# Math Homework Help

### Showing All Questions Answered Popular Recommended Unanswered Editor's Choice in Math

• Math
The project lasts for 7 weeks. Initially 100 workers are employed. As work progresses every Monday an additional 60 workers are hired. By the end of the project the total number of people hired is...

• Math
We'll write sin^-1 x = arcsin x. To determine the antiderivative of arcsin x, we'll have to determine the indefinite integral of arcsin x. Int arcsin x dx We'll solve the integral by parts: Int udv...

Asked by mikok on via web

• Math
To integrate y = x*(sin 2x) we use integration by parts which gives us : Int [ u dv] = u*v - Int [ v du] Let u = x , du = dx dv = sin 2x => v = - cos 2x / 2 Int [ x*(sin 2x)] => x*(-cos 2x /...

Asked by sokolof on via web

• Math
If you know f'(x) and need to find f(x) you have to integrate f'(x). f(x) = Int [ f'(x) dx] => Int [ 8x^7-3x^2 dx] => (8/8)*x^8 - (3/3)*x^3 + C => x^8 - x^3 + C The function f(x) = x^8 -...

Asked by solvedphyz on via web

• Math
We have to prove that (x+y)^5 - (5yx^2+5xy^2)(x^2+xy+y^2) = x^5 + y^5. (x + y)^5 = x^5 + 5*x^4*y + 10*x^3*y^2 + 10x^2*y^3 + 5*x*y^4 + y^5 (5yx^2+5xy^2)(x^2+xy+y^2) = 5yx^4 + 5y^2x^3 + 5y^3x^2 +...

Asked by pengui on via web

• Math
We have to solve the system of equations: y = -x - 3 ...(1) x = -z - 2...(2) y(x+z) = 2 - xz...(3) substitute x = -z - 2 in (1) => y = (z + 2) - 3 = z - 1 Substitute x = -z - 2 and y = z - 1 in...

Asked by singwriter on via web

• Math
If the line (2x - y - 10 = 0) is tangent to x^2+y^2-4x+2y=0, the two touch each other only at one point. 2x - y - 10 = 0 => y = 2x - 10 Substituting in x^2+y^2-4x+2y=0 => x^2 + (2x - 10)^2 -...

Asked by lessoflot on via web

• Math
Two parallel lines have equal slopes. The slope of the line 2y + 4x - 8 = 0 can be found by writing it in the form y = mx + c where m is the slope. 2y + 4x - 8 = 0 => 2y = -4x + 8 => y = -2x...

Asked by electrika on via web

• Math
At the points where two curves intersect the x and y coordinates are the same. Now we have y^2 = x^2 - 9 and y = x - 1. y^2 = x^2 - 9 => (x - 1)^2 = x^2 - 9 => x^2 + 1 - 2x = x^2 - 9 =>...

Asked by orlovolga on via web

• Math
The integral of f(x) = ln x can be found using integration by parts which gives. Int[u dv] = u*v - Int[v du] Let u = ln x, du = 1/x dv = 1, v = x Int[ ln x] = x*ln x - Int [ x/x dx] => x*ln x -...

Asked by for3cast on via web

• Math
Here we need to prove that cos C / sin (90 - C) - 1 = 1 - cos B / sin(90 - B)Use the relation sin (90 - x) = cos x and cos (90 - x) = sin xLet's start with the left hand sidecos C / sin (90 - C) -...

Asked by riverwave on via web

• Math
We have the integrals A and B defined as A = Int[x*(cos x)^2 dx] and B = Int[x*(sin x)^2 dx] A + B => Int[x*(cos x)^2 dx] + Int[x*(sin x)^2 dx] => Int[x*(cos x)^2 + x*(sin x)^2 dx] =>...

Asked by bookofhth on via web

• Math
Supposing that you want to solve the equation cos x = sin x + 1, we'll start by saying that this equation is linear and we'll re-write it moving the function sin x, to the left. cos x - sin x = 1...

Asked by jaybyrd10 on via web

• Math
First, we'll differentiate the function to get f'(x): f'(x) = a/x Now, we'll substitute x by 1: f'(1) = a/1 But, from enunciation, f'(1) = 2 => a = 2. We'll evaluate the definite integral of...

