### Find the length and width of a rectangle that has the given area and a minimum perimeter.

Area of Rectangle A = 49 ft^(2) The aim of this article is to find the dimensions of a rectangle whose area A is known and it is assumed that it has the minimum perimeter P. The basic […]

### The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base. Find the volume of the Solid.

This question aims to find the volume of the solid whose base forms an elliptical region. The cross-section perpendicular to the x-axis forms isosceles right triangles with hypotenuse as seen in the line shown in Figure 1. The concept of this question is based on the basic geometry of shapes like the area and volume […]

### Estimate the angle to the nearest one-half radian.

Figure (1): Angle given in the question statement The aim of this question is to develop the ability to estimate angles to the nearest half radian just by visualizing them. To estimate such angles, we need to imagine a circular scale of our choice in accordance with our required precision. If we choose a circular […]

### If the atomic radius of lead is 0.175 nm, calculate the volume of its unit cell in cubic meters.

The aim of this question is to calculate the volume of a unit cell, giving due attention to the lettuce structure of the given metal. The uniform spatial arrangement scheme of atoms, molecules, and/or ions is called crystal structure. The overall crystal structure can be divided into smaller basic elements that can be spatially repeated to […]

### Find the point on the hyperbola xy = 8 that is closest to the point (3,0).

To solve this question, we have to determine the point on the hyperbola xy = 8 that is closest to the point (3,0). A hyperbola is defined as a conic section that is produced by the intersection of a plane and circular cone at any given angle so that halves of the circular cone are […]

### How many square feet is Rhode island?

The aim of this question is to learn unit conversions between different customary units in use in the United States of America. Rhode Island is the smallest state out of all the states within mainland of the United States of America. Its area is 776,960 acres. Although the international unit of area is square meters, there […]

### Find the point on the line y = 4x + 3 that is closest to the origin.

The aim of this problem is to find a point that is nearest to the origin. We are given a linear equation which is only a straight line in the xy-plane. The nearest point from the origin will be the vertical distance from the origin to that line. For this, we need to be aware […]

### Find the point on the line y=2x+3 that is closest to the origin.

This problem aims to find a point that is closest to the origin. A linear equation is given, which is just a simple line in the xy-plane. The closest point from the origin will be the vertical distance from the origin to that line. For this, we need to be familiar with the distance formula […]

### Find the area of the parallelogram whose vertices are listed. (0,0), (5,2), (6,4), (11,6)

This article aims to find the area of the parallelogram. This article uses the concept of the area of the parallelogram. A parallelogram bounds a parallelogram‘s area in a given two-dimensional space. As a reminder, a parallelogram is a particular type of quadrilateral with four sides, and the pairs of opposite sides are parallel. In parallelogram, opposite sides […]

### The minute hand of a certain clock is 4 in long, Starting from the moment when the hand is pointing straight up, how fast is the area of the sector that is swept out by the hand increasing at any instant during the next revolution of the hand?

This article aims to find the area of a sector. This article uses the concept of the area of a sector. The reader should know how to find the area of the sector. Area of sector of a circle is the amount of space enclosed within the boundary of the sector of circle. The sector always starts from […]

### Rectangle has area 16 m^2. Express the perimeter of the rectangle as a function of the length of one of its sides.

– If the length of the rectangle is assumed to be larger than its width, calculate the domain of the Perimeter $P$ in terms of interval notation. The purpose of this guide is to derive an expression for the perimeter $P$ of the given rectangle in terms of the length of one of its sides […]

### Identify the surface whose equation is given. ρ=sinθsinØ

The aim of this question is to find the surface corresponding to the Spherical Coordinates $p=sintheta sinphi$ by utilizing the Cartesian Coordinate system and Equation of Sphere. First, we will explain the concept of Sphere, its Equation, and its Coordinates in the Cartesian Coordinate System. A Sphere is defined as a $3D$ geometrical structure have […]