devyy To find the axis of the graph of the function f(x) = 4x² + 8x – 7, we need to identify the vertex of the parabola, as this point will lie on the axis of symmetry. The standard form of a quadratic equation is: f(x) = ax² + bx + c In our case, the … Read more
To express a complex number in the form of a + bi, where i is the imaginary unit, we start with the polar representation of complex numbers. The polar form of a complex number is given by: r(cos θ + i sin θ) Here, r is the magnitude and θ is the angle in degrees … Read more
The expression arccos(sin(x)) is interesting because it involves the inverse cosine function applied to the sine of x. To find its exact value, we can analyze this step by step: 1. **Understanding the Functions**: The sin(x) function outputs values within the range of -1 to 1. This means we can safely apply the arccos function … Read more
Finding the Maclaurin Series for f(x) = cos(x^3) The Maclaurin series is a special case of the Taylor series centered at 0. To find the Maclaurin series for the function f(x) = cos(x^3), we start by recalling the Taylor series expansion for the cosine function: cos(x) = ∑ n=0 (−1)n / (2n)! * x2n We … Read more
To find the equation of the function y = 2x after it has been translated, we need to follow a couple of simple steps. Translations in the coordinate plane can be expressed mathematically by adjusting the function in the following ways: 1. **Translating Left/Right**: To translate a function to the left, you subtract from the … Read more
To find the diagonal of a square garden when you know its area, you can follow these steps: 1. **Calculate the side length of the square**: The area of a square is given by the formula: Area = side × side Given that the area is 200 m², you can find the side length by … Read more
To simplify the expressions involving square roots, we’ll break them down step by step. Here’s how we can simplify each one: 1. Simplifying √24: First, we can factor 24 into its prime factors: 24 = 4 × 6 = 2² × 2 × 3 Now, we can take the square root of the perfect square … Read more
To express the product of 6 and 34 in radical form, we first need to calculate the product: 6 × 34 = 204 Next, we can express 204 in radical form. To do this, we look for perfect squares that can factor into 204: The prime factorization of 204 is: 204 = 2 × 102 … Read more
To solve for the value of x, we first need to understand the relationship between the angles in triangles RST and MSTU. Given that the angles are expressed in terms of x (specifically, angle RST is 7x and angle MSTU is 8x), we can set up an equation based on the fact that the sum … Read more
To find the distance between two points in a two-dimensional space, you can use the distance formula, which is: D = √((x2 – x1)² + (y2 – y1)²) In this case, the coordinates for point P are (2, 8) and for point Q are (3, 8). We’ll denote: X1 = 2 Y1 = 8 X2 … Read more