Asked by agneslund on via web

• Math
We notice that if x is located in the interval [1/e , 1], the values of ln x are negative. If x is located in the interval [1 , e], the values of ln x are positive. According to these, we'll solve...

Asked by articsonia on via web

• Math
We'll recall the rules of multiplying 2 integers: - multiplying 2 positive integers, you'll get a positive integer, too: (+2)x(+3) = +6 - multiplying a positive integer and a negative integer,...

Asked by bhalachandra on via web

• Math
We need to find the value of lim x-->3 [ (3 - x^2)/(x - 3)] Substitute x = 3, we get -6/0 We see that the denominator has a root at x = 3. Therefore the graph has a vertical asymptote at x = 3....

Asked by xetaalpha2 on via web

• Math
The general equation of a circle with center at (h,k) and radius equal to r is given by (x - h)^2 + (y - k)^2 = r^2. Here, we have the endpoints of a diameter as (2, -5) and (-4 , 3) The mid point...

Asked by xetaalpha on via web

• Math
The tower casts a shadow that is 176 meters long. The height of the tower is 250 meters. We can construct a right triangle with the base equal to 176 m and the height equal to 250 m. The angle that...

Asked by anonymousse2 on via web

• Math
It is given that Luc is 8 years older than Kate. After 10 years the sum of their ages would be 88. Let Luc's age now be L. As Kate is 8 years younger that Luc her age is L - 8. After 10 years Luc...

Asked by thomas666 on via web

• Math
If a number has to be divisible by 3^n it should have at least n number of 3 when we determine its prime factors. 10! = 10*9*8...*1 In 10! the numbers that are divisible by 3 are 9, 6 and 3 9 =...

Asked by justinenotes2 on via web

• Math
It is given that x = 2 sin x - 3 and y = 2 cos x +1. We have to prove that (x+3)^2+(y-1)^2=4 Now (x + 3)^2 + (y - 1)^2 => (2*sin x - 3 + 3)^2 + (2*cos x + 1 - 1)^2 => (2*sin x)^2 + (2*cos...

Asked by justinenotes on via web

• Math
You are only allowed to ask one question at a time. Here's the solution to your first question. The diagonal of a square and any two sides form a right triangle with the diagonal as the hypotenuse....

Asked by harmonyshay101 on via web

• Math
Don't need an answer any more for this question.Thank-you anyway.

Asked by linnie4352 on via web

• Math
The original equations given by Maxwell is: B/A = (sin 2a - sin 2b) / (sin 2a + sin 2b) To convert this to a form that does not use double angles we use the following relation: sin 2x = 2*sin x *...

Asked by lastxdeth on via web

• Math
The answer to the question was \$11,056.

Asked by linnie4352 on via web

• Math
We are given that: (x^2 y^6)/z = 3 ...(1) (x^2 z^5)/y^2 = 27 ..(2) We need to find one value of x^2y^2z^2 Multiply (1)*(2) => [(x^2 y^6)/z]*(x^2 z^5)/y^2 = 3*27 Open the brackets and simplify...

Asked by lbawa on via web

• Math
You should remember that if you multiply both sides by `x + 1` yields: `(x + 1)(x^4 - x^3 + x^2 - x + 1) = 0` `x^5 - 1 = 0 => x^5 = 1` You should notice that the equation `x^5 - 1 = 0` has...

Asked by casanova0404 on via web

• Math
We have the complex numbers z1 = 27 - 13i and z2 = 18 + 7i z1*z2 = (27 - 13i)(18 + 7i) open the brackets and multiply => 27*18 + 27*7i - 13*18i - 13*7i^2 simplify noting that i^2 = 1 => 486 +...

Asked by elvache on via web

• Math
We'll take the equationsquare root (x-1) =1 – square root(2-x). Since it is impossible for a square root to have a negative radicand, we'll impose that the radicand to be positive, or zero. We'll...

Asked by doorsreb on via web

• Math
We have to solve 4^x+4^(x+1)+4^(x-1)=1344 4^x+4^(x+1)+4^(x-1)=1344 => 4^x + 4^x*4 + 4*x/4 = 1344 => 4^x(1 + 4 + 1/4) = 1344 => (4^x)(21/4) = 1344 => 4^x = 1344*4/21 => 4^x = 256...

