# Math Homework Help

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• Math
The logarithmic function is defined such that if log(a) b = c, we have b = a^c. The equation to be solved is log(4) (x - 2) = -1 => x - 2 = 4^(-1) => x - 2 = 1/4 => x = 2 + 1/4 => x =...

Asked by victor-enotes on via web

• Math
The graph of the function of the form y = a*x^2 becomes more steep as the value of a in increases. For the same increase in x the value of y changes by a larger extent as x is being multiplied by a...

Asked by rbeaker91 on via web

• Math
Let the number we need to find be x and y. The sum of the numbers is x + y = 720...(1) We also know that one number is half the other. x = y/2 substitute y = 2x in equation (1) x + y = 720 => x...

Asked by thomas666 on via web

• Math
We have z = x - iy and w = y - ix We need the values of z that satisfy z^2 = w z^2 = (x - iy)^2 = x^2 - y^2 - 2xyi = w So we have x^2 - y^2 - 2xyi = y - ix equate the real and complex coefficients...

Asked by elvache on via web

• Math
We have to prove that : (1+ sin 2x) / sin^2 x = csc^2 x + 2cot x Start from the left hand side: (1+ sin 2x) / sin^2 x use the relation sin 2x = 2*sin x*cos x => (1 + 2*sin x*cos x) / (sin x)^2...

Asked by xetaalpha2 on via web

• Math
We have to prove that: (1 - sec(x))/(1 + sec(x)) = (cos(x) - 1)/(cos(x) + 1) Let's start from the left hand side (1 - sec(x))/(1 + sec(x)) use the fact that sec x = 1/cos x => (1 - (1/cos x))/(1...

Asked by xetaalpha on via web

• Math
We have to solve the system of equations: 3x + 4y = 38…(1) 5x + 5y = -30…(2) (2)*(3/5) => 3x + 3y = -18 Subtract this from (1) => 3x + 4y – 3x – 3y = 38 + 18 => y = 56 substitute y...

Asked by justinenotes on via web

• Math
The vertical asymptotes are vertical lines that pass through the zeros of the denominator. Here, we have [2x^2 + x + 1] / [x + 2], We can see that equating the factors of the denominator to 0 gives...

Asked by lance3 on via web

• Math
The integral of f(x)=(x+1)/(x^2+2x) can be found using substitution. If y = x^2 + 2x dy/dx = 2x + 2 = 2(x + 1) => (1/2)dy = (x + 1)dx Int[(x+1)/(x^2+2x) dx] => Int[(1/2)*(1/y) dy] =>...

Asked by merishorverde on via web

• Math
It is given that f(x)=2x+1 and g(x)=x+2. We need to solve the equation gogog(x)=fofof(x) gogog(x) => gog(x + 2) => g(x + 2 + 2) => g(x + 4) => x + 6 fofof(x) => fof(2x + 1) =>...

Asked by maxine60 on via web

• Math
x-2y = -11............(1) -x + 5y = 23...........(2) We will use the substitution method to solve the system. First we will rewrite equation (1). ==> x = 2y-11 Now we will substitute into...

Asked by dollface0817 on via web

• Math
We need to find x for lg(x)+lg(x+1)=(lg90) to exist. Lets simplify the expression: lg(x) + lg(x+1) = lg(x*(x + 1)) = (lg 90) x(x + 1) = 90 x^2 + x = 90 => x^2 + x - 90 = 0 => x^2 + 10x - 9x -...

Asked by maisaphie on via web

• Math
We need to solve x=1+square root(1+square root x) x = 1 + sqrt (1 + sqrt x) => x - 1 = sqrt (1 + sqrt x) square the sides => x^2 + 1 - 2x = 1 + sqrt x => x^2 - 2x = sqrt x square the...

Asked by purpl3pink on via web

• Math
We know that Pn(x)=(x-1)(x-2)...(x-n). We have to solve the inequality P1(x)/P2(x)>=2 P1(x) = (x- 1) P2(x) = (x - 1)(x - 2) P1(x) / P2(x) = (x- 1)/(x - 1)(x - 2) >=2 => (x - 1)>=2*(x -...

Asked by denyss on via web

• Math
We need to find the integral of y = 6x^5 + 2x - 1. Use the property that the integral for x^n is (1/(n + 1))*x^(n + 1) for each of the terms. Int[6x^5 + 2x - 1 dx] => 6*x^6 / 6 + 2*x^2/2 - x/1...

Asked by ulichh on via web

• Math
We'll write the sum: Sum k(k + 3), where k is an integer number whose values are from 1 to n. Sum k(k+3) = Sum (k^2 + 3k) Sum (k^2 + 3k) = Sum k^2 + Sum 3k Sum k^2 = 1^2 + 2^2 + ... + n^2 =...

