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To find f(1) from the function f(x) = 2x + 3, we need to substitute x with 1. Starting with the given function: f(x) = 2x + 3 Now, replace x with 1: f(1) = 2(1) + 3 Next, perform the multiplication: f(1) = 2 + 3 Finally, add the numbers together: f(1) = 5 … Read more

To determine the quadrant in which the angle of 8 degrees lies based on the values of cosine and cotangent, we need to understand the signs of these trigonometric functions in different quadrants. 1. **Cosine (cos)**: The cosine function is positive in the first quadrant

To determine the angle θ that maximizes the area of a triangle when the lengths of two sides are known (let’s call them ‘a’ and ‘b’), we can use the formula for the area of the triangle: Area = (1/2) * a * b * sin(θ) The sine function, sin(θ), reaches its maximum value of … Read more

In geometry, the concept of lines and planes is fundamental to understanding how different shapes and dimensions interact. A key principle is that a plane is defined by at least two distinct points, which means that it inherently requires at least two lines to be established correctly within that plane. To delve deeper, consider the … Read more

The equation of a parabola can be expressed in several forms, but when the vertex is known, the vertex form is the most useful. The vertex form of a parabola is given by: y = a(x – h)² + k In this equation, (h, k) represents the vertex of the parabola. Given that the vertex … Read more

To find the positive integer n that satisfies the given conditions, we can represent the problem using modular arithmetic. 1. The first condition states: when n is divided by 3, the remainder is 2. In mathematical terms, we can express this as: n ≡ 2 (mod 3) 2. The second condition states: when n is … Read more

To determine the relationship between the coefficients a and b in the polynomial ax³ + bx² + c when it is divisible by x² + bx + c, we first need to utilize the principles of polynomial division. Since ax³ + bx² + c is divisible by x² + bx + c, it implies that … Read more

The equation of the parabola is given in the standard quadratic form as f(x) = 5x² + 30x + 6. To find the vertex of this parabola, we can use the vertex formula derived from the general form of a quadratic equation f(x) = ax² + bx + c, where: a = 5 b = … Read more

When a single six-sided die is tossed, it has six possible outcomes, which are the numbers: 1, 2, 3, 4, 5, and 6. To find the odds against rolling a number greater than 4, we first need to identify the outcomes that meet this criterion. The numbers greater than 4 on a die are 5 … Read more

To prove that tan(1) = cot(1), we can start by recalling the definitions of the tangent and cotangent functions. The tangent of an angle is defined as: tan(x) = sin(x) / cos(x) And the cotangent is the reciprocal of the tangent, defined as: cot(x) = 1 / tan(x) = cos(x) / sin(x) Now, let’s focus … Read more