a) Chứng minh ab \( / / \mathrm{cd} \) b) Chứng minh \( \mathrm{MN} \perp \) ab c) Tính số đo góc FGK d) Tia phân giác của góc I I. Chứng minh: \( \mathrm{IF} \perp \mathrm{I} \) 3. Cho hình vẽ bên, biết \( C \) đường thẳng yy'. Chứn a) Hai đường thằng xx’ và b) Đường thẳng m vuông c) Cho \( \overline{A B H}=\overline{H A C} \), chứn với đường thẳng AC .

Consider the line \( y=\frac{2}{5} x \) What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line:

ind the values of the trigonometric functions of the angle (in standard position) whose terminal sid \( (\sqrt{6},-\sqrt{2}) \) \( \sin \alpha=\frac{-1}{2} \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions fo \( \cos \alpha=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for

[6.4] En los ejercicios 61-70 resuelve cada ecuación. \( \begin{array}{llll}\text { 61. } \frac{3}{4}=\frac{12}{x} & \text { 62. } \frac{x}{1.5}=\frac{x-4}{4.5} & \text { 63. } \frac{3 x+4}{5}=\frac{2 x-8}{3} & \text { 64. } \frac{x}{4.8}+\frac{x}{2}=1.7 \\ \text { 65. } \frac{2}{y}+\frac{1}{5}=\frac{3}{y} & \text { 66. } \frac{2}{x+4}-\frac{3}{x-4}=\frac{-11}{x^{2}-16} & \text { 67. } \frac{x}{x^{2}-9}+\frac{2}{x+3}=\frac{4}{x-3} \\ \text { 68. } \frac{7}{x^{2}-5}+\frac{3}{x+5}=\frac{4}{x-5} & \text { 69. } \frac{x-3}{x-2}+\frac{x+1}{x+3}=\frac{2 x^{2}+x+1}{x^{2}+x-6} & \text { 70. } \frac{x+1}{x+3}+\frac{x+2}{x-4}=\frac{2 x^{2}-18}{x^{2}-x-12}\end{array} \)

Un objeto se mueve a lo largo de un eje horizontal de modo que su posición \( S \) está dada por: \( S(t)=t^{3}-12 t^{2}+36 t-30 \), donde \( S \) se mide en metros y t en segundos. ¿Cuándo la velocidad del objeto es cero? ¿Cuando la velocidad del abjeto es positiva?

WORKSHEET: ADolications of Integration For a manufacturer, the marginal cost (in dollars) per unit, \( C^{\prime}(x) \), when producing units is given by \( C^{\prime}(x)=3 x^{2}-60 x+400 \). (a) Given that the total cost of producing the first 2 units is \( \$ 900 \), use integration (b) Herme calculate the total cost of producing the first 5 units.