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...

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...

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...

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...

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)...

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...

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...

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...

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 +...

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...

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...

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...

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...

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...

Let x and y be the two numbersWe want x-y = 8 and xy=P as small as possibleAs you wrote, x=8+yOnce you have that, you can substitute into the other equation, and getP=(y+8)y = y^2 + 8yJust as you...

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...

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...

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...

Inequalities are arguably used more often in "real life" than equalities. Businesses use inequalities to control inventory, plan production lines, produce pricing models, and for...

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...

We know the given eqaution y=mx+b represents a straight line with slope m and the y intercept b. So now let us see how to graph the equation y=5x+(-6): Putting x=0, we get y=-6 which implies one...

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 -...

Using F = ma to the direction of travel; `-F = 1000*a` -F is due to the reverse direction of the frictional force. `F = 0.8*1000*9.81 = 7850 N` `-7850 = 1000*a` `a = -7.85m/s^2`...

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

Hello! When a hexagon maps onto itself, their vertices must map to vertices and sides to sides. Please look at the picture attached: the nearest vertex for the A1 is A2. There are 6 angles between...

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...

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 +... +...

We can answer this question by looking at the acceleration in the y direction. After the ball leaves Nolan Ryan's hand, the only force acting on it is gravity, in the -y direction. The equation for...

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...

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 +...

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...

The cost function is `C(x)=15000+600x-2.8x^2+0.004x^3` and the revenue function is `P(x)=4200-7x` Here we have to find the production level that will maximize the profit. For maximum profit, the...

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.

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...

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)' =...

`f(x)= ax^3 + bx^2 + cx + d` f(0)= 0 ==> d = 0 f(2)= 4 ==> 8a + 4b + 2c = 4 ==> 4a + 2b + c = 2 .............(1) `f'(x)= 3ax^2 + 2bx + c` f'(2)= 0 ==> 12a + 4b + c = 0...........(2) 8a...

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...

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

To write sin x in terms of cos x use the relation `sin^2x + cos^2x=1` => `sin^2x = 1 - cos^2x` Taking the square root of both the sides gives two values of sin x `sin x = sqrt(1 - cos^2x)` and...

Calculate the probability of being dealt a diamond from a standard deck of 52 cards. Since there are 4 suits in a deck of cards (hearts, clubs, spades and diamonds) we can find the number of...

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...

Hello! The formula for an average speed is a distance travelled divided by a time spent, `V=d/t.` In our problem the average speed `V` and the distance `d` are given, and we are looking for the...

It is given that f(5)=4, f'(5)=5, g(5)=9, g'(5)=8 (fg)'(5) = f'(5)*g(5) + f(5)*g'(5) = 5*9 + 4*8 = 45 + 32 = 77 (f/g)'(5) = (f'(5)*g(5) - f(5)*g'(5))/(g(5))^2 = (5*9 - 4*8)/81 = (45 - 32)/81 =...

We need write the area of a square as a function of the perimeter. Let us write the equation of the perimeter. Let the side of a square be x. Then the perimeter P = 4x. ==> x = P/4 Now we...

The derivative `f(f(x))'=f'(x)*f'(f(x))` `F'(8)=f'(8)*f'(f(8))=6*f'(4) ` because `f'(8)=6` and `f(8)=4` `F'(8)=6*3=18` `G'(x)=2F'(x)F(x)` `G'(8)=2F'(8)F(8) ` `F'(8)=18`...

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...

Given the point (-5,-2) , we need to find the the image point under translation T(3, -4) Then, the x coordinate will increase by 3 and the y-coordinate will decrease by 4 point. ==> p' (x, y) =...

TThe ratio of boys to girls is 12 to 16, 12:16 or 12/16 (all different ways this can be written). The fraction form 12/16 can be reduced by dividing by the greatest common factor. Both 12 and 16...

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...

Two numbers whose sum is 16 and whose product is a maximum have to be determined. Let one of the numbers be X, the other number is (16 - X) The product of the numbers is P = X*(16 - X) = 16X - X^2...