Math: Page 21

In this video, the instructor shows you how to graph quadratic equations. When you have a quadratic equation in terms of x and y, first try to identify the coefficients of the terms. Now use front end of the quadratic formula to find the line of symmetry which is the first half of the vertex using the formula x = -b/2a. This gives the line of symmetry. Next, plot the line using a few points starting at the line of symmetry. Take sample values of x and find the corresponding values of y on...

This video shows how to find the formula of a piecewise function when given a graph. The first step is to write a definition for the graph, which is done by identifying the different domains shown in the graph. The second step is writing formulas for each domain specified by the lines in the graph. The point-slope formula is used to identify the slope and y-intercept for the leftmost domain, which has a sloped line. A point and horizontal line make for simpler equations in the other pieces of...

The tutorial is part of a full lesson of pre algebra. This video teaches you what reflection is as a mathematical term. In the beginning of the video, the video maker draws 4 shapes labeled MNOPQ, ABCDE, FGHIJ and RSTUV. The first question in the video asks to "Name the figure that represents a reflection of ABCDE over the X-axis." The woman in the video repeats the question, stating the horizontal line is the X-axis and asks for the reflection image. She puts her hand on ABCDE and flips her...

Keith M. Bower explains the meaning of mean and standard deviation. This educational video gives insight in the basics of statistics. The relations between population mean and sample mean and between population standard deviation and sample standard deviation are explained. The mean gives an idea on the central tendency. Standard deviation gives an idea about how spread out the data are. Keith also explains how these two parameters, the joint sufficient statistics, define a normal distribution....

This video shows the method to simplify expressions with different exponents. The video starts with the explanation of 16 raised to the power 1/4. This can be solved by taking the nth or the 4th root of 16 where n stands for the denominator of the fraction. Then the video explains 8 raised to power 4/3. This can be solved in two ways. First one involves taking the cube root of 8 and raising it to the power of 4. The second method involves converting 8 into 2 raised to the power 3 and taking the...

In this video, Robert Ahdoot becomes "surfer dude" and shows us the ways of deductive reasoning, as relating to geometry. He begins with a simple example of a syllogism, taking two premises and using them to form a conclusion. This is called the Law of Syllogism. This concept is then used for geometric statements. If two angles are complementary, they sum to 90 degrees. If two angles sum to 90 degrees, then they are acute. By the law taught, it can be said that if two angles are complementary,...

This is a mathematical instructional video on finding the point slope form of a line equation. This technique allows you to find the x and y intercepts of a line. The point slope form is (y-y1)=m(x-x1). The instructor tells you what each of the variables represents, and shows an example. He then shows you how to find the slope-intercept form from the point slope form. Finally, he shows you how to graph the line using both of the equations. He shows you how to find the equations with different...

In this video the instructor shows how to solve mixture problems using two variables. Usually in these kind of questions the problem statement goes like, if A costs $x for a pound and B costs $y for a pound, in what ratio should they be mixed such that one pound of the new mixture sells for $z a pound. So, in these kind of problems start with a box where you list down all the given data in the form of a table as shown in the video. Now denote the unknown quantity of A and B by two variables and...

JustMathTutoring This video shows the procedure of finding derivatives using the Chain Rule. The Chain Rule states that the derivative of a composition of functions is the derivative of the outside function evaluated at the inside multiplied by the derivative of the inside. This can be stated as if h(x) = f[g(x)] then h'(x)=f'[g(x)]g'(x). This is explained by two examples. In the first example we find the derivative of the sine of square of 'x'. We take the derivative of sine at square of 'x'...

You Tube User robichaudd teaches you how to simplify a complex fraction with 3 fractions top and bottom. Your result should be 1 fraction over 1 fraction. To do this you must find the L.C.D. at the top, which x cubed. That is the largest variable there. Thus, the L.C.D. at the bottom is x squared. Now you want to make each x below the fraction line be x cubed, respectively x squared. You then have one large fraction over one large fraction. But that is just one large fraction multiplied by the...

The video shows us how to solve a system of equations with the elimination method. First write the two equations one on top of the other, as it is going to be elimination method and it is recommended to write it in that way. Here the 2 equations are x+y=-3 and x-y=1. In the elimination method we need to add the 2 equations by columns. So adding it column wise we get to have 2x=-2 and solving this we will get the value of x=-1. Then you need to substitute this value of x in any of the two...

In this video the instructor shows how to sketch the graph of x squared and square root of x. The first equation is the x squared which is y = x * x. Now to sketch this take a sample values of x and substitute in the equation to get the value of y. Similarly find the set of points for the equation. Finally plot these points and sketch this graph which is in the form of a parabola. The curve is in the form of alphabet 'U' with its vertex at the bottom. Now similarly take the square root of x...

This video teaches the method to find the area of triangle using law of cosines and law of sines together with the area formula. Law of cosines is used when you have the length of three sides. It states that the square of side 'a' is equal to addition of the squares of sides 'b' and 'c' minus the product of 2, b, c and cosA. The values of sides are substituted and angle A is found. This is substituted in the area formula which states that the area of a triangle is equal to the half of the...

