
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...

Math
The 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...

Math
Hey 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...

Math
Primary 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...

Math
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)...

Math
Another 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...

Math
We 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...

Math
Without 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...

Math
You 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...

Math
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...

Math
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...

Math
This is a minimization problem hence, you need to find a function that models the distance between a point `A(x,y)` that lies on the given curve and the fixed point `(3,0).` You need to use the...

Math
Graph 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...

Math
You 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...

Math
This question is a little vague. It's difficult to simply "verify" a given linear approximation without some parameters. Let's assume that it means that at `x = 0`, the logarithm and the...

Math
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=(xp)(xq) where p,q are the xintercepts. One way to...

Math
e^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...

Math
We 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 *...

Math
A 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...

Math
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...

Math
The equation of the line through (2, 3) and tangential to the parabola y = x^2 + x has to be determined. The slope of a tangent to a curve y = f(x) at the point x = c is f'(c) y' = 2x + 1 Let the...

Math
f(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,...

Math
A line that is perpendicular to the xaxis 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...

Math
If 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.

Math
This 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...

Math
Find 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...

Math
The 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...

Math
The curve y=(x1)/(x+1). At any point on the curve, the slope of the tangent to the curve is equal to the value of y' at that point. As equations of the tangents have to be determined that are...

Math
Note: 1) if y = x^n ; then dy/dx = n*x^(n1) Thus, If y = (1+4x)^(1/3) ; then Let f(x) = x^(1/3)...........(1) And g(x) = (1+4x).........(2) Thus, f(g(x)) = (1+4x)^(1/3) .................Answer...

Math
2cosx + 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
1 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
To 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...

Math
Let 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:...

Math
Empirical 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...

Math
Let x and y be the two numbersWe want xy = 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...

Math
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...

Math
The 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...

Math
We are given the equation x^25xy+3y^2=7 and we have to find dy/dx. Differentiating each term of x^2  5xy + 3y^2 = 7 with respect to x, we get 2x  5x(dy/dx) 5y + 6y(dy/dx) = 0 taking the terms...

Math
You 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)...

Math
You 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
Let x and y be the length and width of the rectangular corral.Since the two rectangular corrals are adjacent to each other, let one side of each corral (x) share a common fence.So, their total...

Math
Let `a(t)` and `b(t)` be functions denoting length and width of the rectangle at time `t.` Since area of rectangle is product of length and width we have `A(t)=a(t)b(t)` To get the the rate of...

Math
The correct answer is c, identical to free fall. This is true because the only force acting on an object in the vertical direction is the gravitational force. Whether an object is moving upward...

Math
Let 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...

Math
Reallife limits are used any time you have some type of realworld application approach a steadystate solution. As an example, we could have a chemical reaction in a beaker start with two...

Math
To convert 57% to decimal, move the decimal point two places to the left. 57.0% ===> 0.570 Hence, the equivalent decimal form of 57% is 0.57. To convert percent to fraction, divide the number by...

Math
Let Hanna's money be represented by the variable: x. Let Francine's money be represented by the algebraic expression: 120  x Peter's money can be represented by 6 times Francines or 6(120  x)...

Math
The sum of the numbers on the clock would be 78 (1 + 2 + 3 . . + 12). So 78/3 = 26 so you would have to find the number combinations that would give you 26. The only three combinations that work...

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

Math
f(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...