
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...

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...

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...

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...

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...

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...

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...

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...

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 =>...

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...

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)...

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...

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...

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...

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...

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...

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...

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...

MathA "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...

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...

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,...

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...

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...

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.

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

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...

Math`lim_(x>0)(sqrt(1+2x)sqrt(14x))/x` `=lim_(x>0)((sqrt(1+2x)sqrt(14x))(sqrt(1+2x)+sqrt(14x)))/(x(sqrt(1+2x)+sqrt(14x)))` `=lim_(x>0)((1+2x)(14x))/(x(sqrt(1+2x)+sqrt(14x)))`...

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

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...

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 *...

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...

MathTo graph the equation y = 4x + 3 by hand choose any two values of x. For example x = 1 gives y = 7 and x = 0 gives y = 3. The graph of the equation is a straight line drawn between the points (0,...

MathWhen you were 4 years old, your sister was half your age. Half of 4 is 2, your sister was 2 years old when you were 4 years old or she is 2 years younger to you. Your present age is 100, as your...

Mathdy/dx = x  yUse substitution:v = x  yDifferentiate with respect to xdv/dx = 1  dy/dxdy/dx = 1  dv/dxNow we use above substitutions in differential equationsdy/dx = x  y1  dv/dx = vdv/dx = 1 ...

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 binomial distribution helps in finding the probability that a number k of successful event is happening in a given series of attempts, while the geometric distribution helps in finding the...

MathA circles area is pi times the square of its radius or area A of the circle is given by: A = pi*r^2 So,if the radii of the two circles are a and b, then their areas are pi*a^2 and pi*b^2, where pi...

MathIn 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...

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 square root of 169 is 13. This is so because 13 times 13 gives 169  the definition of a square root of a number k is the number such that when you multiply it by itself you get k. Note that...

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...

Math`2(3/4)` Since 4/4=1 then 8/4 must equal 2. We have 3 left over which we would add to the 8 to make it 11/4. Or you can also multiply the denominator by the whole number and add the numerator ` `

MathEvaluate `int (lnx)/x dx` : We ` `` `let `u=lnx` . Then `du=1/xdx` and we have: `intudu=1/2u^2+C` . Substituting for `u` we get `1/2(lnx)^2+C` . Thus the integral evaluates as `1/2(ln(x))^2+C`

MathWe need to verify that sinx/(1xosx)= (1+cosx)/sinx We know that sin^2(x) + cos^2(x)=1 ==> sin^2(x)= 1cos^2(x) ==> sin^2(x)= (1cos(x))(1+cos(x)) ==> (sinx)(sinx)= (1cosx)(1+cosx) Now...

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...

Mathx^2  y^2 = 4 x + y = 2 This system can also be solved graphically. First, set each equation to the form y= x^2  y^2 = 4 y = sqrt(x^2  4) x + y = 2 y = 2  x Here...

MathDetemine the point estimate of the population mean and margin of error if the confidence interval...Given `125.8<=mu<=152.6` : The confidence interval for the mean is of the form: `bar(x)"error"<=mu<=bar(x)+"error"` where `bar(x)` is the point estimate for the mean. Here we have...

MathGiven that sin^2 x = 1/4 We need to find x. First we will take the square root for both sides: ==> sin(x) = + 1/sqrr2 = +sqrt2/2 Now we know that x = pi/4 ==> When sin(x) = sqrt2/2 ==> x...
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