Evaluate \( \int \sec (11+12 x) \cdot \tan (11+12 x) d x \)

\( \begin{array}{l}A=5^{2} \times 7^{4} \times 11^{p} \\ B=5^{m} \times 7^{n-5} \times 11 \\ m, n \text { and } p \text { are integers such that } \\ m>2 \\ n>10 \\ p>1\end{array} \) (b) Find the highest common factor (HCF) of \( A \) and \( B \) \( \quad \) Give your answer as a product of powers of its prime factors.

Debido a un error en su programa, el contador de tiempo en un reproductor de vídeo no comenzó a contar hasta que el video ya había avanzado varios segundos. El reproductor empezó a contar en 0 segundos, aunque el vídeo ya había avanzado 190 cuadros. El vídeo reproduce 25 cuadros por segundo. ¿Cuántos cuadros había avanzado el vídeo cuando el tiempo era igual a \( -3 \frac{2}{5} \) segundos?

Fill in the blank so that the following statement is true. The first step in solving \( \frac{x-7}{x+8}=\frac{x-1}{x+4} \) is to multiply both sides by The first step in solving \( \frac{x-7}{x+8}=\frac{x-1}{x+4} \) is to multiply both sides by

The function \( f(x)=2 x^{3}-36 x^{2}+210 x+9 \) has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. This function has a local minimum at \( x=7 \) with output value: and a local maximum at \( x=\square \) with output value:

Find the angular speed \( \omega \) for the following. a wind turbine with blades turning at a rate of 11 revolutions per minute The angular speed for a wind turbine with blades turning at a rate of 11 revolutions per minute is (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any