Asked by l0l1 on via web

• Math
You need to use the following derivative rules, such that, power rule, quotient rule and chain rule, in this order. `f'(x) = (1/2)((cos2x)/(x^2+x+1))^(1/2 - 1)*((cos2x)'(x^2+x+1) -...

Asked by jolenta on via web

• Math
We have to find the roots of 9x^2 - 6x + 21 = 0 by completing the square. 9x^2 - 6x + 21 = 0 => (3x)^2 - 2*3x + 1 = -20 => (3x - 1)^2 = -20 => 3x - 1= sqrt -20 and 3x + 1 = -sqrt (-20)...

Asked by greta92 on via web

• Math
We have to find the roots of (4^2)^x-3*4^x+2=0 (4^2)^x-3*4^x+2=0 Let 4^x = y => y^2 - 3y + 2 = 0 => y^2 - 2y - y + 2 = 0 => y(y - 2) - 1(y - 2) = 0 => (y - 1)(y - 2) = 0 => y = 1...

Asked by creativluana on via web

• Math
A sequence is convergent if the sum of n terms of the sequence approaches a constant value as n tends to infinity. Here, we have the sequence made up of 1, -1, 1, -1, 1, -1... If we add up the...

Asked by bchacon09 on via web

• Math
Trigonometry is the branch of mathematics that deals with the relation between the angles of a triangle and its sides. The functions in trigonometry find application in defining periodic functions...

Asked by jameshall on via web

• Math
We notice that 0 <= fn(x) <= x^2n if x belongs to the range [0,1). We'll integrate and we'll get : 0 <= int fn(x)dx <= int x^2ndx We'll calculate int x^2ndx=x^(2n+1)/(2n+1) We'll apply...

Asked by betzishor on via web

• Math
We have to find the second derivative of f(x) = (x^3+3x)*(3x^2-6x) + 9x^2/(x-1) f(x) = (x^3+3x)*(3x^2-6x) + 9x^2/(x-1) f'(x) = (3x^2 + 3)(3x^2 - 6x) + (x^3 + 3x)(6x - 6) + 18x/(x - 1) - 9x^2/(x -...

Asked by raydusol on via web

• Math
We have x o y = xy - x - y + 2 and f(x) = x + 1. f(xy) = xy + 1 f(x) o f(y) = (x + 1) o (y + 1) => (x + 1)(y + 1) - (x + 1) - (y + 1) + 2 => xy + x + y + 1 - x - 1 - y - 1 + 2 => xy + 1 We...

Asked by printsaltr on via web

• Math
We have to find the derivative of f(x) = e^[x/(x+2)] We use the chain rule here: f'(x) = e^[x/(x + 2)]*[(1/(x + 2) - x/(x + 2)^2] => e^[x/(x + 2)]*[((x + 2 - x)/(x + 2)^2] => e^[x/(x +...

Asked by browntim3 on via web

• Math
We have to differentiate y = ln(1 + 3x + 4x^2) We use the chain rule here. y = ln(1 + 3x + 4x^2) y' = [1/(1 + 3x + 4x^2)]*(3 + 8x) The required derivative of y = ln(1 + 3x + 4x^2) is [1/(1 + 3x +...

• Math
You may also use reminder theorem, such that: `p(x) = (x - 1)^2*q(x) + r(x)` The problem provides the information that the polynomial `p(x)` is exactly divided by `(x - 1)^2` , hence, `r(x) = 0.`...

Asked by ingw33 on via web

• Math
You need to solve for x the following irrational equation, such that: `x - a = sqrt(x^2 - 1)` The problem provides the information that `a = 0` , such that: `x = sqrt(x^2 - 1) => x^2 = (...

Asked by andrzej on via web

• Math
We are given that 25x^2+a+36y^2 and 9x^4/25-b+25x^2/9 are squares and we need to determine a and b. The two can be squares of the form (a - b)^2 and (a + b)^2 25x^2+a+36y^2 = (5x)^2 + (6y)^2 + a a...

Asked by clockbeige on via web

• Math
We need to find the value of ad - bc if a,b,c,d are the terms of a geometric series. As a, b, c and d are terms of a geometric series. b=a*r, c=a*r^2 and d = a*r^3 a*d = a^2*r^3 and b*c = a^2r^3 We...

