
Math
The letters R, Q, N, and Z refers to a set of numbers such that: R = real numbers includes all real number [inf, inf] Q= rational numbers ( numbers written as ratio) N = Natural numbers (all...

Math
The easiest way I have for knowing the difference between linear and nonlinear is the exponent value on the variable x. It is important to understand the root word in linear. It is LINE. A...

Math
Your sister is 2 years younger than you as when you are 4 she is 2(half your age); therefore when you are 100 your sister is 98 years old.

Math
Primary and secondary data fall within the scope of statistics and can be used as part of a research method. The collected data may assist a company in measuring, assessing and discussing the...

Math
f(x) = 2x g(x) = x + 3 First let us find (fog)(x) (fog)(x) = f(g(x) = f(x+3) = 2(x+3) = 2x + 6 ==> (fog)(x) = 2x + 6 Now let us find (gof)(x): (gof)(x)...

Math
We know that the area of the circle is given as the following function: A = (r^2)*pi where r is the radius. But we know that: C = 2r ( c is the circumference) ==> r = C/2 Now substitute...

Math
A square and a rectangle each have 4 sides and 4 angles. The only difference between them is that a square is a rectangle with equal sides. Both have 4 90 degree (right) angles. A triangle has 3...

Math
Math is necessary for even the most basic of life functions. Whether you're buying groceries, determining a budget for yourself, calculating interest on investments, or carrying out a whole myriad...

Math
Another method is knowing to take the derivative of f(x) = sin^2(x) + cos^2(x) f '(x) = 2 sin(x) cos(x) + 2 cos(x) (sin(x)) = 2 sin(x) cos(x)  2 cos(x) sin(x) = 0 Since the derivative is zero...

Math
We are traveling at a speed S = 60 m/h The distance we are traveling is D = 50 m We know that: Speed (S) = distance (D)/ Time (T) 60 = 50 / T ==> T = 50/60 = 5/6 hour ==> T = 5/6 * 60 minutes...

Math
The average of the four numbers is 8. This gives the sum of all the four numbers as 8*4 = 32. As the sum of three of the numbers is 22, the fourth number is 32  22 = 10. The correct answer is...

Math
A ball is thrown into the air with an initial velocity of 40 ft/s vertically upwards. t seconds after it has been thrown up, the height of the ball is given by the function `f(t) = 40t  16t^2` ....

Math
What you have to remember here is the formulas for area and circumference of a circle. The area of a circle is equal to the square of its radius times pi. The circumference of a circle is equal to...

Math
Hey Shelly, All of these answers are great, but unless you get a better conceptual understanding of the basic parts of a slope intercept equation you will continue to struggle with these equations...

Math
A linear function is one that has the form f(x) = ax + b. Here for each value of x there is only one corresponding value of f(x) and every value of f(x) is due to only one particular value of x. In...

Math
Method 1 : Use the base 10, 100, 1000 system to find the decimal. Make sure you mark 0.3 with a repeating 3. Methond 2: Divide the numerator of the fraction by the denominator (e.g. 4/9 = 4 ÷...

Math
Let the length be "L" and the width "W" We know that the ration is 5:3 Then, L/W = 5/3 Cross multiply: ==> 3L = 5W ==> L = (5/3)*W .......(1) Also, it is given that the perimeter P is 32:...

Math
1 year consists of 365 days. 1 day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. This gives the number of seconds in an hour as 60*60 = 3600 and the number of seconds in a...

Math
We need to prove that: sec^2 x +csec^2 x = (sec^2 x)(csec^2 x) Let us start with the left side: We know that secx= 1/cosx and csec x = 1/sinx ==> sec^2 x+ cosec^2 x= 1/cos^2 x + 1/sin^2 x =...

Math
tan75: method (1): tan75 = sin75/cos75 = sin(45+30)/cos(45+30) = (sin45cos30+sin30cos45)/(cos45cos30  sin45sin30) = [sqrt2/2*sqrt3/2 +...

Math
First we need to calculate the area of the floor Since it is a rectangulal floor, then the area to be covered is L*I= 9*3=27 m ^2 =270,000 cm^2 Now we need to cover the area with (n)...

Math
In arithmetic the least common multiple (LCM) of two numbers a and b is the smallest positive integer that is a multiple of both a and b. So, the multiples of 3 are : 3, 6, 9, 12, ...The multiples...

Math
Empirical probability of an event is estimated by observing results of actual experiments. For example, if you wanted to know the probability of the number 6 turning up when a fair die is rolled...

Math
The circle should pass through the three points (7,4),(4,5) and (0,3) Call the center of the circle P. Then PA=PB=PC since all radii of a circle are congruent. PA=PB implies that P lies on the...

Math
f(x)= x^2  5 The domain are all x values that has images. As you see, we do not have any restrictions on the values of x . ==> Therefore, the domain is all real numbers. As for the range,...

Math
The square root of 169 is 13. This is so because 13 times 13 gives 169  the definition of a square root of a number k is the number such that when you multiply it by itself you get k. Note that...