It is easy to find out that right triangle is only half of the square. And again there is a rectangle with a triangle shaded in red color. The red triangle is half the area of the rectangle. But to calculate just the area of triangle, we can calculate the area of the rectangle whose area is length times width. When we have a rectangle with its length and width as 4u and 2u respectively then the area of that rectangle will be equal to 8u(squared). But we already know that the triangle is half of...

In this video the instructor teaches about equivalent fractions. When given a problem to determine if two fractions are equivalent fractions the first thing to do is write them in the lowest terms. A fraction is said to be in the lowest terms if the greatest common divisor of both numerator and denominator is one. So cancel the common factors in the numerator and the denominator till you arrive at the lowest form and finally compare them to determine if they are equivalent. An equivalent...

The video is about how to find the variance of the set of data. They found the variance by using the variance formula. Variance formula was represented by square of S, whereas S is the Standard Deviation.

In this video the instructor shows the different methods of solving quadratic equations. There are many methods to solve quadratic equations each with its pros and cons, each method suitable for a particular situation. The first method to solve quadratic equation is factoring. The advantage of using this method is that it is quick and easy. But the problem is not all equations can be factored very easily. This method requires a lot of practice and intuition. Use this method when the...

In this video the instructor shows how to solve systems of linear equation by graphing. A system of linear equation is equations of two lines that are to be graphed on the same coordinate axes. Now take the first equation and write it to form y = mx + b. Now extract the value of slope m and graph the line as shown in the video. Similarly graph the equation of the second line as shown in the video. Now if the two lines intersect at a point, that point is the solution to the system of that linear...

In this how-to video the person gives a detailed evaluation of the functions of the ti-89 calculator. The video is a short but informative look at the Ti-89 calculator. During the video the person shows a difficult math problem and shows how to use the Ti-89 calculator to solve that problem. The video uses some of the functions on the calculator and shows a display of where the buttons are located on the calculator. It also shows how to properly use the calculator to solve the problem while...

In this video the instructor shows how to do temperature conversions using y = m*x + b. Now if Celsius is represented by the variable C and Fahrenheit is represented by the symbol F, you can replace then in the previous equation in place of the variables x and y giving you the equation C = m*F + b. Now to solve for the values of the constants m and b you need to have values of two sample temperatures in both Celsius and Fahrenheit. Take the first sample and substitute in the above equation...

Taking this formula 9x²+y²=9 your instructor shows you how to find the solution for the variable y. Finding a second derivative is no more difficult that finding the first derivative, you only have to do the problem equation through twice. The derivative of 9x² will be 18, of y² will be 2y [this is the same as 2(y), 2 x y or 2 * y]. The problem now goes -18x + 2y dy/dx=0. This equation is solved for dy/dx making the next step in the problem go -18x 18x+2y dy/dx=0-18x, 2y dy/dx= -18x. The next...

In this video the instructor shows how to graph linear inequalities. A linear in a equation is almost similar to a linear equation except for the sign in the equation. Now treat the in equation as a linear equation and graph the line. So substitute the lesser than or greater than symbol in the liner in equation with the equals to sign and graph the equation. Find the slope of the equation and identify the points that the line passes through. Now take a point on the either side of the pointed...

In this video the instructor shows how to factor the GCF and difference of squares. When you are asked to factorize a number or monomial or a polynomial, the way to do is break it down into individual terms. When asked to factorize a binomial, try to pull out any common terms and factorize the simplified equation. When you are asked to factorize the difference of squares use the general formula which states that the factors of (a*a - b*b) is (a-b) * (a+b). Now substitute the given values in...

YAYMATH. This video is a demonstration of usage of the distance formula to find the distance between two given (x,y) points. In this video, the tutor guy who is teaching the distance formula to his students takes an example of two (x,y) points such as (5,-1) and (11,7). He then writes the distance formula on the board. The formula goes like this, the distance between two points, denoted by 'd' is equal to the square root of the sum of the square of (x2-x1) and the square of (y2-y1) where (5,-1)...

In this video the instructor shows how to solve rational equations. If you have fractions in your equation, then you need to factorize the denominators first. Now compute the least common denominator of all the denominators of the fraction. Next multiply both sides of the equation with the least common denominator. This cancels out all the denominators of all the fractions and you are left with a linear equation. Now simply multiply the remaining terms in the numerator and add common terms to...

Video Nerd thinks that when your doing long division with decimals you should first take out the decimal. Write the number as if it didn't have a decimal. For example if the problem was 12.5 divided by 5 then you will just use 125 and divide that by 5. Next divide the first digit of the dividend by the divisor an write the number up top. Next you multiply, after your done multiplying the numbers subtract, and when your done subtracting the numbers drop the reaming numbers in the dividend down....

