Evaluate integral_0^1/16 integral_y^1/4 ^1/2 cos(16 pi x^5)dx dy find the surface area of the sphere x^2 + y^2 + z^2 = 16 inside cylinder x^2 + y^2 = 4y (use the polar coordinate) find the volume of the solid of the cylinder x^2+ y^2 = 16 between the planes z = 1 and x + z = 5 find the volume of the solid that lies in the cone z = squareroot 3x^2+ 3y^2 and below the sphere x^2 + y^2 + z^2 = 4 (use the spherical coordinate) evaluate integral_r (2x^2 + y^2)da where r is the region in the 1^st quadrant bounded by xy = 1, xy = 4, y = 2x, y = 1/2x using x = u and y = v/u assume u > 0 and v > 0

Explain why the two figures below are not similar. use complete sentences and provide evidence to support your explanation. (10 points) figure abcdef is shown. a is at negative 4, negative 2. b is at negative 3, 0. c is at negative 4, 2. d is at negative 1, 2. e

Eric has challenged himself to walk 24,000 steps in 4 days. if eric walks the same number of steps each day, which function represents the number of steps eric still needs to walk to reach his goal with respect to the number of days since he started his challenge? a. y = 8,000x − 24,000 b. y = -8,000x + 24,000 c. y = 6,000x − 24,000 d. y = -6,000x + 24,000

Which scenarios are most effectively explored by conducting an experiment? there is more than one correct answer. select all that apply. researchers want to study the effectiveness of a particular drug for treating migraines. they want to know which dosage of the drug yields the best results with the least side effects. to ensure fair results, the researchers want to ensure that participants and dosage administrators do not know which dosage participants receive. a teacher wants to plan a class fieldtrip and quickly determine where students prefer to go for the class fieldtrip. a car mechanic wants to know which of two engine brands makes better-performing engines. he wants to test the engines in identical situations and rate their performance in a way that can be fairly measured. a chemist studies the properties of a metal compound. she wants to know how the sample size of the metal affects its ability to conduct electricity. she wants to conduct the research in a controlled environment to minimize bias. a realty company wants to know the average income of its clients. the company wants to gather data income from current clients.