devyy To find the values of b such that the function f(x) = x² + bx + 14 has a maximum value of 86, we start by observing the structure of the function. This function is a quadratic equation in the standard form f(x) = ax² + bx + c, where a = 1, b = … Read more
The radius of a circle is a fundamental concept in geometry that refers to the distance between the center of the circle and any point on its circumference. To put it simply, if you draw a line from the very center of the circle straight out to the edge, that line is the radius. To … Read more
To analyze the concavity of the given curve, we first need to establish the equations for dydx and d²ydx². The given parametric equations are: x = 2sin(t) y = 3cos(t) 1. **Finding dydt**: We must first find the derivatives of x and y with respect to t: dx/dt = 2cos(t) dy/dt = -3sin(t) 2. **Finding … Read more
Understanding the Axis of Symmetry In the context of a quadratic equation, the axis of symmetry is a vertical line that divides the graph into two mirror images. It plays a crucial role in understanding the properties of the graph, particularly when it comes to identifying the vertex and the direction in which the parabola … Read more
Converting a decimal to a fraction may seem tricky at first, but it’s a straightforward process! Here’s a step-by-step guide to help you: Identify the decimal: Start with the decimal you want to convert. For example, let’s use 0.75. Count the decimal places: Next, determine how many digits are after the decimal point. In our … Read more
To find all solutions of the equation tan(x) sec(x) = 1 within the interval [0, 2π], we start by rewriting the equation in a more manageable form. Recall that: tan(x) = sin(x)/cos(x) sec(x) = 1/cos(x) Now, substituting these definitions into the equation: tan(x) sec(x) = (sin(x)/cos(x))(1/cos(x)) = sin(x)/cos²(x) Setting this equal to 1, we have: … Read more
To determine the greatest common factor (GCF) of the polynomial terms 12×4, 27×3, and 6×2, we start by breaking down each coefficient and the variables. Step 1: Factor the coefficients – The coefficients are 12, 27, and 6. – The prime factorization of each coefficient is as follows: 12 = 22 × 3 27 = … Read more
To find the equation of a line that passes through the point (6,3) and is perpendicular to the line represented by the equation 4x + 5y = 10, we need to follow a few steps involving some basic concepts of linear equations and slopes. Step 1: Find the slope of the given line The first … Read more
Dividing the Expression by x² To divide the expression (3x³ + 2x² + x + 2) by (x²), we will break the division down and simplify it term by term. Step-by-Step Process Start with the expression: 3x³ + 2x² + x + 2. Separate the expression by dividing each term by x²: 3x³ ÷ x² … Read more