QuestionWhich of the following is a factored form of 3x^3y^3 + 3xy? A. 3xy(x^2y^2 + 1) B. 3(3x^2y^2) C. (3x + 3y)(3x + 3y) D. 3x^2y^2(xy) E. 3x(x^2y^2 + 3) AnswerThe correct answer is A. This problem requires you to find the Greatest Common Factor. The Greatest Common Factor is 3xy, because each term has at least 1 factor of 3, 1 factor of x, and 1 factor of y. When you factor 3xy out of 3x^3y^3 you are left with x^2 y^2 , and when you factor 3xy out of 3xy, you are left with 1. Therefore, when factored, 3x^3 y^3 + 3xy = 3xy(x^2 y^2 + 1).
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Free Image from Pixabay Astronomers have found over 400 planets orbiting stars. The discovered planets have a variety of compositions, masses, and orbits. Despite the variety, the universal rules of physics and chemistry allow scientists to broadly categorize these planets into just a few types: Gas Giant, Carbon Orb, Water World, and Rocky Earth. Table 1 shows the composition of the various planet types and typical mass ranges relative to Earth. Table 2 shows a sampling of planets orbiting various stars described in Table 1. These planets are merely numbered 17. Table 2 details the masses and orbital radii of the planets. Questions:1. The data in Table 1 and Table 2 support which of the following statements? A. Gas Giant planets have the largest orbital radii. B. Orbital radius is directly related to mass. C. Orbital radius is inversely related to mass. D. The data does not support a correlation between mass and orbital radius. 2. According to Table 1 and Table 2, which of the following stars has the most massive Gas Giant planet orbiting it? F. Gliese 777 G. OGLE TR 132 H. PSR 1257 J. Gleise 581 3. If a new planet were discovered, with a mass of 325, an orbital radius of 1.5, and a composition of mostly hydrogen, what would be its most likely classification? A. Carbon Orb B. Water C. Rocky Earth D. Gas Giant Answers1. D
2. F 3. D QuestionA waffle ice cream cone is pictured above. If the volume of the cone is 14.4pi cubic inches, what is the diameter of the cone (in inches)? AnswerAnswer is 6.
Solution: The volume of a cone is found by using the formula V= 1/3 x pi x r^2 x h, where r is the radius of the circular base and h is the height. Input the known data and solve for r. 14.4pi = 1/3 pi r^2 (4.*) 14.4 = 1.6 r^2 9 = r^2 3 = r or, d, the diameter is 6. Free Image from Pixabay Question:A gymnast has a routine in which he sways back and forth on a high bar, making an arc that measures 135 deg. As he swings, the bottom of his shoes create an arc that measures 9 feet. At the conclusion of his routine, he swings completely around for one full circle around the bar. What is the circumference of that circle (answer in feet)?
Image from Pixabay Questions:1. An element consists of three isotopes in the relative abundance given below. What is the atomic mass of this element?

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