If f(x) = 2x^2 + 1, what is f(x) when x = 3?
To find f(x) when x = 3, we need to substitute 3 into the function f(x) = 2x² + 1. First, we calculate x²: 3² = 9 Next, we multiply this result by 2: 2 * 9 = 18 Finally, we add 1 to this value: 18 + 1 = 19 So, f(3) = 19. […]
Describe Inverse Trigonometric Functions
Inverse trigonometric functions are functions that reverse the action of the standard trigonometric functions. When we apply a trigonometric function to an angle, we get a ratio (like sine, cosine, or tangent). The inverse trigonometric functions allow us to take that ratio and find the angle that produces it. For example, the sine function takes […]
Find the slope of the function which is the slope of the tangent line to the graph of the function y = x² + 2x + 3 at the point x = 1
To find the slope of the tangent line to the function y = x² + 2x + 3 at the point x = 1, we first need to calculate the derivative of the function. The derivative represents the slope of the tangent line at any given point. We start by differentiating the function: y’ = […]
What is the value of x if one exterior angle of a regular pentagon measures 2x degrees?
To find the value of x, we first need to determine the measure of an exterior angle of a regular pentagon. The formula for the measure of an exterior angle of a regular polygon is: Exterior Angle = 360° / n Where n is the number of sides of the polygon. For a pentagon, n […]
Triangle ABC is an Isosceles Right Triangle. What is the Measure of One Base Angle?
In an isosceles right triangle, two sides are of equal length, and the angles opposite those sides are also equal. By definition, an isosceles right triangle has one 90-degree angle and two other equal angles. Since the sum of all angles in a triangle must equal 180 degrees, we can calculate the measure of the […]
The product of two consecutive negative integers is 600. What is the value of the lesser integer?
To find the lesser of two consecutive negative integers whose product is 600, we can start by defining the integers. Let’s denote the lesser integer as x. Therefore, the next consecutive integer can be defined as x + 1. Based on the problem, we can set up the equation as follows: x 0(x + 1) […]
How to Solve the Initial Value Problem: xy² dx + 2xy – x² dy = 0 with y(1) = 1?
To solve the initial value problem given by the equation xy² dx + 2xy – x² dy = 0, we start by rearranging the equation. 1. Rewrite it in a more manageable form: xy² dx = x² dy – 2xy 2. Now, divide both sides by xy² to isolate dy/dx: dy/dx = (2xy – xy²) […]
How to Graph the Solution of y = x² + 2x
To graph the solution of the equation y = x² + 2x, follow these steps: Identify the Type of Function: This is a quadratic function, which means its graph will be a parabola. The general form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants. […]
What is the quotient when 3x³ + 11x² + 26x + 30 divided by x + 5?
To find the quotient of the polynomial division of 3x³ + 11x² + 26x + 30 by x + 5, we can use polynomial long division. Step 1: Divide the leading term of the dividend (3x³) by the leading term of the divisor (x). This gives us 3x². Step 2: Multiply the entire divisor by […]
What is the quotient 3x³ ÷ 10x² ÷ 10x ÷ 4 ÷ 2?
To find the quotient of the expression 3x³ ÷ 10x² ÷ 10x ÷ 4 ÷ 2, we need to simplify it step by step. First, let’s break it down: Start with the coefficients: 3, 10, 10, 4, and 2. The variables are all some power of x. Now, simplify the coefficients: First, divide 3 by […]