In triangle ABC, the measure of ∠B is 90˚, BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sin F?
Triangle ABC is a right triangle with its right angle at B. Therefore, AC is the hypotenuse of right triangle ABC, and AB and BC are the legs of right triangle ABC. According to the Pythagorean theorem, AB = 12. Since triangle DEF is similar to triangle ABC, with vertex F corresponding to vertex C, the measure of angle∠F equals the measure of angle∠C. Therefore, sinF=sinC. From the side lengths of triangle ABC, sin F= AB/AC = 12/20 = 3/5. Answer: 3/5 or 0.6
Solve the equation sin^2 x + sin x=0 for 0≤ x < 2π.
sin^2 x + sin x = 0 ------> sin x ( sin x + 1 ) = 0 -------> sin x = 0 and sin x + 1 = 0 --------> x= 0, π and x= 3π/2 Answer: x= 0, π, 3π/2
A sample of rats was fed glucose (C6H12O6) containing radioactive oxygen. After a few minutes, where would the radioactive oxygen be found?
In cellular respiration, glucose undergoes glycolysis and is broken down into two pyruvate molecules. These pyruvate pass through the Krebs or citric acid cycle, producing 3 molecules of CO2 (where the radioactive oxygen is found after a few minutes). Answer: CO2