# Math Homework Help

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• Math
We need to find the angle that satisfies: (tan x)^2 = 6*sec x - 10 (tan x)^2 = 6*sec x - 10 =>(sin x)^2 / (cos x)^2 = 6 / cos x - 10 => [(1 - (cos x)^2)/(cos x)^2] = 6 / cos x - 10 let y =...

Asked by lesoir on via web

• Math
We have to determine the real roots of x^2 - 9 = -6/(x^2-4) x^2 - 9 = -6/(x^2-4) => (x^2 - 9)(x^2 - 4) = -6 => x^4 - 9x^2 - 4x^2 + 36 = -6 => x^4 - 9x^2 - 4x^2 + 42 = 0 => x^4 - 13x^3 +...

Asked by sokolof on via web

• Math
The equation to be solved is : 7^5x-7^x*7^36=0 7^5x - 7^x*7^36 = 0 => 7^5x - 7^(x + 36) = 0 => 7^5x = 7^(x + 36) As the base is the same we equate the exponent 5x = x + 36 => 4x = 36 =>...

Asked by bookofhth on via web

• Math
We have y = 54 + 11x^3 - 11x^5 y' = 33*x^2 - 55*x^4 y' = 0 => 33*x^2 - 55*x^4 = 0 => 11x^2( 3 - 5x^2) = 0 => x = 0 and 3 - 5x^2 = 0 => 5x^2 = 3 => x^2 = 3/5 => x = sqrt (3/5) and...

Asked by matveie on via web

• Math
We have to calculate the value of lim x-->1 [(x^2+12x-13)/(x-1)]. We cannot substitute x = 1 directly as that yields an indeterminate form. Instead we do the following. lim x-->1...

Asked by emilien on via web

• Math
You cannot ask more than one question at a time. So I am only providing one basic method. We need to find the derivative of the function y=2x^2-10x+13 +2(x^2-5x+6). y= 2x^2-10x+13 +2(x^2-5x+6)...

Asked by zuzuman on via web

• Math
We have to solve : 5^x^2 = 15625 / 5^x 5^x^2 = 15625 / 5^x => 5^x^2 = 5^6 / 5^x => 5^x^2 = 5^(6 - x) As the base 5 is the same we can equate the exponent => x^2 = 6 - x => x^2 + x - 6 =...

Asked by drole on via web

• Math
A Cartesian plane can be divided into 4 parts known as quadrants based on the value of the x and y co-ordinates. Starting from the top right quadrant which is the first quadrant in a clockwise...

• Math
We have to find the value of lim n-->+inf. [ a^(1/n)] We know that as n tends to infinity 1/n tends to 0. lim n-->+inf. [ a^(1/n)] => lim (1/n)-->0 [ a^(1/n)] Any number raised to the...

Asked by n1kaa on via web

• Math
We have to verify that (1+ (tan x)^2) *(cos x)^2 = 1 Starting with the left hand side (1+ (tan x)^2) *(cos x)^2 tan x = sin x / cos x => (1 + (sin x)^2/(cos x)^2) * (cos x)^2 => [(cos x)^2 +...

Asked by iszabelle on via web

• Math
We are given that m+4n=5 and 2m+4n=6. We need to find the value of 3m + 4n We solve the given equations for m and n m + 4n = 5 ...(1) 2m + 4n = 6 ...(2) (2) - (1) => m = 1 substitute in (1) 1 +...

Asked by siteulove on via web

• Math
First, we'll substitute x by the value of accumulation point. lim ln(x-2)/(x-3) = ln(3-2)/(3-3) = ln1/0 = 0/0 We've get an indetermination, so, we'll apply L'Hospital rule. We'll differentiate both...

Asked by aarie on via web

• Math
The linear function through the given points is a straight line. The equation of the line passing through (x1, y1) and (x2, y2) is: (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1) Here we have the points...

Asked by arundel on via web

• Math
First, we'll substitute x by 5 and we'll verify if it is an indetermination: lim (x^2-6x+5)/(x^2-25) = (5^2-6*5+5)/(5^2-25) = (30-30)/(25-25) = 0/0 Since we've get an indetermination, that means...

Asked by majaarmour on via web

• Math
We have to find the first derivative of y=(4x^2+2x)/x^2. Here it is not necessary to use the quotient rule. y=(4x^2+2x)/x^2 => y = 4x^2 / x^2 + 2x / x^2 => y = 4 + 2/x => y = 4 + 2*x^-1 y'...

Asked by wondergirl on via web

• Math
We have F(x) = direct integral from 1 to x^2 of ((t^3)+(t^(1/2))) dt and we have to find F'(x). F(x) = Int[ (t^3 + t^0.5)dt], t = 1 to x^2 => F(x) = [t^4/4 + t^1.5 / 1.5 + C], t = 1 to x^2 =>...

