devyy To determine the finance charge on a loan, we first understand that the finance charge represents the total cost of borrowing, which includes interest rates and any additional fees. In this case, we have: Loan Amount: $8,000 Monthly Payment: $162.80 Loan Term: 60 months 1. **Find the Total Amount Paid Over the Loan Term:** Start … Read more
To find the component form of the vector v that lies in the first quadrant, we start by using the information provided: the angle θ is π/3 (or 60 degrees) with respect to the positive x-axis and the magnitude of the vector is 8. The component form of a vector can be expressed as: v … Read more
The trigonometric identity we want to prove is cos(3x) = 4cos^3(x) – 3cos(x). This identity relates the cosine of triple angles to the cosine of a single angle. To demonstrate this identity, we can employ the angle addition formula for cosine. The cosine of the sum of two angles can be expressed as: cos(A + … Read more
Solving the Differential Equation Using Separation of Variables The given differential equation is: x (dy/dx) = 6y To solve this differential equation by the method of separation of variables, we need to rearrange the equation such that all the terms involving y are on one side and all the terms involving x are on the … Read more
To find the zeros of the polynomial function f(x) = 5x^3 – 2x^2 + 8x – 3, we must first set the function equal to zero: 5x^3 – 2x^2 + 8x – 3 = 0 This is a cubic polynomial, which can potentially have up to three real zeros. We can use various methods to … Read more
To convert the quadratic function from vertex form to standard form, you first need to understand what both forms look like. The vertex form of a quadratic equation is typically given as: f(x) = a(x – h)^2 + k Where: a is a coefficient that affects the width and direction of the parabola. (h, k) … Read more
The slope of a line is a measure of how steep the line is, and it is calculated by using the formula: Slope (m) = (y2 – y1) / (x2 – x1) In this case, the two points given are (1, 5) and (3, 2), where: (x1, y1) = (1, 5) (x2, y2) = (3, … Read more
To determine the length of a long rod in foot spans after measuring it initially with pace spans, we first need to understand the relationship between the two types of measurements. A pace span typically refers to the distance covered by one full step of an individual, often measured at an average of 2.5 to … Read more
The quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8), and D(8, 5) can be classified as a trapezoid and more specifically, a right trapezoid. Here’s why: 1. **Understanding the Vertices**: The vertices of the quadrilateral are A(4, 4), B(5, 8), C(8, 8), and D(8, 5). When we plot these points on a Cartesian … Read more
To find the equation for the nth term of the given arithmetic sequence, we first need to identify the properties of the sequence. An arithmetic sequence is defined by the fact that the difference between consecutive terms is constant. 1. **Identify the First Term and Common Difference**: From the sequence: 15, 6, 3, 12, we … Read more