Math
To find 10% of a number, just move the decimal one place to the left. 10% of 123 is 12.3 or, multiply the number by the decimal equivalent. 10% is also written as .10 500 x .10 = 50. 20% is also...

Math
Given f(x) = e^3x We need to find the first derivative f'(x) using the chain rule. We will assume that u= 3x ==> u' = 3 ==> f(x) = e^u ==> Now we will differentiate: ==> f(x) = (e^u)' =...

Math
e^2x3e^x +2 =0 Let us assume that e^x =y. Now substitute: ==> y^2 3y +2 =0 Factorize:\ (y2)(y1)=0 y1= 2 ==> y1=e^x1= 2 ==> x1=ln2 y2=1 ==> y2=e^x2= 1 ==> x2=0 The solution for...

Math
This should be soled as integrals by parts. In Integrals by parts it says if U and V are fuctions then, `intUdv = UVintVdu` So let us take U= x and V=e^(2x) Then by differentiation with respect to...

Math
Think about what you know. First, you are dealing with fractions, which means that each part has to be equal. Second, you know that if you add 3 of those equal parts together you get 15. The next...

Math
Give the formula for the following sequence: 4, 12, 36, ... Since 4 x 3 = 12, and 12 x 3 = 36, you can determine that this is a geometric sequence in which the common ratio is 3. Geometric...

Math
Graph y=x. This is not a function so you will not be able to enter it directly into the y= screen of the TI83. You will have to break it into two different functions. y=x ==> x=y for...

Math
A "mixed number," in math terms, is a whole number with a fraction attached to it. What you have posted in your question is essentially an "improper fraction," a situation that occurs when the top...

Math
`121 = 11 X 11` `==> sqrt121 = sqrt(11X 11) = 11` `==> sqrt121 = 11` `` ``

Math
Melody has two coins that equal 15 cents. What are the two coins if one of them is not a nickel? This really is a word problem. That is to say, it is a trick problem. One of the coins is not a...

Math
You need to remember that the vertices of the square lie on the circumference of circle and the center of circle is also the midpoint of diagonals of the square. Notice that diagonals of the...

Math
The number "x" is represented as a letter because it is a variable. This is the idea of the type of math that is named algebra. Replacing the variables with single letters (sometimes English...

Math
f(x)=x^3+2 To find the inverse function f(x)^1 , we will assume" y=x^3+2 y2= x^3 ==> x= (y2)^1/3 ==> f(x)1= (x2)^1/3 https://www.youtube.com/watch?v=Ec5YYVxyq44

Math
The result of the following have to be found by applying the rules of BODMAS: 3 x (10+5) + (48/6)/4  7 = 3 x 15 + 8/4  7 => 45 + 2  7 => 40 3 + 4x6  8 = 3 + 24  8 = 27  8 = 19 6  (7+3)...

Math
Problem 1. When a die is thrown the outcome can be any of the numbers from 1 to 6. If two dice are thrown the set of outcomes that ensure the sum is 9 is {(3, 6), (6,3), (4, 5), (5, 4)}. The total...

Math
We have to find x if the distance between (3,5 ) and ( x,8) is 5. Now the distance between ( x1, y1) and ( x2, y2) is given by sqrt[(x1x2)^2+(y1y2)^] Here x1 = 3, y1 = 5, x2 = x and y2 = 8 =>...

Math
We have to solve for x: x^3 +x^2 +x +1 = 0 x^3 +x^2 +x +1 = 0 => x^2( x + 1) + 1(x + 1) = 0 => (x^2 + 1)(x + 1) = 0 x + 1 = 0 => x = 1 x^2 + 1 = 0 => x^2 = 1 => x = i , i The...

Math
`sqrt(3)sinx+cosx=1` `sqrt(3)sinx=1cosx` `3sin^2x=12cosx+cos^2x`  square both sides `3(1cos^2x)=12cosx+cos^2x`  Pythagorean relationship `4cos^2x2cosx2=0`  clear parantheses and...

Math
How do you find the vertex of the graph of a quadratic function written in intercept form? Intercept form is also known as factored form: y=(xp)(xq) where p,q are the xintercepts. One way to...

Math
Reallife limits are used any time you have some type of realworld application approach a steadystate solution. As an example, we could have a chemical reaction in a beaker start with two...

Math
We can view a function as something that maps things of one type to things of another type. The inverse of a function tells you how to get back to the original value. We do this a lot in everyday...

Math
You need to expand the binomial using the formula `(ab)^2 = a^2  2ab + b^2` . Hence, substituting x for a and 2 for b yields: `(x  2)^2 = x^2  4x + 4` You may also use distributive...

Math
You should check if the tangent function is continuous, hence, you need to check if `lim_(x>1, x<1) tan(pi*x/2) = lim_(x>1, x>1) tan(pi*x/2)` such that: `lim_(x>1, x<1)...

Math
In determining the factorization, it is a good trick to know that when the coefficient of the x^2 is indeed one (as it is in this case), solving for the two factors is much easier. Basically, what...