Asked by eligia on via web

• Math
We have the function f(x) = (2x+4/3x-1)^3. The derivative f'(x) can be found using the chain rule. f'(x) = 3*(2x+4/3x-1)^2*(2x+4/3x-1)' f'(x) = 3*(2x+4/3x-1)^2*(-(2x+4)*(3x - 1)^-2*3 + (3x -...

Asked by sylli on via web

• Math
The partial fractions can be found in a very easy way using the following method. (3x-2)/(x-3)(x+1), the roots of the denominator are x = 3 and x = -1. Representing as partial fractions we get the...

Asked by luna9219 on via web

• Math

Asked by crisie7 on via web

• Math
l 2m +3 l <12 We need to find the values of m such that m belongs to Z. By definition we will rewrite: ==> -12 < 2m+3 < 12 We will subtract 3 from both sides. ==> -15 < 2m...

Asked by clara2 on via web

• Math
Given the points (x,2) and (2,-4). The distance between the points is 5 units. We need to find the values of x We will use the distance between two points formula to find the values of x. We...

Asked by nano75 on via web

• Math
Given the graph x^2 - 5x - 1 and the line y= 2x-7 We need to find the intersection points between the curve and the line. The points of intersections are the points that verifies both...

Asked by totoo on via web

• Math
Given the quadratic function 3x^2 -5x -7 = 0 We will use the quadratic formula to find the roots. We know that the quadratic formula is given by: ==> x = [ -b +- sqrt(b^2-4ac)]/2a a = 3 b= -5...

Asked by feres on via web

• Math
To find which value if greater, we will calculate the value of each percentage. ==> 10% of 325 = 10/100 * 325 = 32.5 ==> 15% of 295 = 15/100 * 295 = 44.25 ==> 25% of 250 = 25/100 * 250 =...

Asked by jude69 on via web

• Math
Given the curve x^2 -5x +1 We need to find the area bounded by the curve and the lines x= 1 and x= 2 Then we will find the integral of the curve between 1 and 2 Let F(x) = Int (x^2 - 5x +1) Then...

Asked by ryanomar on via web

• Math
Given that g(x) = (2x-1)/(3x+2) We need to find the f'(0) First we will find the first derivative f'(x) ==> Let f(x) = u/v such that: u= 2x-1 ==> u' = 2 v= 3x+2==> v' = 3 ==> f'(x)...

• Math
Given the curve f(x) = -3x^2 + 12x -1 We need to find the extreme value. First we will look at the coefficient of x^2 and we note that the sign is negative, then the function has a maximum...

Asked by lalooo on via web

• Math
Given that the sum of a and b is 35 Then, we will write: a + b= 35.........(1) Now we know that b is one more than a. ==> b = a+ 1......(2) Now we will substitute (2) into (1). ==> a + (a+1)...

Asked by kokibrazil on via web

• Math
3x-4y = 5.........(1) 2x+y = 7 ...........(2) We will use the elimination method to solve for x and y. First we will multiply (2) by 4 and add to (1). ==> 4*(2) 8x + 4y = 28 Now we will add to...

Asked by yasmin130 on via web

• Math
The height and the radius forms a right angle triangle such that the hypotenuse is h and the sides are 11 and 16. We will calculate the length of the hypotenuse. ==> h= sqrt( 11^2 + 16^2) ==>...

Asked by seniormoment on via web

• Math
You need to use the information provided by the problem, such that: `{((fof)(x) = (x-1)+1/(x^2+x+1)),((fof)(x) = 0):} => (x-1)+1/(x^2+x+1) = 0` You need to bring the terms in equation to a...

Asked by jane1992 on via web

• Math
You need to evaluate the indefinite integral such that: `int 1/(root(3) (x - 2))dx = int (x - 2)^(-1/3) dx` `int (x - 2)^(-1/3) dx = ((x - 2)^(1 - 1/3))/(1 - 1/3) + c` `int (x - 2)^(-1/3) dx =...

Asked by markusg on via web

• Math
You also may use elimination method, hence, if you need to eliminate the variable x, you need to multiply by -2 the first equation and add the new equation to the second equation of the system,...

Asked by katibatt on via web

• Math
You need to substitute `x + 2` and ` x - 2` for x in equation of function `f(x) = mx + n` , such that: `f(x + 2)*f(x - 2) = (m(x + 2) + n)(m(x - 2) + n)` `f(x + 2)*f(x - 2) = (mx + n + 2m)(mx + n...

Asked by roperswen on via web

• Math
You need to find the new composed function, hence, you need to replace the equation of v(t) for t in equation of u(t), such that: `(uov)(t) = 2(t - 1)^2 - 1 => (uov)(t) = 2(t^2 - 2t + 1) - 1`...

Asked by else9393 on via web