The roots of the quadratic function f(b) = b² – 75 can be found by solving the equation for when f(b) = 0. This leads us to: b² – 75 = 0 To find the roots, we can rearrange the equation to: b² = 75 Next, we take the square root of both sides: b … Read more
When all values in a data set are the same, the sample variance is equal to zero. To understand why this is the case, let’s first define what variance is. Variance measures the spread of data points in a data set. It quantifies how much the values deviate from the mean (average) of the data … Read more
To calculate the probability of drawing a heart or a 9 from a deck of cards, we first need to understand the composition of a standard deck. A full deck contains 52 cards, which are split into 4 suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Among these, there are also 4 … Read more
To find the equation of the tangent line to the curve y = sin(x) at a given point, we will perform the following steps: Determine the point of tangency: In this case, the point given is (p, 0), where we need to ensure that y = sin(p) should equal 0. For this to be true, … Read more
To find the value of b² – 4ac for the quadratic equation x² + 5x + 4 = 0, we first need to identify the coefficients a, b, and c from the standard form of a quadratic equation, which is: ax² + bx + c = 0 From the given equation: a = 1 (coefficient … Read more
To find the value of wb
To create a function f(x) that has a domain of [0, 5] and a range of [0, 0], we need to ensure that for every x in the domain, the output of the function is constrained to only one value—namely, 0. An example of such a function is: f(x) = 0 In this case, no … Read more
To completely factor the expression x2 + 8x + 16, we first need to identify if it can be factored into the product of two binomials. The approach we will take involves recognizing it as a perfect square trinomial. A perfect square trinomial takes the form (a + b)2 = a2 + 2ab + b2. … Read more
Finding the Length of the Curve y = 5 – 8x³ + 2x + 1 To find the exact length of a curve defined by a function, you can use the formula for arc length. The general formula for the length of the curve from x = a to x = b is given by: … Read more
To solve for f(3) and f'(3), let’s start by understanding the situation with a tangent line. We know that the tangent line to the function y = f(x) at the point (3, 2) indicates that: 1. The value of the function at x = 3 is f(3) = 2. 2. The slope of the tangent … Read more