Asked by hallman on via web

• Math
We'll re-write the general term of the string: an = (1/n)*Sum sqrt(1 + k/n) We'll identify a function f(k/n) = sqrt(1 + k/n) an = (1/n)*Sum f(k/n) If the function is continuous and it is, then the...

Asked by tarja19 on via web

• Math
f(x) = ln x / sqrtx ==> u= ln x ==> du = 1/x dx ==> dv = (1/sqrtx) ==> v = 2sqrtx ==> Int u dv = u*v - INt v du = 2sqrtx*ln x - Int (2sqrtx/x) dx...

Asked by bibiloi on via web

• Math
Yes. If you know the derivative of a function you can identify the original function by integrating what you have. During integration constants in the original function cannot be identified as they...

Asked by xmassfood on via web

• Math
For the general function f(x) = sqrt (ax + b), the inverse can be computed as follows. let y = sqrt (ax + b) => y^2 = ax + b => ax = y^2 - b => x = (y^2 - b)/a interchange x and y => y...

• Math
We'll write both bases as power of 2, using the rule of negative powers: 2^-(2x+2) < 2^-4(x-1) Since the bases are matching, we'll use one to one property of exponentials: -2(x+1) < -4(x-1)...

• Math
Let us assume you know the sine of 2x. Let sin 2x = y, we need to find tan x in terms of y tan x = sin x / cos x => sin x* cos x/ (cos x)^2 => [(2*sin x * cos x)/2] / [(cos 2x + 1)/2] =>...

Asked by studylike on via web

• Math
Using slopes to prove that lines are parallel is the easiest way to o the same. Else we need to find the equation of the lines and solve them to determine any points of intersection. If no points...

Asked by majaarmour on via web

• Math
We'll write the integral of the given function: Int f(x)dx = Int 2xdx/(x^2+1) + Int 5dx/(x^2+1) We'll solve the first integral using substitution technique. We'll note x^2 + 1 = t. We'll...

Asked by autos on via web

• Math
To find lim x --> 5 [ ln(x-4)/(x-5)], if we substitute x = 5 , we get ln 1/0 or 0/0 which is an indeterminate form. We can use l'Hopital's rule here and use the derivatives of the numerator and...

Asked by idaberg on via web

• Math
We have the functions f(x)=x^2-16 and g(x)=x+2 and we need to solve fog(x)=0 fog(x) = 0 =>f(g(x)) = 0 => f(x + 2) = 0 => (x + 2)^2 - 16 = 0 => (x + 2 - 4)(x + 2 + 4) = 0 => (x - 2)(x...

Asked by edithmo on via web

• Math
A fraction consists of two numbers with a horizontal line drawn between them. The number written on top is called the numerator and the number below the horizontal line is called the denominator. A...

• Math
We'll use the formula that is interchanging the base and argument. log(a) b = 1/log(b) a According to this formula, we'll have: log(2x)4 = 1/log(4) 2x We'll apply the product rule of logarithms:...

Asked by bhalachandra on via web

• Math
The vertex of a parabola is the extreme point of the function. To determine the extreme point, we'll determine the critical points that are the roots of the first derivative of the function....

Asked by tapisrouge on via web

• Math
To determine the primitive, we'll take the antiderivative of the function f'(x). Int f'(x)dx = F(x) + C We notice that the argument of the logarithm is the expansion of a binomial raised to cube....

Asked by joemauv on via web

• Math
We notice that the function f(x) = ln x is continuously and it could be differentiated, we'll apply Lagrange's rule, over a closed interval [k ; k+1]. According to Lagrange's rule, we'll have:...

• Math
We'll determine first the critical points. f'(x) = 16x - 1/x To determine the critical points, we'll put f'(x)=0 16x - 1/x = 0 16x^2 - 1 = 0 Since it is a difference of 2 squares, we'll substitute...

Asked by gateau66 on via web

• Math
We have to find lim x-->0 [(cos x - cos 7x)/x] If we substitute x with 0, we get the form 0/0 which is indeterminate, this allows us to use l'Hopital's rule and substitute the numerator and the...

Asked by braunem on via web

• Math
1 + (1/tan^2 x) = 1/(sin^2 x) We will use trigonometric identities to simplify. We know that tanx = sinx/cosx ==> 1+ (1/tan^2 x ) = 1+ (1/(sin^2x/cos^2 x) = 1+...

Asked by thomas666 on via web