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To find the acceleration of a car that decreases its speed from 20 miles per hour (mph) to 10 mph in a duration of 5 seconds, we can use the formula for acceleration: Acceleration (a) = (Final Velocity – Initial Velocity) / Time In this case: Initial Velocity (u) = 20 mph Final Velocity (v) … Read more

To find the value of cos(θ) given that sin(θ) = 1/3 and tan(θ) = 0, we’ll start by dissecting the provided information. The equation tan(θ) = 0 implies that θ is at a position in the unit circle where the y-coordinate (which corresponds to sin(θ)) is zero. This typically occurs at θ = 0 or … Read more

To find a vector that has the same direction as the vector (4, 4, 6) but a different length, we need to perform a series of steps that involve normalization and scaling. Step 1: Calculate the length (magnitude) of the original vector The length of a vector (x, y, z) is calculated using the formula: … Read more

To find the value of y in triangle FGH, where points J and K are the midpoints of sides FG and FH, we can utilize the properties of midpoints and the Triangle Midsegment Theorem. According to the Triangle Midsegment Theorem, the segment connecting the midpoints of two sides of a triangle (in this case, segment … Read more

The sequence defined by the formula 4n + 3 can be analyzed for its first ten terms. To calculate the sum, we first need to determine each of the first ten terms: For n = 1: 4(1) + 3 = 4 + 3 = 7 For n = 2: 4(2) + 3 = 8 + … Read more

Finding the Second-Degree Polynomial We are looking for a second-degree polynomial of the form: p(x) = ax2 + bx + c We have the following constraints based on the question: p(2) = 5 p(3) = 3 p(2) = 2 There’s an inconsistency in the conditions provided. If we are to maintain that p(2) = 5 … Read more

To analyze the function y = \frac{(3x + 1)(x – 1)}{(x + 5)} for vertical asymptotes and holes, we need to examine both the numerator and the denominator. Step 1: Identify the Holes Holes occur in the graph of a function where both the numerator and the denominator are equal to zero at the same … Read more

One acre of land is equal to 43,560 square feet. This measurement is standardized and widely used in real estate, agriculture, and land development. To put it in perspective, think of an acre as a piece of land that is roughly a football field in size, minus the end zones. It’s enough space to build … Read more

The system of inequalities consists of two distinct parts: y < 0.75x and y > 3x + 2. To determine where the solution set lies, we need to analyze each inequality separately, and then find the region where they overlap on the graph. 1. **Inequality 1:** y < 0.75x - This inequality represents all the ... Read more

To find a unit vector that is orthogonal to both vectors i + j and i + k, we can follow a systematic approach using the cross product. The vectors can be represented as: v1 = i + j = (1, 1, 0) v2 = i + k = (1, 0, 1) Now, we will … Read more