Which point is on the circle centered at the origin with a radius of 5 units?
To find a point that lies on a circle centered at the origin with a radius of 5 units, we can use the equation of a circle: x² + y² = r² Here, r is the radius of the circle. In this case, r = 5, so the equation becomes: x² + y² = 25 […]
The function gx is defined as shown below what is the value of g3?
To determine the value of g3, we first need to understand the function gx as it is defined in your specific context. However, let’s assume gx is a standard function, such as a polynomial or a piecewise function. Without the exact definition of gx, we can’t give a precise value for g3. Typically, you would […]
Find the center, vertices, and foci of the ellipse with equation 5x² + 9y² = 45
To start, we need to rewrite the given ellipse equation in standard form. The original equation is: 5x² + 9y² = 45 First, divide all terms by 45: x²/9 + y²/5 = 1 This can be expressed as: (x²/9) + (y²/5) = 1 Now we can identify the components of the ellipse: The center of […]
What are the dimensions of a rectangular window with a side length ratio of 15 to 1 and an area of 1350 square inches?
To find the dimensions of the rectangular window, we start by letting the length of the window be represented as 15x and the width as 1x, based on the given ratio of 15 to 1. The area of a rectangle is calculated by multiplying its length by its width. Therefore, we can set up the […]
How to Find the Exact Value of Trig Functions Without a Unit Circle
Finding the exact values of trigonometric functions without using the unit circle might seem challenging, but there are effective methods to do so. One of the main techniques involves using special angles and identities. First, it’s essential to remember that some angles have known values for sine, cosine, and tangent. For instance: sin(0°) = 0 […]
How to Solve for the Inverse Function of f(x) = 5x + 4 – 6 when x = 19?
To find the inverse function of f(x) = 5x + 4 – 6 when x = 19, we will first simplify the function and then solve for its inverse. First, let’s rewrite the function: f(x) = 5x – 2 Next, to find the inverse, we replace f(x) with y: y = 5x – 2 Now, […]
A parabola has a vertex at (1, 0) and opens down; what is the equation of the parabola?
To derive the equation of a parabola that has its vertex at a certain point and opens in a specific direction, we can use the vertex form of a parabola’s equation. The vertex form is given as: y = a(x – h)² + k In this equation, (h, k) represents the coordinates of the vertex, […]
What is the divisibility rule for 9?
The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. For example, consider the number 729. To determine if it is divisible by 9, we first add its digits: 7 + 2 + 9 = 18. Since 18 is divisible by 9, […]
How to Find the Arc Length Function for the Curve y = 2x^3 with Starting Point P(0, 54)
To find the arc length function for the curve defined by the equation y = 2x^3, we use the arc length formula: L = ∫√(1 + (dy/dx)²) dx First, we need to calculate the derivative dy/dx. For the given curve: y = 2x³ Taking the derivative: dy/dx = 6x² Now, we substitute this into our […]
Which equation is the inverse of 2x + 22 = 87y?
To find the inverse of the equation 2x + 22 = 87y, we need to solve for y in terms of x. First, we start by isolating y on one side of the equation. Subtract 22 from both sides: 2x = 87y – 22 Next, add 22 to both sides: 2x + 22 = 87y […]