In this video tutorial, viewers learn how to solve for the circumference and area of a circle. The circumference is the distance around a closed curve. The formula for circumference is C= pi x d. The diameter is two times the radius (d= 2r or r= d/2). The value of pi is approximately 3.14. The formula for the area of a circle is A= Pi x r^2. This video provides examples and demonstrations on how to use and solve with both the formulas. This video will benefit those viewers who are struggling...

This video shows the way to name a line segment. A line segment begins and ends with an end point. We can name a line segment by naming the two end points of the line segment. The example shown in the video shows a line segment that ends with points named 'A' and 'C'. So, we can name this line segment as segment 'AC'. This can also be named as segment 'CA'. The example shown consists of a point 'B' in between 'A' or 'B'. We cannot name the line segment as segment 'AB' or 'BA' and segment 'BC'...

If you are given an equation of ellipse in the form of a function whose value is a square root, you may need to simplify it to make it look like the equation of an ellipse. Now equate the function to a variable y and perform squaring on both sides to remove the radical. Now simplify the equation and get it in the form of (x*x)/(a*a) + (y*y)/(b*b) = 1 which is the general form of an ellipse. Now you will have the x and y intercepts which are a and b respectively. Using this values graph the...

This video is a tutorial on how to convert Celsius to Fahrenheit. The title of the film says it will teach you how to convert Fahrenheit to Celsius, but it does not. It does just the opposite. The video begins by comparing Fahrenheit and Celsius. He points out that Fahrenheit measures water to freeze at 32 and water to boil at 212. Celsius measures water to freeze at 0 and water to boil at 100. To convert Celsius to Fahrenheit, multiply the Celsius temperature by 1.8 and add 32. Many countries...

Algebra – The Distance Formula.This video describes how to find the distance between 2 points of a graph in a step by step method. Made by Ya Math, the instructor assists the class in finding the distance between (6,8) and (3,4) by showing us the equation d=v((x_1-x_2 )^2+(y_1-y_2 )^2 ) In this equation, 6 and 3 are the x axis numbers and the 8 and 4 are the y axis numbers respectively, thus v((6-3)^2+(8-4)^2 ) Working from the inside the radical, the instructor subtracts the parenthesis...

In this video, the instructor shows how to find the order of operations with fractions and decimals. If you have an equation with both fractions and decimals, you can convert the decimals to fractions, or fractions to decimals to have the entire equation in either decimals or fractions. In this video, the instructor shows how to do this in either way. To convert fractions to decimals, just divide the numerator with the denominator. This method cannot be used if the decimals are repeating...

In this video the instructor shows how to factor a trinomial with negative leading coefficient. Most of the students are confused when they have to factor a trinomial with a negative leading coefficient. But there are many ways to solve these kind of problems as shown in this video. One way you can do is that take out the greatest common factor (GCF) of -1 from the equation. So pulling the -1 gives you the original trinomial with all the signs of the terms changed. Now go on and factor the new...

This video focuses on how to do long division. She starts by dividing 1548 by 26, going incrementally between each value. She first take 26 into the first three numbers of 1548 (154) and gets 5, then takes the remainder of 24 (154-130) and brings down the 8 to get 248. She then divides 248 by 26 to get 9 with a remainder of 14. She then goes into some detail as to how to extract the decimal from the remainder by continuing the long division and adding zeros to the end of the divisor. At...

Here we look at squaring expressions that involve radicals because people tend to make some common mistakes while solving such expressions. Take 5 times the square root of y quantity squared, the answer here is not 5y. Here's the reason, square means to multiply something with itself so the square of 5 root y would be 5 root y into 5 root y. So 5 x 5 is 25 and under root y into under root y equals just y so the answer will be 25y.Now take under root of (x-3) being added into 7 quantity...

In this video the instructor shows how to solve a quadratic equation. If you have a quadratic equation with complex fractional terms and you find that a particular term is repeating then equate that term to a new variable and replace the variable in the given equation. Now try to get the equation a*x*x + b*x + c = 0, and solve for the roots of the equation which gives the values of the intermediate variable. But this variable was replaced instead of another term. So equate that term to the...

The following are the steps to describe how-to factor a number:

In this video the instructor talks about Pythagorean theorem and how to apply it to right triangles. Pythagorean theorem states that in any right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse the sum of the squares of the lengths of the legs is equation to the square of the length of the hypotenuse. That is a*a + b*b = c*c. This theorem works only for right angled triangle. So if you have the lengths of the two legs of a right triangle substitute the...

When you need to compute the square root of a number you can do it by breaking it into perfect squares. When you can split the given number into small perfect squares you can cancel out the square root of the expression to the square of the perfect squares. You cannot always write the number inside the square root as a perfect square, but try to write this number as a product of a perfect square and another number. Now you can pull out the perfect square out of the radical and leave the...

In this video the instructor shows how to find out an equation of a perpendicular line. If you need to find the equation of a line passing through the given point and perpendicular to another line, the first thing you need to do is compute the slope of the given line. Obtain the slope of the equation by writing it in the form of y = mx + b. Now the product of slopes of two perpendicular lines is negative one. So the slope of our required line will be negative inverse of the slope of given line....