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Finding the Solutions of the Equation x4 + 3×2 – 20 = 0 To solve the equation x4 + 3×2 – 20 = 0, we can make a substitution to simplify the problem. Let us set: y = x2 This transforms our equation into: y2 + 3y – 20 = 0 Now, we can solve … Read more

To convert polar coordinates to rectangular coordinates, we can use the formulas: x = r × cos(θ) y = r × sin(θ) Here, r is the distance from the origin, and θ is the angle in radians. Given the polar coordinates (3, 3π/2): r = 3 θ = 3π/2 Now, we can plug in the … Read more

Calculating the Area of a Parallelogram The area of a parallelogram can be found using a simple formula: Area = base × height In this case, if we consider the base to be x + 4 and the height to be x + 3, we can substitute these values into the formula: Area = (x … Read more

To calculate the percentage gain from the sale of the farm, you can follow these steps: Determine the cost price (CP) and selling price (SP): The man bought the farm for $2400 (CP) and sold it for $2700 (SP). Calculate the gain: Gain can be calculated using the formula: Gain = Selling Price – Cost … Read more

To find the exponential function of the form f(x) = ab^x that passes through the given points, we need to use the y-intercept and the point we know. Here are the step-by-step instructions: Start with the general form of an exponential function: f(x) = ab^x. Given the y-intercept (0, 2), substitute x = 0 into … Read more

Calculating the Sum of the Arithmetic Sequence The arithmetic sequence you provided starts at 8 and has a common difference of 6 (14 – 8 = 6 and 20 – 14 = 6). To find the sum when there are 22 terms, we can use the formula for the sum of an arithmetic sequence: Sum … Read more

To convert a Cartesian equation into its polar form, we need to use the relationships between polar coordinates (r, θ) and Cartesian coordinates (x, y). In polar coordinates, the following equations hold: x = r * cos(θ) y = r * sin(θ) Given the Cartesian equation y², we’ll start off by rewriting y in terms … Read more

To solve for y in the equation 3y = 3x, we first need to isolate y. We can do this by dividing both sides of the equation by 3: 3y = 3x => y = x This means that y is equal to x. This form tells us that for every value of x on … Read more

To determine the measure of angle 1 in the diagram of circle C, we first need to understand the properties of circles and the angles formed within them. The measure of angles in a circle can be influenced by several factors such as the position of points on the circumference and the relationships between various … Read more

To express 125×9 + 64y12 as a sum of cubes, we can follow the formula for factoring a sum of cubes, which states: A3 + B3 = (A + B)(A2 – AB + B2) In this case, we need to identify the cubic terms: Recognize that 125 is 53 and 64 is 43. Thus, we … Read more