What is the measure of the angle?
The measure of an angle is defined as the amount of rotation needed to bring one ray of the angle into alignment with the other ray. Angles are measured in degrees or radians. Commonly, angles in a geometric context are measured in degrees where a full circle is 360 degrees. Therefore, you could say a […]
Find the General Solution of the Given Second Order Differential Equation 3y” + 2y’ + y = 0
To solve the second order differential equation 3y” + 2y’ + y = 0, we will use the characteristic equation method. First, we rewrite the equation in standard form, dividing through by 3: y” + (2/3)y’ + (1/3)y = 0 The associated characteristic equation for this differential equation is obtained by substituting y = e^{rt}, […]
How do you write three hundred and sixty seven thousand seven hundred and fifty two in numbers?
Three hundred and sixty seven thousand seven hundred and fifty two is written in numbers as 367752. To break it down: the term ‘three hundred and sixty seven’ refers to the number 367, which represents three hundred (300), sixty (60), and seven (7). The word ‘thousand’ indicates that we need to multiply this number by […]
What is the percent decrease when the balance in a bank account goes from $300 to $60?
To calculate the percent decrease, we first need to determine the amount of decrease and then find out what percentage that decrease is of the original amount. 1. **Calculate the decrease**: Start by subtracting the final amount from the initial amount. Decrease = Initial Amount – Final Amount Decrease = $300 – $60 = $240 […]
What is the reflection of point P(1, 6) on the line x = 1?
To find the reflection of the point P(1, 6) on the line x = 1, we can follow these steps: The line x = 1 is a vertical line that runs through all points where the x-coordinate is equal to 1. This means that any point reflected across this line will have the same x-coordinate […]
What is fx = 8x^2 + 4x written in vertex form?
To convert the quadratic function f(x) = 8x² + 4x into vertex form, we need to complete the square. 1. First, factor out the coefficient of x² from the first two terms: f(x) = 8(x² + rac{4}{8}x) Which simplifies to: f(x) = 8(x² + rac{1}{2}x) 2. Next, to complete the square, we take the coefficient […]
Simplify the square root of 5 multiplied by the cube root of 5
To simplify the expression √5 × ∣5, we start by rewriting the roots in exponent form. The square root of 5 can be expressed as 5^(1/2), and the cube root of 5 can be expressed as 5^(1/3). Therefore, we have: √5 × ∣5 = 5^(1/2) × 5^(1/3) When multiplying numbers that have the same base, […]
What is the name of polyhedrons with twelve flat faces?
The name of polyhedrons with twelve flat faces is a dodecahedron. A dodecahedron is one of the five Platonic solids, which are convex polyhedra with congruent faces of regular polygons. Specifically, a regular dodecahedron consists of twelve regular pentagonal faces. The symmetry and geometric properties of a dodecahedron make it a frequently studied shape in […]
Find the number of sides of a regular polygon if each of its interior angle is 162 degrees.
To determine the number of sides of a regular polygon based on its interior angle, we can use the formula for the interior angle of a regular polygon: Interior Angle (I) = (n – 2) * 180 / n Where n is the number of sides. In this case, we know that each interior angle […]
How can we confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x?
To confirm that the functions f and g are inverses of each other, we need to show that f(g(x)) = x g(f(x)) = x Let’s take each of these statements one at a time: Step 1: Show that f(g(x)) = x To start, we will substitute g(x) into the function f. Let’s assume: g(x) = […]