devyy The sequence you’ve presented is 2, 4, 8, 16, 32. To find the general term of this sequence, we first need to identify the pattern between the numbers. Each term in the sequence is obtained by multiplying the previous term by 2: 2 × 2 = 4 4 × 2 = 8 8 × 2 … Read more
The Formula for sin(3x) The formula for sinus of a triple angle, specifically sin(3x), can be derived using the angle addition formulas and identities from trigonometry. The formula is given by: sin(3x) = 3sin(x) – 4sin3(x) This means that the sine of three times an angle x can be expressed in terms of the sine … Read more
To factor the polynomial f(x) = x³ + 2x² + 5x – 6, we will follow a systematic approach involving a combination of factoring techniques. Step 1: Identify potential rational roots We can use the Rational Root Theorem to identify possible rational roots of the polynomial. The potential rational roots are the factors of the … Read more
In India, the monetary system uses different units to make large sums of money easier to understand. One of these units is the crore. To clarify, 1 crore is equal to 10 million (10,000,000). Now, when it comes to larger amounts, such as a trillion, the calculation becomes quite straightforward: 1 trillion = 1,000,000,000,000 (1 … Read more
Finding the radius of a circle when you have the length of a chord and the distance from the chord to the center of the circle involves a bit of geometry and algebra. Here’s a step-by-step process to guide you: Steps to Calculate the Radius: Understand the Components:Identify the chord length (let’s call it c) … Read more
To find the completely factored form of the expression xy³ + x³y + xyy + xy + x + xyy + xy + x, we first need to reorganize the terms for clarity. Let’s rewrite the expression: xy³ x³y xyy xy x xyy (again) xy (again) x (again) Now, combining like terms, we have: xy³ … Read more
To solve the quadratic equation x² + 6x + 7 = 0 by completing the square, we’ll follow these steps: Rearrange the equation: Start by moving the constant term to the right side of the equation: x² + 6x = -7 Complete the square: To complete the square, we need to turn the left side … Read more
In a 30-60-90 triangle, the sides are in a specific ratio that helps us easily determine the lengths of the sides based on the shortest leg. The ratio of the sides in a 30-60-90 triangle is 1 : √3 : 2. This means: The shortest leg (opposite the 30-degree angle) is 1 part. The longer … Read more
To find the volume of a sphere when given its diameter, we first need to determine the radius. The radius (r) is half of the diameter, so if the diameter of the sphere is 4 centimeters, the radius is: Radius (r) = Diameter / 2 = 4 cm / 2 = 2 cm Next, we … Read more
To solve the inequality 4 × x + 3 × 2 × 2 × x, let’s first clarify it. The expression needs to be correctly phrased as an inequality. For instance, we could be looking at something like 4x + 3 < 2(2x), which is common in solving inequalities. 1. **Combine Like Terms**: First, simplify ... Read more