### The graph of a function f is shown. Which graph is an antiderivative of f?

This question explains the concept of antiderivative and how to draw its graph from the function graph. The antiderivative of a function is the indefinite integral of the function. If we take its derivative, it will give out the original function. The derivative and antiderivative or indefinite integral are inverse of each other. The derivative […]

### A bridge is built in the shape of a parabolic arch. The bridge has a span of 130 feet and a maximum height of 30 feet. Choose a suitable rectangular coordinate system and find the height of the arch at distances of 10, 30, and 50 feet from the center.

This question aims to find the height of a parabolic bridge 10 feet, 30 feet, and 50 feet from the center. The bridge is 30 feet high and has a span of 130 feet. The concept needed for this question to understand and solve include basic algebra and familiarity with arches and parabolas. The equation of the […]

### A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. Find the following:

What is the electric potential at the point on the x-axis where the electric field is zero? What are the magnitude and direction of the electric field at the point on the x-axis, between the charges, where the electric potential is zero? This question aims to find the electric potential at the point on x-axis […]

### Solve the system of equations and show all work.

y = x^2 + 3 y = x + 5 This question aims to solve the linear equation system and calculate the variable’s values. In mathematics, a set of simultaneous equations, also known as a system of equations or equation systems, is a limited set of mathematics equations required by the exact solutions. The mathematical […]

### Find an expression for the function whose graph is the given curve. The expression of the curve is x^2 + (y – 4)^2 = 9.

This question aims to find an expression for the function whose graph is given by the curve $x^2 + (y – 4)^2 = 9$. The graph is shown in Figure 1. This question is based on the concept of circle geometry and basic calculus. We can find an expression of the function from the given […]