The inequality 3 < 7c < 4 presents a compound inequality that can be broken down into two separate parts. Let’s analyze what each part means and how we can solve for the variable c. ### Breaking Down the Inequality This inequality essentially states that: 7c > 3 7c < 4 ### Solving the Inequalities … Read more
To find the maximum height attained by the object described by the equation h = 10t – 5t², we can use calculus or complete the square. This equation is a quadratic function of the form h(t) = at² + bt + c, where: a = -5, which is negative, indicating that the parabola opens downward … Read more
To simplify the expression √x^2 × √x^2, we can break it down step by step. The expression can be written as: √x^2 × √x^2 According to the properties of roots, we know that: √A × √B = √{A × B} Applying this property: √x^2 × √x^2 = √x^2 × x^2 This simplifies to: √x^4 Now, taking the fourth root of x^4: … Read more
Understanding the Problem In this scenario, we’re dealing with a class where the final exam scores follow a normal distribution. The mean score for the exam is 73, with a standard deviation of 78. We want to find out the probability that the average score of a randomly selected group of 24 students is less … Read more
Understanding the Graphs of y = 3x and y = 3 * x At first glance, you might think that the expressions y = 3x and y = 3 * x represent two different equations. However, they actually express the same linear function. Let’s break down what this means visually and mathematically: 1. Same Linear … Read more
To find the magnitude of the average force exerted by the bat on the baseball, we can use the impulse-momentum theorem. This theorem states that the impulse (force multiplied by time) is equal to the change in momentum of the object. Step-by-Step Calculation 1. Convert Units: First, we need to convert the speed of the … Read more
To find the completely factored form of the expression 3×5 + 7×4 + 6×2 + 14x, we start by factoring out the greatest common factor (GCF) from all the terms. 1. **Identify the GCF**: The terms are: 3×5 7×4 6×2 14x The coefficients are 3, 7, 6, and 14. The GCF of these coefficients is … Read more
Understanding the Hyperbola The equation of the hyperbola is given as: 16x² – 4y² = 64 To analyze this hyperbola, we first need to rewrite it in standard form. Dividing the entire equation by 64 gives us: \( \frac{x²}{4} – \frac{y²}{16} = 1 \) Identifying the Standard Form The standard form of a hyperbola centered … Read more
To determine the value of m for which the quadratic equation y = 18x² + mx + 2 has exactly one x-intercept, we need to analyze the conditions under which a quadratic equation has a unique solution. This occurs when the discriminant of the quadratic equation is zero. The standard form of a quadratic equation … Read more
To find the height of the airplane above the water when the pilot sights the atoll at a 10-degree angle of depression, we can use some basic trigonometry. The angle of depression is the angle formed by the line of sight of the pilot looking down at the atoll and the horizontal line from the … Read more