The roots for the given quadratic equation are x1 ≈ 2.46625 and x2 ≈ -1.21625. For solving the quadratic equation 4x² – 5x – 12 = 0 we apply the quadratic formula, this method is a steadfast solution strategy when facing any quadratic equation of the form ax² – bx – c = 0. Below we […]

# Category Archives: Algebra Q&A

Expert Answer: The greatest integer function is not differentiable on any real value of x because this function is discontinuous on all the integer values, and it has no or zero slopes on every other value. We can see the discontinuity in Figure 1. Let f(x) is a floor function which is represented in Figure […]

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 […]

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 […]

This problem aims to find the average value of a function on a given interval and also find the slope of that function. This problem requires knowledge of the fundamental theorem of calculus and basic integration techniques. To find the average value of a function on a given interval, we will integrate and divide the […]

This question aims to learn the basic methodology for optimizing a mathematical function (maximizing or minimizing). Critical points are the points where the value of a function is either maximum or minimum. To calculate the critical point(s), we equate the first derivative’s value to 0 and solve for the independent variable. We can use the […]

[ h(x) = (x + 2)^3 ] The question aims to find the functions f and g from a third function which is a composition of the function of those two functions. The composition of functions can be defined as putting one function into another function that outputs the third function. The output from one […]

This problem aims to understand the exponential growth and exponential decay. An exponential function is a function in which the exponent is a variable, and the base is positive and $cancel{=}space 1$. For example, $f(x)=4^x$ is an exponential function and the exponent is not a mutable but a specified constant. $f(x) =x^3$is a fundamental polynomial […]

The main objective of this question is to find the maximum revenue for the given conditions. This question uses the concept of revenue. Revenue is the sum of the average selling price multiplied by a number of units sold, which is the amount of money generated by a business’s typical operations. Expert Answer First, we […]

$60cdot 60cdot 24cdot 7cdot 365$ $1000cdot 60cdot 60cdot 24cdot 365$ $24cdot 60cdot 100cdot 7cdot 52$ $1000cdot 60cdot 24cdot 7cdot 52$ The goal of this question is to convert a year into milliseconds by selecting a suitable formula from the list provided. For this operation, disregard the use of months in the calculation. They have irregular […]

The question aims to find the standard form of an algebraic equation. The question is based on the concepts of algebraic equations, particularly linear equations with two variables. Linear equations are algebraic equations with variables only having an exponent of one. These equations represent a linear straight line as shown in Figure 1. The equation of […]

-The two lines with the following equations intersect at a point. [r=(2,3,0) + t (3,-3,2)] [r=(5,0,2) + s (-3,3,0)] -(a) Find out the point of intersection of these two lines. -(b) Find the equation of the plane having these two lines. In this question, we have to find two things: the point of intersection and […]

The main objective of this question is to find the coefficient of the term $x^5y^8$ in the expansion of $(x+y)^{13}$ using the Binomial theorem or expansion. The binomial theorem was first mentioned in the fourth century BC by Euclids, a famous Greek mathematician. The binomial theorem also known as binomial expansion in elementary algebra represents […]

This problem aims to find the Taylor polynomials up to $3$ places for a given function $f$, centered at a point $a$. To better understand the problem, you must know about Power Series, as it forms the basis of the Taylor Series. Taylor series of a function is defined as an infinite sum of derivative […]

This problem aims to find the values of a function having alternate independent variables. A table is given to address the values of $x$ and $y$. These formulas would be required to find the solution: [ f_x(x,y)=lim_{h to 0}dfrac{f(x+h, y)-f(x,y)}{h}] [ f_y(x,y)=lim_{hto 0}dfrac{f(x, y+h)-f(x,y)}{h}] [ f_{xy}=dfrac{partial}{partial y}left(frac{partial f}{partial x} right)=dfrac{partial}{partial y}(f_x] Expert Answer: Part a: […]

3 and 16 2 and 4 4 and 8 4 and 16 In this question, we have to find the pair of numbers for which the LCM is 16. LCM stands for Least Common Multiple, defined as the smallest multiple common number between the required numbers for which LCM is to be determined. It is […]

The main objective of this question is to find the next number in the given series. The number sequence is an important mathematical tool for assessing intelligence. Many aptitude exams include number series problems. These questions usually follow a numerical pattern along with a logical rule. Sequences and series are important in many aspects of […]

the function that assigns to each pair of positive integers the first integer of the pair. the function that assigns to each positive integer the largest decimal digit. the function that assigns to a bit string the number of ones minus the number of zeros in that string. the function that assigns to each positive […]

This question aims to explain the concepts of maxima and minima. Formulas to calculate the extreme values of the function. Further, it explains how to calculate the distance between the points. In mathematics, the length of the line segment between the two points is the Euclidean distance between two points. The Pythagorean theorem is used […]

The purpose of this question is to prove that $n$ is a positive and even integer if and only if $7n + 4$ is also even. Even numbers can be equally divided into two pairs or groups and are completely divisible by two. For instance, $2, 4, 6, 8$, and so on are said to […]