Asked by dhot8728 on via web

• Math
We have to solve (x+18)(x-14)(x+5) > 0. Now (x+18)(x-14)(x+5) > 0, if either none of the factors are negative or two of the factors are negative. None of the factors are negative (x+18) >...

Asked by dhopkins895 on via web

• Math
We have f(x) = 4x^2 + 4 and g(x) = 3x - 2. (fg)(x) = f(x) * g(x) => (4x^2 + 4)(3x - 2) open the brackets and multiply => 4x^2*3x + 4*3x - 2*4x^2 - 8 => 12x^3 + 12x - 8x^2 - 8 => 12x^3 -...

Asked by torrip996 on via web

• Math
We have to simplify (sec x - cosec x) / (tan x - cot x) further. (sec x - cosec x) / (tan x - cot x) use sec x = 1/ cos x, cosec x = 1/ sin x , tan x = sin x / cos x and cot x = cos x / sin x =>...

Asked by greg1234 on via web

• Math
We have to solve cos 2x - 2*(sin x)^2 + 2 = 0 cos 2x - 2*(sin x)^2 + 2 = 0 Use the identity cos 2x = 1- 2^(sin x)^2 => 1- 2*(sin x)^2 - 2^(sin x)^2 +2 = 0 => -4*(sin x)^2 = -3 => (sin x)^2...

• Math
We have to determine if the equation 5/(x+5) - 5=0 has a unique root. 5/(x+5) - 5=0 => 5/(x+5) = 5 => 5 = 5x + 25 => 5x = -20 => x = -20/5 => x = -4 Actually we don't need to solve...

Asked by pengui on via web

• Math
At the point of intersection of the lines the x and y co-ordinates are the same We have y = -x +14 and y = 4x - 11. Equating the y-coordinates ,we get -x + 14 = 4x - 11 => 5x = 25 => x = 5 y...

Asked by agneslund on via web

• Math
We have to prove the identity 3+(4+x)^3=x^3+12x^2+115 Starting with the left hand side 3+(4+x)^3 => 3 + 4^3 + x^3 + 3*16*x + 3*4*x^2 => 3 + 64 + x^3 + 48x + 12x^2 => x^3 + 12x^2 + 48x +...

Asked by edithmo on via web

• Math
The equation of a line in the form x/a + y/b = 1 gives the x and y intercepts as a and b The line we have is y = 12x + 8 y = 12x + 8 => y - 12x = 8 divide all the terms by 8 => -12x/8 + y/8 =...

Asked by portoruj on via web

• Math
We have to factor x^18 - y^18. x^18 - y^18 => (x^9)^2 - (y^9)^2 => (x^9 - y^9)(x^9 + y^9) => (x^3^3 - y^3^3)(x^3^3 + y^3^3) => (x^3 - y^3)(x^6 + y^6 + x^3*y^3)(x^3 + y^3)(x^6 + y^6 -...

Asked by boroboacana on via web

• Math
We have z - 2z' = 2 - 4i As z = x + i*y and z' = x - i*y z - 2z' = 2 - 4i => x + i*y - 2*(x - i*y) = 2 - 4*i => x + i*y - 2*x + 2*i*y = 2 - 4*i => - x +3*i*y = 2 - 4*i equate the real and...

Asked by blueglove on via web

• Math
An example of two imaginary numbers which when multiplied give a real number is of the form a+ bi and a - bi. They are called complex conjugates. When two complex conjugates are multiplied, the...

Asked by ggenius on via web

• Math
If the derivative of a function is 0, it indicates an extreme point. y = x^2 - 6x + 3 y' = 2x - 6 If y' = 0 => 2x - 6 = 0 => x = 3 f(3) = 3^2 - 6*3 +3 => 9 - 18 + 3 => - 6 At x = 3, we...

Asked by pavelpimen on via web

• Math
The equation will become: 3sin x/cos x + cos x/cos x = 4sin x/cos x We'll substitute the fraction sin x/cos x = tan x 3*tan x + 1 = 4*tan x We'll subtract 4*tan x both sides: 3*tan x + 1 - 4*tan x...

Asked by pufsipene on via web

• Math
Given the equation of the circle: x^2 - 6x + y^2 - 2y = 14 We need to find the radius and the center of the circle. Then, we need to rewrite into the standard form as follows: (x-a)^2 + (y-b)^2 =...

Asked by noralbbig on via web

• Math
To prove that the polynomial is divisible by (x-1)^2, that means that x = 1 is a root of polynomial and it's first derivative. For this reason, we'll substitute x by 1 in the expresison of...

