \) (3) \( 1+\cot ^{2} \theta=\csc ^{2} \theta \) (4) \( \sin \theta \csc \theta=1, \cos \theta \sec \theta=1, \tan \theta \cot \theta=1 \) (5) \( \tan \theta=\frac{\sin \theta}{\cos \theta}, \cot \theta=\frac{\cos \theta}{\sin \theta} \)

VALUATE dentify the type of proportion that the following problems illustrate. Then solve A car is able to travel 210 km in 3 hours. How far can it travel in 5 hours? A s only 2 people are available, hov

Решите уравнение: \( \log _{3}\left(\sqrt{2} \cos \left(\frac{\pi}{2}-x\right)+\sin 2 x+81\right)=4 \) Найдите все корни этого уравненшя, принадлежашие отрезку \( \left[\pi ; \frac{5 \pi}{2}\right] \)

2. Introducir convenientemente factores \( y \) simplificar: a) \( 2 \sqrt{2}= \)