### Math Questions and Answers

Math

### What do the letters R, Q, N, and Z mean in 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

### How do you place 0.2, 0.22, 0.222, 0.2222, and 0.22222 on a number line?

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...

Math

### Prove that tanA + tanB + tanC = tanA tanB tanC for any non-right angle triangle

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 +...

Math

### How do I determine if this equation is a linear function or a nonlinear function?

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...

Math

### Please explain the following: If x + y = xy, then dy/dx = ?

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...

Math

### What is the domain and range of the function f(x) = |x - 2|

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...

Math

### If you are traveling 50 miles at 60mph how long would it take you to get there????

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

### If the radius of a circle is doubled, what effect does this have on the area of the circle? On the circumference? ...

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

### The sum of square of two consiquative natural number is 313.find the number?

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 -...

Math

### What is the square root of 3 + 4i?

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...

Math

### 1. When 2 dice at thrown, what is the probability of the sum being 9? 2. Two cards are picked at random from a...

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

### Given f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+3

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

### Calculate sin^2 1+sin^2 2 +...+ sin^2 90.

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 +... +...

Math

### How to represent -5/3 on the number line?

-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 =...

Math

### A class has 11 boys, 9 girls. Two students will be selected at random to serve on committee. What's probability that...

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...

Math

### How are limits (Calculus limits) used or applied to daily life? Or applied to the real world problems? I need a...

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...

Math

### what if you have an B 86% in a class and you fail your final exam that is 15 % of your grade, then what percentage...

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...

Math

### Give a real-world example of how permutations and combinations can be used. Explain what your numeric result means in...

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,...

Math

### A bag contains 4 red balls, 3 green balls, and 5 yellow balls. What is the probability of drawing a red or a green...

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...

Math

### The letters of the word EQUATION are arranged in a row. Find the probability that the all vowels are together.

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...

Math

### If 1 year is equal to 365 days, how many seconds are there in a year.

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

### What is the integral of cosec 2x dx ?

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...

Math

### How do you determine a linear function from a table and graph?

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...

Math

### Add 1 plus 2 plus 3 plus 4. . . all the way to 100.

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.

Math

### #2 What is dy/dx if y = log(x+1/x).

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...

Math

### The value of (log2(3))(log3(4))(log4(5))(log5(6))(log6(7))(log7(8)) is equal to; A) 2 B) 4 C) log7(8) D) log2(7)...

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;...

Math

### When 2 dice are thrown the sum of the numbers that turns up is 10. What is the probability that one of the dice has a...

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...

Math

### Find the nth term of the series 1, 3 , 9 , 27...

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...

Math

### Give a practical example of the use of inverse functions.

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

### Determine if its a growth or decay.Then find the percent increase of decrease. 1.y=16(.25)^x 2.y=0.8(1.28)^x...

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...

Math

### 3/5 Of 15

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...

Math

### The digits of which two digit number are reversed when 27 is added to it.

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 =>...

Math

### In how many ways can the letters of the word COMBINE be arranged so that vowels and consonants do not come together.

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...

Math

### Prove that the set {1,w,w^2}, where w(omega) is a cube root of unity, is a cyclic group with respect of multiplication.

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...

Math

### Evaluate the integral of function y=cos2x/cos^2x*sin^2x.

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 =...

Math

### Find the mean, mode and median from the following 15, 20, 25, 30, 35, 40, 45, 50, 55

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...

Math

### Find the inverse function of f(x)=x^3+2?

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

Math

### If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance R measured in ohms...

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 +...

Math

### Which is the module of the complex number z = 3 - 4i ?

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...

Math

### How do you find the vertex of a function in intercept form?

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...

Math

### If x = log[a]bc y = log[b]ca z = log[c]ab ptove that x+y+z+2 = xyz

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...

Math

### What's the common ratio for 4, 12, 36, 108, ... ?

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...

Math

### State and prove Raabe's Test.

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...

Math

### What Is The Probability Of Getting A 6 Each Time If A Die Is Rolled 4 Times?

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...

Math

### If a line has no y-intercept, what can you say about the line? What if a line has no x-intercept? Think of a...

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...

Math

### The equation of a line that is perpendicular to the x-axis and passes through the point (2, -1).

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...

Math

### 5/3 As A Mixed Number

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

### What happens to the mean of a set of numbers when a zero is added to the set?

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...

Math

### A number from 1 to 10 is chosen at random. What is the probability of choosing a 5 or an even number?

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...

Math

### Solve for b2:A= 1/2h (b1+b2)

A = 1/2h(b1+b2) Multiply both sides by 2 2A = h(b1+b2) Multiply both sides by 1/h 2A/h = b1+b2 Add -b1 to both sides 2A/h + -b1 = b2 Answer: b2 = 2A/h - b1

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