
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...

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...

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...

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)...

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...

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...

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...

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,...

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...

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...

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...

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...

MathGraph y=x. This is not a function so you will not be able to enter it directly into the y= screen of the TI83. You will have to break it into two different functions. y=x ==> x=y for...

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 expand the binomial using the formula `(ab)^2 = a^2  2ab + b^2` . Hence, substituting x for a and 2 for b yields: `(x  2)^2 = x^2  4x + 4` You may also use distributive...

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...

MathYou should check if the tangent function is continuous, hence, you need to check if `lim_(x>1, x<1) tan(pi*x/2) = lim_(x>1, x>1) tan(pi*x/2)` such that: `lim_(x>1, x<1)...

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...

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...

Math`y=2x^2+4x3`To find the vertex, use the formula `x=b/(2a)`Here we have `x=4/(2*2) = 1`To find the yvalue of the vertex, plug in the x value:`y=2(1)^2+4(1)3=5`So the vertex is (1,5)To...

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...

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.

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...

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...

MathFind the slope of the line `y= 5x1` . The equation is written in slopeintercept form: `y =mx+b` , where `m` represents the slope and `b` represents the yintercept. Therefore, 5 is the slope...

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...

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...

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...

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.

Mathf(x)=x^3+2 To find the inverse function f(x)^1 , we will assume" y=x^3+2 y2= x^3 ==> x= (y2)^1/3 ==> f(x)1= (x2)^1/3 https://www.youtube.com/watch?v=Ec5YYVxyq44

Math`121 = 11 X 11` `==> sqrt121 = sqrt(11X 11) = 11` `==> sqrt121 = 11` `` ``

MathThe fractions obtained by dividing 1 by 3 is equal to 0.3333... the series of 3 after the decimal point goes on for ever. To convert 0.33 to a fraction you would have to use approximation,...

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...

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...

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)`...

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)...

MathTranslate the written/verbal expression "twice a number x" into mathematical/symbolic notation: Twice a quantity usually indicates to take two of the things in question; usually this indicates to...

MathThe line is perpendicular to the yaxis means that it is horizontal or parallel to the xaxis, that means that the slope (m)=0 We hav the point (6,1) pass through the line: yy1= m(xx1) y+1=0...

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...

MathFirst, change the decimal to a fraction: .2= 2/10 Then, write the mixed number: 2 2/10 Finally, change the mixed number to a fraction by multiplying the whole number (2) x 10 (the...

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:...

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...

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...

MathReciprocal of a number is 1/number. It does not affect its sign. Thus the reciprocal of 2 is `1/2`

MathThe short answer is no, pi/2 radians and 1.57 radians are not exactly the same thing  though they are close; pi is an irrational number, and as such has no exact decimal representation. Hence,...
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