devyy When considering how the volume of a cell changes in relation to its surface area, it is essential to understand the mathematical relationship between the two. In biological systems, the surface area (SA) and volume (V) of a cell influence its function, transport of materials, and overall growth. The relationship between surface area and volume … Read more
To determine the domain of the equation y = x² + 6x + 1, we need to consider the values of x that can be used without resulting in undefined expressions. This is a polynomial equation, specifically a quadratic equation, where the highest power of x is 2. Quadratic functions are defined for all real … Read more
Converting centimeters to meters is a straightforward process since both units are part of the metric system. The metric system is based on powers of ten, which makes conversions easier than in some other measurement systems. To convert centimeters to meters, you simply need to know the conversion factor: 1 meter = 100 centimeters Therefore, … Read more
To find the slope of a line that is perpendicular to another line, we can use the concept of negative reciprocals. When two lines are perpendicular, the slopes of those lines will multiply together to equal -1. Given that the slope of the original line is 27, we can denote this slope as m. Therefore: … Read more
To find the y-coordinate of the vertex of a parabola given by the equation in the form of y = ax² + bx + c, we can follow these steps: 1. **Identify coefficients**: In our case, the given equation is y = x² + 2. Here, a = 1, b = 0, and c = … Read more
To compute the dot product of vectors v and w in an equilateral triangle, we start by understanding the properties of the triangle and the vectors involved. In an equilateral triangle, all sides are of equal length, which in this case is 1. The angles between each pair of sides are all 60 degrees. Assuming … Read more
To find the cosine of an angle θ whose terminating side passes through the point (20, 21), we need to use the definition of cosine in relation to the coordinates of a point in the Cartesian plane. 1. **Understanding the Coordinates:** In this case, the point (20, 21) represents a position on the terminal side … Read more
To find the values of the six trigonometric functions given that cos(θ) = 4/5 and that the angle θ lies in the third quadrant, we can follow these steps: Step 1: Understanding the Signs of Trigonometric Functions in the Third Quadrant In the third quadrant (from 180° to 270°), the cosine and sine functions are … Read more
To find the best approximate solution of the system of linear equations given by: Equation 1: y = 15x + 1 Equation 2: y = 1 We can start by substituting the expression for y from Equation 2 into Equation 1. Since Equation 2 states that y = 1, we can substitute this value into … Read more
The mode of a data set is the value that appears most frequently within that set. In simpler terms, it is the number or category that occurs with the highest frequency. Understanding the mode is important because it provides insights into the characteristics of the data and helps to identify trends or patterns. For example, … Read more