Questions

To determine both the distance covered and the displacement of the athlete after 2 minutes and 20 seconds, we must first understand the physical properties involved in circular motion. 1. **Calculate the Circumference of the Track:**The circumference (C) of a circle is calculated using the formula: C = π × d Where d is the … Read more

To grasp the graph of the compound inequality x < 3 or x > 9, we first need to understand what the individual parts of this inequality mean. The compound inequality consists of two separate inequalities: x < 3 and x > 9. 1. Analyzing the first part: x < 3 This inequality means that … Read more

To find angle mfeh in a circle, we need to consider some fundamental properties of angles in circles. Since we know that mfgh measures 50 degrees, we can use the concept of angles subtended by the same arc. In a circle, angles that subtend the same arc are related. Specifically, if angle mfgh subtends arc … Read more

The sequence presented is a fascinating example of a number pattern where the differences between the consecutive numbers seem to follow a specific trend. Let’s analyze it step by step! Here are the numbers in the sequence: 107 98 90 83 77 68 65 Now, if we calculate the differences between each consecutive pair: 107 … Read more

To estimate the volume of the solid that lies below the surface z = xy and above the rectangle R defined by 0 ≤ x ≤ 6 and 0 ≤ y ≤ 4, we can use double integration. The volume V can be represented as: V = ∬R z dA Here, R is the projection … Read more

To find the total number of tickets sold over the four days, you will need to gather the number of tickets sold each day. Let’s assume you have the following data: Day 1: 150 tickets Day 2: 200 tickets Day 3: 180 tickets Day 4: 220 tickets Next, you add these amounts together: 150 + … Read more

Understanding the Algebraic Expression The algebraic expression 2x + 7 + 10 can be rewritten for clarity. We can simplify this expression by combining like terms. The constants 7 and 10 add up to give us 17. Now, the expression looks like this: 2x + 17 This leads us to the phrase that corresponds to … Read more

Finding the Vertex and Axis of Symmetry To find the vertex and axis of symmetry of the given quadratic function, we can follow a systematic approach. Step 1: Identify the coefficients In the quadratic function f(x) = 3x² + 12x + 6, we can identify the coefficients: a = 3 b = 12 c = … Read more

To find the length of AB, we can use the properties of tangent lines and the relationships between the tangent, radius, and chord. Given: AO (the radius) = 24 BC = 27 (a chord passing through point B) First, we need to realize that when a tangent segment (AB in this case) meets the radius … Read more

To determine how many different committees of 7 people can be formed from a group of 10 people, we can use the concept of combinations from combinatorial mathematics. The formula for combinations is given by: C(n, r) = n! / (r! * (n – r)!) Where: n is the total number of items to choose … Read more