devyy Solutions to the Quadratic Equation To find the solutions of the quadratic equation 3x² + 14x + 16 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / (2a) In this equation, the coefficients are: a = 3 b = 14 c = 16 Now, … Read more
The area of a circle can be calculated using the formula: A = πr2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle. In this case, the radius (r) is given as 4. To find the area, we will substitute the … Read more
To find the derivative of the function y tan x with respect to x, we need to apply the product rule of differentiation. The product rule states that if you have a function that is the product of two functions, say u and v, the derivative is given by: (uv)’ = u’v + uv’ In … Read more
A triangular pyramid, also known as a tetrahedron, consists of four triangular faces. When a plane intersects this pyramid, the shape of the resulting cross-section depends on the position and angle at which the plane cuts through the pyramid. For a plane to slice through a triangular pyramid and produce a quadrilateral cross-section, it must … Read more
In triangle ABC, when we refer to it as a right triangle, we’re acknowledging that one of its angles is a right angle, which measures 90 degrees. By definition, a right triangle has one angle that is exactly 90 degrees, and the other two angles must be acute angles, meaning they are less than 90 … Read more
To solve the quadratic equation x² + 5x = 0, we can utilize the method of factoring. First, let’s factor the equation to find its roots. 1. Begin by rewriting the equation: x² + 5x = 0 2. Next, factor out the common term, which is x: x(x + 5) = 0 3. Now, set … Read more
To understand whether sin(30°) is equal to sin(150°), we can start by using the unit circle and understanding the properties of sine in different quadrants. The sine function is defined as the ratio of the opposite side to the hypotenuse in a right triangle. It can also be visualized on the unit circle, where the … Read more
An obtuse angle is defined as any angle that measures more than 90 degrees but less than 180 degrees. Visually, you can identify an obtuse angle by its broad appearance; it looks more open and ‘sprawled out’ compared to acute angles, which are sharp and narrow, and right angles, which form a perfect corner at … Read more
To determine the factors of the polynomial x² + 20, we will look for expressions that can multiply to give us this polynomial. Firstly, we notice that x² + 20 does not factor easily into linear factors with real coefficients because it doesn’t equal zero for any real values of x. However, it can be … Read more
When we talk about 4 to the second power, we are referring to the mathematical expression 42. This means that we multiply the number 4 by itself. To break it down: 42 = 4 x 4 Now, let’s calculate: 4 x 4 = 16 So, 4 to the second power equals 16. This is a … Read more