
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...

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...

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...

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)...

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...

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...

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...

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...

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...

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...

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...

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...

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 =>...

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.

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...

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...

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...

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...

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...

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 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:...

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,...

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 *...

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...

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...

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...

MathWe 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...

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...

MathFirst 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)...

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...

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

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 hands will be opposite to each other 22 times in 24 hours actually (kindly ignore the typing mistake in the last line of my earlier answer). Here is another method to solve the problem: The...

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...

MathThe common factor of the given expressions has to be determined. x^2x6 = x^2  3x + 2x  6 = x(x  3) + 2(x  3) = (x + 2)(x  3) x^2 5x +6 = x^2  3x  2x + 6 = x(x  3)  2(x  3) = (x  2)(x...

MathIn the above question the given conditions are: let 1st digit=a 2nd=b 3rd=c 4th=d 5th=e 1.a=(b)2 2.b+c=10 3.d=b+1 4.e+c=14 5.a+b+c+d+e=30 => (b)2+b+c+d+e=30 (a=(b)2) =>...

MathFor a function y=f(x), the inverse function g(x) is such that g(f(x))=1. For the functions you have provided: f(x)=x^3 y=x^3 Take the cube root of y and x^3, => y^(1/3)=x Therefore the inverse...

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...

Math`f(x) = x^2+2x+9` By completing square; `f(x) = (x+1)^2+8` `1/f(x) = 1/((x+1)^2+8)` We know that `(x+1)^2>=0` always. Hence `(x+1)^2+8>0 ` always. When `f(x)` is increasing then `1/f(x)`...

MathMelody 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...

Mathx+y=30.....(1) and xy=2......(2) so(1)+(2)......x+y+xy=30+2 so 2x=32...x=16 now apply x=16 in (1) so we get......16+y=30 so .......y=14

Mathe^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...

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...

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.

Mathtan75: method (1): tan75 = sin75/cos75 = sin(45+30)/cos(45+30) = (sin45cos30+sin30cos45)/(cos45cos30  sin45sin30) = [sqrt2/2*sqrt3/2 +...
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