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Akshay K.
Tutor for 5 years, College Senior in Computer Science
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Pre-Calculus
TutorMe
Question:

Solve the equation sin(x) = -1/2 on the domain [0, 2pi].

Akshay K.
Answer:

Since sin(x) is negative we know the answers will lie in quadrant 3 and quadrant 4 (where tangent and cosine are the only positive values respectively). We take the arcsin of both sides leaving us with arcsin(sin(x)) = arcsin(-1/2) which equals x = arcsin(-1/2). That means that x will be the angle, a, that is formed when sin(a) = -1/2. sin(a) = 1/2 when a is pi/6, or 30 degrees. Therefore the coterminal angles for pi/6 in quadrants 3 and 4 are 7pi/6 and 11pi/6.

Java Programming
TutorMe
Question:

A number group contains a group of integers defined in some way. It could be empty, or it could contain one or more integers. a) Write an interface named NumberGroup that represents a group of integers. The interface should have a single contains method that determines if a given integer is in the group. A range represents a number group that contains all (and only) the integers between a minimal value and a maximum value, inclusive. b) Write the Range class, which is a NumberGroup. The Range class represents the group of int values that range from a given minimum value up through a given maximum value, inclusive.

Akshay K.
Answer:

a) public interface NumberGroup{ boolean contains(int x); } b) public class Range implements NumberGroup { private int min; private int max; public Range(int mi, int ma) { min = mi; max = ma; } public boolean contains (int x) { if( x >= min && x <= max) { return true; } else { return false; } } }

Biology
TutorMe
Question:

Fossils of lobe-finned fishes, which are ancestors of amphibians, are found in rocks that are at least 380 million years old. Fossils of the oldest amphibian-like vertebrate animals with true legs and lungs are found in rocks that are approximately 363 million years old. Three samples of rocks are available that might contain fossils of a transitional species between lobe-finned fish and amphibians: one rock sample that is 350 million years old, one that is 370 million years old, and one that is 390 million years old. a) Select the most appropriate sample of rocks in which to search for a transitional species between lobe-finned fishes and amphibians. b) Describe TWO pieces of evidence provided by fossils of a transitional species that would support a hypothesis that amphibians evolved from lobe-finned fishes.

Akshay K.
Answer:

a) Rocks from the 370 million year old sample should be used to identify a transitional species between lobe-finned fishes and amphibians since transitional fossils are found between 380 million years ago and 363 million years ago. b) To support the hypothesis that amphibians evolved from lobe-finned fishes we would have to look at similarities in the DNA or the combination of phenotypic traits expressed by both amphibians and lobe-finned fishes.

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