### Evaluate the double integral y^2 dA, D is the triangular region with vertices (0, 1), (1,2), (4,1)

This article aims to find the double integral of the triangular region with vertices. This article uses the concept of double integration. The definite integral of a positive function of one variable represents the area of the region between graph of the function and the $x-axis$. Similarly, the double integral of a positive function of two […]

### Find the area of the region that is inside r=3cos(Θ) and outside r=2-cos(Θ).

This article aims to find the area under the given curves. The article uses the background concept of the area under the curve and integration. The area under curve can be calculated in three simple steps. First, we need to know equation of the curve $(y = f(x))$, the limits over which area is to be calculated, and axis […]

### At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of $40$ freshmen sharing a common lounge area.

How many international students would you expect to find in a typical cluster? With what standard deviation? This question aims to find the expected number of international students in a typical cluster along with their standard deviation. Take into consideration what a random variable is: a collection of numerical values resulting from a random process. […]

### A major League baseball diamond has four bases forming a square whose sides measure 90 feet each. The pitcher’s mound is 60.5 feet from home plate on a line joining home plate and second base. Find the distance from the pitcher’s mound to first base. Round to the nearest tenth of a foot.

This problem aims to familiarize us with trigonometric laws. The concepts required to solve this problem are related to the law of cosines, or more commonly known as the cosine rule, and the significance of postulates. The Law of cosines represents the connection between the lengths of sides of a triangle with reference to the […]

### Simplify tan(sin^{-1}(x))

This question aims to simplify a trigonometric expression. In mathematics, trigonometric functions (also called circular functions, angle functions, or trigonometric functions) are fundamental functions that relate angle of a right triangle to the ratios of two side lengths. They are widely used in all geometry-related sciences, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among […]