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To find the volume of a cone, you can use the following formula: Volume (V) = (1/3) × π × r² × h Where: V is the volume of the cone. r is the radius of the base of the cone. h is the height of the cone. π (Pi) is approximately 3.14159. In your … Read more

To solve the expression 222 x 33 x 66, we need to perform the multiplication step by step. First, let’s multiply 222 by 33: 222 x 33 = 7,326 Now that we have the result of the first multiplication, we can take that result and multiply it by 66: 7,326 x 66 = 484,956 Putting … Read more

The function f(x) = 6x^4 – x^2 is a polynomial function characterized by a few key traits: Degree and Leading Coefficient: The degree of the function is 4 (the highest exponent of x), and the leading coefficient is 6, which is positive. This indicates that as x approaches positive or negative infinity, the graph of … Read more

The formula for the volume of a sphere is given by: V = (4/3)πr³ Where V represents the volume, and r represents the radius of the sphere. In this case, we know that: V = 5003π To find the radius r, we can set the two expressions for volume equal to each other: (4/3)πr³ = … Read more

To find the component form and magnitude of the vector qp given the points p(5, 11) and q(6, 4), we need to perform the following steps: Step 1: Find the Component Form The component form of a vector is determined by subtracting the coordinates of the initial point from the coordinates of the terminal point. … Read more

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio. In this case, we have the first term: a1 = 625 and the second term: a2 = 125 To find the common ratio (r), we can use … Read more

Finding the Arc Length Function for the Curve To determine the arc length of a curve defined by a function, we can use the arc length formula. For a function y = f(x), the formula for the arc length L from point x = a to x = b is given by: L = ∫ab … Read more

Finding the Linearization of the Function To find the linearization of the function f(x) = x^4 – 6x^2 + 1 at a specific point a, we can follow a systematic approach involving calculus, specifically the concept of derivatives. Step 1: Choose the Point First, we need to determine the point a at which we want … Read more

To find the function f(x), we need to start from the given equation: f(g(x)) = 3x² + 2x + 1 where g(x) = 2x + 2. This means we need to express the input of f in terms of x using g. First, let’s define g(x): g(x) = 2x + 2 Next, we will solve … Read more

To calculate the volume of a cube, you need to know its dimensions. In this case, we have the dimensions 11 cm, 110 cm, and 110 cm. However, it’s important to clarify that these dimensions do not constitute a typical cube since a cube has equal dimensions on all sides. Instead, this shape is a … Read more