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

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
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
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
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
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
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
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 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
`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
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
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
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
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
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
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
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
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
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
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
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
To 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,...

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

Math
The sum of the exterior angles of any regular polygon is 360 degrees. The exterior angles of a regular polygon are also equal. Allow s to represent the number of sides of the polygon. Therefore......

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
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
The integral `int sin^6 x dx` has to be determined. `int sin^6 x dx` => `int (sin^2 x)^3 dx` => `int (1  cos^2x)^3 dx` => `int cos^6 x + 3*cos^4x  3*cos^2 x + 1 dx` Now use the...

Math
`int x^3 ln(x) dx` To evaluate, use integration by parts. The formula is` int udv = uv  int vdu` . So let, `u = ln (x) ` and `dv= x^3 dx` `du = 1/x dx `...

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
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
We have to prove that: sin 2x/ (1 + cos 2x) = tan x To do this we use the relations : sin 2x = 2 sin x*cos x and cos 2x = (cos x)^2  (sin x)^2. sin 2x/ (1 + cos 2x) => [2 sin x*cos x] / [1 +...