
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
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
As a general rule, to find the surface area of an object you have to find the area of each shape that make up the surface of the object. There are four of steps to finding the surface area of a...

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
It's not possible to answer this question accurately without resolving the ambiguity about area. Is 1824 sq ft the area of the rectangle, or of the deck?

Math
sin 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...

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
Geometry is a branch of mathematics that deals with the properties, measurement, and relationships between points, lines, surfaces, and solids. The word, geometry, comes from the Greek word...

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
i) The question is not clear as to what are A2,B2 and C2.Assuming that normally capital letters are used for naming the angles and vertices, a solution is given. Normally a triangle is said to be...

Math
Trigonometry is used in geography and navigation . The sailors were known to have been using it to detrmine their position , when they were in the middle of the see. In astronomy to calculate the...

Math
If 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...

Math
We have to find Int[sin^2 x cos^3 x dx] Int[sin^2 x cos^3 x dx] => Int[sin^2 x (1  sin^2 x)cos x dx] let t = sin x , dt = cos x dx => Int[t^2(1  t^2) dt] => Int[t^2  t^4 dt]...

Math
Given: Mass of crate = m = 15 kg Force required to set the crate in motion = f1 = 64 N Force required to keep the crate in moving at constant speed = f2 = 57 N Acceleration of gravity = g = 9.8...

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...

Calculus
We have to find the integral of cos 2x. Int[ cos 2x dx] let 2x = u du = 2*dx dx = (1/2)*du => Int [ cos u * (1/2) du] => (1/2) sin u + C substitute u = 2x => (1/2) sin 2x + C The required...

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
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
To find the antiderivative of the given function, we'll have to calculate the indefinite integral of the function. Int f(x)dx = Int sec x dx We'll substitute the expression of the function f(x)=...

Math
In mathematics, the constant e has a number of important properties. The brief answer to your question is that it has a value of e=2.7182818284 (to ten decimal places) It is defined as the...

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
Here 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 =>...

Math
A whole number is a number that has no "pieces" attached. A piece of a number is a fraction. If you look at a number line, the numbers named, 1,2,3, and so on are whole numbers, while the spaces...

Math
We all seem to know what is mathematics, but when it comes to define it we seem to fail completely. A dictionary meaning of mathematics could be a science dealing with study of quantities and their...

Math
We have to solve the quadratic equation x^2 + 3x – 4 = 0. One way to do this is by factorization. x^2 + 3x – 4 = 0 => x^2 + 4x – x – 4 =0 => x(x+4) 1(x+4) = 0 => (x – 1)(x + 4)...

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
Given: Weight of block: = m = 0.6 kg Distance moved by block up the inclined plane = 8.0 m Angle of inclined plane = A = 37 degrees Force applied on block = F = 75 N Direction of force applied on...

Math
To solve the equation sinx=1+cos^2x, we use the trigonometrical identiy sin^2+cos^2=1 From the above identity, cos^2x =1sin^2x.Replacing this fact in the given equation we get: sinx=1+(1sin^2x)....

Math
A 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,...

Math
The identity is: atan(x) + acot(x) = pi/2 Your equation is atan(x) + acot(1/3) = pi/2 The only answer is x = 1/3

Math
Because you've tried to build them in plane, two dimensional space (on a table or another plane surface). The secret is to build in space (three dimensional space) and to realise a tetrahedron...

Math
The universal set is the set of all elements that are considered in a specific theory. We'll note the universal set with U. We'll choose as universal set: U = {6,7,8,9,15,16,17,18,20,21}. We have...

Math
Calculus 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...

Math
ln (x+2)  ln (3x+1) = 4 We know that ln a  ln b = ln a/b ==> ln (x+2)/(3x+1) = 4 ==> (x+2)/(3x+1) = e^4 ==> x+2 = (3x+1)*e^4 ==> x+2 = 3(e^4)x + 3^4 ==> 3(e^4)x  x = e^4  2...

Math
The formula for the circumference of a circle is C = ПD (circumference = pi times the diameter). The diameter is two times the radius. Therefore, if you have the radius, C = 2 ПR (twice the...

Math
In mathmatical related sciences we often come accross the parameters and varibles. A parameter for a particular value determines a particular function. For different values of the parametrs we get...

Math
f(x)=3x4 g(x)=x+2f(x)g(x)=3x4x2Gathering the terms in x together and the free ones together, the result will be:f(x)g(x)= (3xx)+(42)=2x6

Calculus
We have to find Int [1/ (1 + 4x^2) dx]. First substitute u = 2x => du /dx = 2 => du /2 = dx Now Int [1/ (1 + 4x^2) dx] => Int [(1/2)*(1/ (1+u^2) du] => (1/2)*Int [1/ (1 + u^2) du] Now...

Math
25% of 90 is what number? .25 times 90 equals 22.57% of 80 is what number? .07(80) = 5.6N% of 3.8 is 38? n%(3.8) = 38; n= 38 divided by 3.8 ; n = 10%70.6 is what percent of 635.4; 70.6=...

Math
This is proportional math.1760 yards = 1 mileX yards = .75 mileWe agree that 3/4 is equal to .75? So X is then number we are missing? With proportions, you cross multiply, and then divide by...

Math
To solve the equation, we'll group the first 2 terms together and the next 2 terms together, so that we can factorize: (x^3  2x^2)  (x  2) = 0 x^2(x  2)  (x  2) = 0 We'll factorize again: (x...

Math
1) 10404 First we notice that the endign number (4) is even, then the number is divisible by 2: 10404= 2* 5202 Now also, 5202 is ending with an even number (2), then it is diisible by 2: 10404=...

Math
2 log 5 + 3 log x = 2 ==> log 5^2 + log x^3 = 2 We know that: log a + log b = log a*b ==> log 25*x^3 = 2 ==> 25x^3 = 10^2 ==> 25x^3 = 100 Divide by 25: ==> x^3 = 100/25 = 4 ==> x...

Math
(secx)^4 = (1+tan^2 x) sec^2 Therefore Integral (sec^4 x) dx = Integral (1+tan^2 x) sec^2 x dx Let tan x=t , then sec^2 x dx = dt , for x=0, t=0 and for x=pi/4 , t=1, with this transformation,...

Math
We have to solve (x + 2)/6 = 3/(x  1) for x. (x + 2)/6 = 3/(x  1) => (x + 2)(x  1) = 3*6 => x^2 + 2x  x  2 = 18 => x^2 + x  20 = 0 => x^2 + 5x  4x  20 = 0 => x(x + 5)  4(x +...

Math
Initial 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...

Math
The probability is the chance that certain event may occur or not occur. To calculate the probability you need to figure out the possible outcomes and then determine the event's outcomes. For...

Math
The angle addition postulate states that if a point is within an angle and you add the two angles that are made by drawing a line through the point that the total will equal the large angle. For...

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)...