Asked by penarul on via web

• Math
Let the number we need to find be N. As half of the number added to its third part is eight less than the number, we get N/2 + N/3 = N - 8 => (3N + 2N)/6 = (N - 8) => 5N = 6N - 48 => N =...

• Math
We have (x-3)/(x-1)=(x+1)/(x+2), and we have to solve for x. (x-3)/(x-1)=(x+1)/(x+2) => (x - 3)(x + 2) = (x + 1)(x - 1) => x^2 - x - 6 = x^2 - 1 => -x = 5 => x = -5 The required value...

Asked by gentzisisaci on via web

• Math
We have to prove that (4 - i*sqrt 6)/(2 - i*sqrt 6)=(sqrt 3 + 2i*sqrt 2)/(sqrt 3 + i*sqrt 2) The left hand side: (4 - i*sqrt 6)/(2 - i*sqrt 6) multiply the numerator and denominator by (2 + i*sqrt...

Asked by hahaz on via web

• Math
The problem provides the equations that relates the binomial coefficients of the `(r-1),r ` and `(r+1)` terms, such that: `(C_n^r)/(C_n^(r+1)) = 1/3 => (C_n^(r+1)) = 3(C_n^r)` Using the...

Asked by sanchita01 on via web

• Math
We have to multiply (x*y^2*z^3-v^4) and (x*y^2*z^3+v^4) We can see that the terms are of the form a - b and a + b with a=x*y^2*z^3 and b = v^4 We use the relation (a - b)(a + b) = a^2 - b^2...

Asked by frontman0 on via web

• Math
The 4 basic arithmetical operations are: addition, subtraction, multiplication and division. If we'll solve any linear equation, we'll fall into one from the 4 forms. For instance: 1) If x + a = b,...

Asked by colorcolour on via web

• Math
We are given that the company makes profits of 50,000 in the first year and they are predicted to increase every year in such a manner that a geometric series is formed. As the common ratio is r,...

Asked by timw996 on via web

• Math
We have to find the extremes of f(x) = ln(2x^2-20x+53). At the extremes the value of the first derivative is 0. f(x) = ln(2x^2-20x+53) f'(x) = 4x - 20 / (2x^2 - 20x + 53) 4x - 20 / (2x^2 - 20x +...

Asked by greynose on via web

• Math
We'll multiply the 1st equation by 1+x both sides: y*(1+x) = 5-x We'll remove the brackets: y + x*y = 5-x We'll move all terms to one side: y+x + x*y - 5 = 0 (3) We'll factorize th second equation...

Asked by bibiloi on via web

• Math
Given the equation: 3x^2 + 5x -12 = 0 We need to solve for x. We will use the formula to find the roots of the quadratic equations. We know that: x = [ -b +- sqrt(b^2-4ac)/ 2a ==> x1= ( -5 +...

Asked by clara2 on via web

• Math
Let the dimensions of the rectangle be L and W. We know that the area is A = L*W ==> L*W = 84 ............(1) Also, we know that the perimeter is given by P = 2L + 2W ==> 2L + 2W = 38 ==>...

Asked by nano75 on via web

• Math
Given that g(x)= (2x^2+3)*ln x We need to find the derivative g'(x). We will use the product rule to determine g'(x). We know that: if f(x) = u*v ==> f'(x) = u'v + uv' We will assume that g(x) =...

Asked by feres on via web

• Math
Given that: f(x) = (2x-5) / (3x+2) We need to find f'(x). We will use the qoutient rule to determine the derivative. ==> We know that : if f(x) = u/v , then f'(x) = ( u'v - uv')/v^2 Then we will...

Asked by totoo on via web

• Math
Given the curve: f(x) = 4x^2 - 4x + 5 We need to find the minimum value of the curve f(x). First we know that the coefficient of x^2 is positive. Then, f(x) has a minimum value. Now we will...

Asked by ryanomar on via web

• Math
Given the point (2,-3) passes through the line. We know that the equation of the line is given by : y-y1 = m(x-x1) where m is the slope and (x1,y1) is any point on the line. We will substitute with...

Asked by jude69 on via web

• Math
Given the line segment AB such that B(3,-3). Also, given that M(-2,4) is the point of AB. We need find the coordinates of the point A. We will use the midpoint formula to determine A. We know...

Asked by lalooo on via web

• Math
We are given the points A and B and we need to find the distance between them. We will use the formula of the distance between two points. ==> D = sqrt(x1-x2)^2 + (y1-y)^2 Now we will subsitute...

Asked by kokibrazil on via web

• Math
Given that 2z +3i = 3z +2 We need to find the absolute value of z. First we need to rewrite the number into the form z= a+ bi. Then the absolute values is lzl = sqrt(a^2+b^2). ==> 2z + 3i =...