# Math

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...

Latest answer posted September 7, 2010 12:47 pm UTC

Math

They're already in increasing order, which is obvious. If you want to "prove" it (in quotes because the fact may be considered so basic as to not need proof), you can always write the numbers with...

Latest answer posted October 24, 2012 5:48 am UTC

Math

We have to prove that tan A + tan B + tan C = tan A*tan B*tan C for any non-right angle triangle. For any triangle the sum of the angles is equal to 180 degrees. If we take a triangle ABC, A + B +...

Latest answer posted June 5, 2011 10:53 pm UTC

Math

A linear equation has the following form: y = mx + b where m is the slopeb is the y-intercept. You can also perform a vertical line test. If the line touches your graphed function in more than...

Latest answer posted October 7, 2013 8:13 pm UTC

Math

Given the equation. x + y= xy We need to find dy/dx We will use implicit differentiation. ==> (x+y)' = (xy)' ==> x' + y' = (x)y' + x'(y) ==> 1 + y' = xy' + y Now we will combine terms with...

Latest answer posted December 6, 2011 8:29 am UTC

Math

The domain and range of the function f(x) = |x - 2| has to be determined. The domain of a function is all values of x for which the value of f(x) is defined. The range of the function is all values...

Latest answer posted August 26, 2014 2:26 pm UTC

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...

Latest answer posted August 3, 2010 12:41 am UTC

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...

Latest answer posted April 24, 2010 5:49 am UTC

Math

Let 1 number be x . Since the numbers are consecutive, the other number would be x + 1. Square both and add together to equal 313. x^2 + (x+1)^2 = 313 x^2 + x^2 + 2x + 1 = 313 2x^2 + 2x -...

Latest answer posted October 27, 2013 8:16 pm UTC

Math

Let the square root of 3 + 4i be x + iy. So (x + iy) (x +iy) = 3 +4i => x^2 + xyi + xyi + i^2*y^2 = 3 + 4i => x^2 – y^2 + 2xyi = 3 + 4i Equate the real and complex terms => x^2 - y^2 = 3...

Latest answer posted December 21, 2010 2:45 am UTC

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...

Latest answer posted July 30, 2014 7:20 am UTC

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)...

Latest answer posted August 17, 2010 8:49 am UTC

Math

We have to find the sum of the series (sin 1)^2 + (sin 2)^2 +...+ (sin 90)^2 (sin 1)^2 + (sin 2)^2 +...+ (sin 90)^2 => (sin 1)^2 + (sin 2)^2 +...+ (sin 90)^2 => (sin 1)^2 + (sin 2)^2 +... +...

Latest answer posted June 21, 2011 1:07 am UTC

Math

-5/3 First you notice if the upper number is larger than the lower number, then the number is greater than 1, so you need to simplify the number by dividing the lower from the upper. So, -5/3 =...

Latest answer posted May 26, 2010 10:28 pm UTC

Math

Given that the number of boys and girls in a class is as follows: Number of boys = 11 Number of girls = 9 Then we conclude that the total number of students in the class= 20 students. Then, the...

Latest answer posted November 29, 2010 7:26 am UTC

Math

Real-life limits are used any time you have some type of real-world application approach a steady-state solution. As an example, we could have a chemical reaction in a beaker start with two...

Latest answer posted September 2, 2012 3:00 am UTC

Math

The answer depends on the margin of how badly you failed your final exam. Here is the equation to calculate your final average, if x=exam grade: .15x + 86 (.85) = Final overall average. So if...

Latest answer posted May 28, 2012 6:30 pm UTC

Math

A very simple example of combinations would be in the number of pizzas one could create given a certain number of criteria. In other word, given that a pizza place has: 3 types of crust -thin,...

Latest answer posted February 10, 2010 1:00 pm UTC

Math

Probability is determined by the number of desired answers divided by the total number of answers. There are 12 possible balls you can draw so the denominator will be 12, there are 4 red balls and...

Latest answer posted June 22, 2010 7:21 am UTC

Math

The letters of the word EQUATION are arranged in a row. The probability that all the vowels are together has to be determined. All the letters of the word EQUATION are unique. The vowels can be...

Latest answer posted March 19, 2012 6:36 pm UTC

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...

Latest answer posted February 26, 2012 10:04 pm UTC

Math

We need to find the integral of cosec 2x dx. Int[ cosec 2x dx] => Int[ 1/ sin 2x dx] => Int[ (sin 2x)/ (sin 2x)^2 dx] => Int[ (sin 2x)/(1 - (cos 2x)^2) dx] => Int[ (sin 2x)/(1 - cos...

Latest answer posted April 7, 2011 5:01 am UTC

Math

You are asking how to determine a linear function from a table and a graph. Linear functions graph as a straight line, no curves allowed. So, if the graph is a straight line, it is the graph of a...

Latest answer posted March 9, 2011 7:59 pm UTC

Math

We have to find the sum of 1+2+3+. . . +100. Here n=100 We have a formula to calculate the sum of n numbers as: Sum=(n(n+1))/2 So we have:  Sum=(100(100+1))/2=5050  Hence the sum is 5050.

Latest answer posted October 9, 2017 12:54 am UTC

Math

Solution: You can answer the problem by rewriting the equation first. That is by using the properties of logarithm. y = log(x + 1/x) y = log((x^2+1)/x) y = log(x^2+1) - log x Now, you have to...

Latest answer posted August 27, 2014 5:40 am UTC

Math

According to logarithm; log_ab = (log_kb)/(log_ka) If we consider k = 10 which is log in base 10 then; log_ab = (logb)/(loga) Similarly we can write;...

