
MathThe 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...

MathThe 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...

MathPrimary 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...

MathHey 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...

MathWithout people who can do math, we would not have many of the things we take for granted. We wouldn't have cars, highways, or plane travelmath is required to design and build such things. Tall...

MathHow can math be used in daily life?I am trying to write an essay, and its topic is 'math in daily...Well, I must admit I never ever thought that I would be answering a question in the Math group, but there you go! As a student who delighted in the fact that I was able to give up Maths at age...

Mathsin x  cos x=0 We could divide the equation by (cos x) and the result will be: sin x /cos x  1 =0 But we know that the ratio between sinx and cos x determine the tangent function. tg x 1 =0...

MathInitial velocity of the ball = 26.3m/s At the highest point the ball reaches 0 velocity because of the pull of the acceleration due to gravity g. So, the time taken to reach the highest point...

Mathf(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)...

MathAnother 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...

MathYou need to work on simple average of the numbers to evaluate the mean such that: Mean = `(12+8+11+10+7+10+15+13+14+9)/10` Mean = `109/10` => Mean = 10.9 You need to evaluate the variance first...

MathIf you want to have a healthy life, and one in which you do not waste money, you use arithmetic all the time. Every time you go to the grocery store, you should be calculating which item of the...

MathWe all seem to know what is mathematics, but when it comes to define it we seem to fail completely. A dictionary meaning of mathematics could be a science dealing with study of quantities and their...

MathA 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...

MathIn a discussion all sets are cosidered to be the subset of big set . Such a big set of which all other sets under discussion are subsets is called the universal set. We normally use the symbol U...

MathWhat 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...

MathHere we have to find x for which cos 2x = cos x. We know that cos 2x = 2(cos x)^2  1. Therefore we can write the expression given as 2(cos x)^2  1 = cos x or 2(cos x)^2  1  cos x = 0 =>...

MathEmpirical 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...

MathTo 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...

Mathf(x)= (4x1)/2x+3 To find the inverse function f(x)^1 we will assume: y=(4x1)/(2x+3) ==> multiply by 2x+3 ==> y(2x+3)= 4x1 ==> 2yx+3y=4x1 ==> 3y+1= 4x2yx ==> 3y+1= x(42y)...

MathThe limit `lim_(x>0) (1cosx)/x^2` has to be determined. If we substitute x = 0, the result `(1cosx)/x^2` is the indeterminate form `0/0` . In this case it is possible to use l'Hospital's rule...

MathWe have to find the chain rule to find the derivative of f(x) = e^3x. The chain rule for the function f(x) = g(h(x)) gives f'(x) = g'(h(x))*h'(x). Here f(x) = e^3x f'(x) = e^3x * (3x)' => e^3x *...

MathYour 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.

MathWe 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...

Math1 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...

MathCalculus is useful in engineering and construction. However, if you are not involved in one of those fields you may not use it regularly. However, calculus is great training for the mind. It...

MathHi, A geometric explanation is very intutive. Look at sin(x) curve below. Sin(1) = Sin(1). it is not symmetric But look at the cos(x) curve below. cos(1) = cos(1). it is symmetric

MathTo solve this problem let's multiply (sin x  cos x) and (1 + sin x* cos x). (sin x  cos x)*(1 + sin x*cos x) = sin x + (sin x)^2 * cos x  cos x  sin x * (cos x )^2 Now (sin x)^2 + (cos x)^2 = 1...

MathLet f(x) = sin3x. We need to find the antiderivative of f(x). Then, we need to find the integral of f(x). ==> intg f(x) = intg sin3x dx Let u = 3x ==> du = 3 dx ==> intg f(x) = intg...

Mathf(x) = 1/(x^2  4) First wewill implify using partial fractions: ==> 1/(x^2 4) = 1/(x2)(x+2) ==> A(x2) + B(x+2) = 1/(x2)(x+2) ==> A(x+2) + B(x2) = 1 ==> Ax + 2A + Bx  2B = 1...

MathThe rate this individual is running is 100m per 15 seconds (distance/time). So, in order to run 1,000m, or 1 kilometer, it would take 150 seconds (15seconds x 10). 150 seconds is equal to 2.5...

MathBefore I answer this question it will be worthwhile to clarify on some confusion that exists between some related terms  digits, letters or alphabets, signs, and characters. This confusion can be...

MathGiven that the volume of the cube is 343 Let x be the length of the side of the cube. Then we know that V = x^3 = 343 ==> x = 7 Now let us calculate the surface are. The surface area of the cube...

Math2cosx + 1 = 0 First we will move 1 to the right side by subtracting 1 from both sides: ==> 2cosx + 1  1 = 01 ==> 2cosx = 1 ==> now we will divide by 2: ==> cosx = 1/2 Now we know...

Mathcos 2x = 1/2 <=> 2x = arccos (1/2) 2x = pi/3 x = pi/6 The first value of x is located in the 1st quadrant. Since we have to determine all convenient values from all 4 quadrants, we'll step in...

MathYou 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...

MathThis 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...

MathThe 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...

MathA fraction is really a division problem. Onethird means ONE divided into THREE parts. So, to find the decimal equivalent, do the division. 1 divided by 3 = 0.33333333 etc. In a case like this,...

MathIf 3/5 is 15, then 1/5 must be 5 (15/3). So 5/5 of that number would be 5 x 5 = 25. So 25 is your answer.

Mathtan^2x  sin^2x = tan^2x(1cos^2x) = (tan^2x)(sin^2x)

MathLet 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:...

MathWhen triangles are similar, they could be congruent. However, they do not have to be congruent in order to be similar. So I guess the answer is not always. When triangles are similar, their...

Mathf(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,...

MathFor the beginning, we'll add 5 both sides, to move the constant on the right side of the equation, so that being more clear what we have to add to the left side to complete the square. x^2 +2x =...

MathThe function `y = x^(ln x)` . The derivative `dy/dx` has to be determined. First, take the natural log of both the sides. As `y = x^(ln x)` , `ln y = ln(x^(ln x))` Use the logarithmic formula: `ln...

MathGive 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...

MathTThe 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...

MathThe given terms of the series are: 1/2, 1/4, 1/6, 1/8, 1/10 1/12, 1/14, 1/16 ... Thus Term number 1 = 1/2 = 1/(1*2) Term number 2 = 1/4 1/(2*2) Term number 3 = 1/6 = 1/(3*2) Term number 4 = 1/8 =...

Mathsinx = 3/5 We know that: sin^2 x + cos^2 x = 1 ==> cosx = sqrt(1sin^2 x) = sqrt(1 9/25) = sqrt( 16/25) = 4/5 ==> cosx = 4/5 Now we know...
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