
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
Your 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.

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
What 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...

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

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
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
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
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
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
`int "tan"^n x dx =` `int ("tan" ^(n2) x) ("tan" ^2 x) dx =` `int ("tan" ^(n2) x) ("sec"^2 x  1)dx = ` `int ("tan" ^(n2) x ) "sec"^2 x dx  int "tan" ^(n2) x dx=` To do the first integral, use...

Math
Give 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...

Math
We 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...

Math
First 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)...

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
A linear function is one that has the form f(x) = ax + b. Here for each value of x there is only one corresponding value of f(x) and every value of f(x) is due to only one particular value of x. In...

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
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
See the attached figure. (ABC are triangle vertices, DEF are midpoints on triagle sides and O is the intersection of medians) In triangles ABD and ACD BD= CD (by median definition) AD= AD...

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
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
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...

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
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
dy/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 ...

Math
sinx = 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...

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
1. `int te^t dt` Integrate by parts. u = t and dv = e^t. Then du = 1 and v = e^t `=te^tint e^t dt` `=te^te^t+c` `=e^t(t1)+c` 2. `int e^(2t)dt` You could use substitution, but I like to...

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
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
Translate 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...

Math
The 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
A very simple example of combinations would be in the number of pizzas one could create given a certain number of criteria. In other word, given that a pizza place has: 3 types of crust thin,...

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
We are given that the mean is 80 and the standard deviation is 6. We want to determine the score that is the cut score at 95%. To find the `z` score that has 5% above and 95% below, we consult the...

Math
`int e^(3x) dx ` `==gt u= 3x ==gt du = 3 dx ` `==gt int e^(3x) dx = int e^u (du)/3 ` `==gt int e^(3x) dx = (1/3) int e^u du = (1/3) e^u + C ` `==gt int e^(3x) dx = (1/3) e^(3x) + C` ``

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
I suggest you to transform the difference of like trigonometric functions into a product such that: sin alpha  sin beta = 2 cos ((alpha+beta)/2)*(sin(alphabeta)/2) sin 4x  sin2x = 2 cos...

Math
The derivative of a function f(x) is defined as `lim_(h>0) (f(x+h)  f(x))/h` . For f(x) = sec x, the derivative from first principles is: `f'(x) = lim_(h>0)(sec(x+h)  sec x)/h` `=...