Latest answer posted July 10, 2013 11:11 am UTC

Math

A lot of it has to do with what perspective you are looking at. If you consider the chart on the webpage given, there are 36 combination of rolls you can get from two dice. When you consider the...

Latest answer posted August 8, 2014 2:20 pm UTC

Math

Looking at the series of numbers, you can see that any number is 3 times the number right before it. So with each additional term, you have multiplied a number by 3 one more time. This means that...

Latest answer posted July 5, 2012 7:22 pm UTC

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...

Latest answer posted August 10, 2011 4:01 am UTC

Math

y= 16(0.25)^x The exponential equation represents an exponential decay because the rate of decay is 0.25 which is less than 1. The general form equation is: y(x)= a(1-r)^x such that r is the decay...

Latest answer posted May 23, 2012 2:05 am UTC

Math

ok - the question is 3/5 of what number = 15. Try writing an equation to solve the problem. "of" means to multiply. put in a variable (x) for the unknown number. 3/5 * x = 15 to get rid of a...

Latest answer posted August 26, 2015 2:45 am UTC

Math

Let the digits of the number we need to find be ab. So the number is 10*a + b. The digits are reversed when 27 is added to it. We can use this to create the equation: 10*a + b + 27 = a + 10*b =>...

Latest answer posted January 17, 2011 10:41 pm UTC

Math

The word COMBINE has 3 vowels and 4 consonants. If the letters have to be arranged such that the vowels and consonants are not together, the consonants should be placed at positions 1, 3, 5 and 7...

Latest answer posted January 10, 2012 8:50 pm UTC

Math

Show that G={1,w,w^2} where w is a cube root of unity is a cyclic group. It suffices to show that the only subgroup H of G that contains w is G itself. Let H<=G,winH . Now the...

Latest answer posted August 3, 2012 6:58 pm UTC

Math

We have y = cos 2x / (cos x)^2*(sin x)^2 y = cos 2x / (cos x)^2*(sin x)^2 => [(cos x)^2 - (sin x)^2] / (cos x)^2*(sin x)^2 => 1/ (sin x)^2 - 1/ (cos x)^2 Now the integral of 1/ (sin x)^2 =...

Latest answer posted December 22, 2010 1:31 am UTC

Math

You need to remember the formula of mean of numerical elements such that: Mean = sum of elements/the number of elements Mean = (15 +20 + 25 + 30 + 35 + 40 + 45 + 50 + 55)/9 Mean = 35 Notice that...

Latest answer posted January 15, 2012 2:14 am UTC

Math

f(x)=x^3+2 To find the inverse function f(x)^-1 , we will assume" y=x^3+2 y-2= x^3 ==> x= (y-2)^1/3 ==> f(x)-1= (x-2)^1/3

Latest answer posted May 29, 2010 12:54 am UTC

Math

The equivalent resistance of two resistances connected in parallel is given by 1/R = 1/R1 + 1/R2 R = (R1*R2)/(R1 + R2) (dR)/(dt) = ((R1*(dR2)/dt + R2*(dR1)/dt)(R1 + R2) - (R1*R2*((dR1)/dt +...

Latest answer posted March 8, 2012 10:14 pm UTC

Math

You should remember that the absolute value of the complex number z is the magnitude of the vector whose coordinates are such that: Hence, evaluating the absolute value of the given complex...

Latest answer posted July 25, 2012 10:36 am UTC

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=(x-p)(x-q) where p,q are the x-intercepts. One way to...

Latest answer posted February 24, 2015 2:15 am UTC

Math

x = log a (bc) y= log b (ca) z= log c (ab) Prove that : x+ y + z + 2 = xyz We will start from left side: x+ y + z + 2 = log a (bc) + log b (ca) + log c (ab) + 2 We know that: log b (x) = log a...

Latest answer posted July 17, 2010 5:56 am UTC

Math

Hello! A common ratio is a term which applies to a geometric sequence. A geometric sequence starts from any number a and any next term is equal to the previous term multiplied by a fixed number...

Latest answer posted January 18, 2016 7:49 am UTC

Math

Raabe's test is the ratio test for convergence of a series. Consider the limit lim_(n->) |a_(n+1)/a_n| = L Raabe's test says that if L<1 then the series converges. If L>1 then the...

Latest answer posted November 27, 2012 2:59 pm UTC

Math

The roll has 6 sides, the probability of rolling a six when the die is rolled once is 1/6 When rolled 4 times, each time has a probability of 1/6. Then the probability is: 1/6 * 1/6 *1/6 *1/6...

Latest answer posted June 25, 2010 10:03 pm UTC

Math

If a line has no y-intercept, that means it never intersects the y-axis, so it must be parallel to the y-axis. This means it is a vertical line, such as x=3 . This slope of this line is...

Latest answer posted September 26, 2012 12:10 am UTC

Math

A line that is perpendicular to the x-axis is a vertical like with a slope equal to infinity. A line parallel to it would have the same slope and will also be a vertical line perpendicular to the...

Latest answer posted July 1, 2012 5:40 pm UTC

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...

Latest answer posted November 4, 2009 6:52 am UTC

Math

When adding a zero to the numbers, the mean will get smaller. Let us prove it by an example. For example: Let "2, 3, 5, 7, 9" be numbers that their mean is as follow. m = (2+ 3 + 5+ 7+ 9) / total...

Latest answer posted November 29, 2010 7:12 am UTC

Math

The numebers chosen are from 1 to 10. Then possible outcomes are: 1,2,3,4,5,6,7,8,9,10 The probability of chosen a 5 OR and even number = probability of chosen a 5 + probability of chosen an even...

Latest answer posted November 8, 2010 12:12 pm UTC