# Math Homework Help

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

• Math
The equation 21 log(3) cube root of x + log(3)9x^2- log(3)9 = 2 has to be solved. 21 log(3) cube root of x + log(3)9x^2- log(3)9 = 2 can be written as 21 log(3) x^(1/3) + log(3) 9x^2 - log(3) 9 =...

Asked by callen202 on via web

• Math
Roots of a function f(x) are the values of x for which f(x) = 0. To find the roots graphically we plot the graph f(x) versus x and find the points where the graph intersects the x-axis. The value...

Asked by bergygi on via web

• Math
Some of the properties of logs are: log(a*b) = log a + log b example: log 6 = log 3*2 = log 3 + log 2 log(a/b) = log a - log b example: log 5 = log(10/2) = log 10 - log 2 log(a^b) = b*log a...

Asked by lilstunna10 on via web

• Math
The house decreases at the rate of 18% every year. If the initial value of the house was P and the rate of depreciation is r, the formula for the value after n years is P*(1 - r)^n We need to find...

Asked by pooyh on via web

• Math
The identity you had given to be proved was : (cos x + sin x)^2 + (cos x*sin x)^2 = 2 (cos x + sin x)^2 + (cos x*sin x)^2 = 2 opening the brackets gave => (cos x)^2 + (sin x)^2 + 2*sin x*cos x +...

Asked by lbawa on via web

• Math
We have to prove that 1 - (sin^6 x + cos^6 x) = 3(sin x)^2 (cos x)^2 Let's start with the left hand side. 1 - [(sin x)^6 + (cos x)^6] => (sin x)^2 + (cos x)^2 - (sin x)^6 - (cos x)^6 => (sin...

Asked by lxsptter on via web

• Math
The identity csc x - cot x = sin x/(1+cos x) has to be proved. Start from the left hand side csc x - cot x csc x = 1/ sin x and cot x = cos x/ sin x => 1/sin x - cos x/sin x => (1 - cos...

• Math
The value of lim x-->3 [sqrt ( x^2 - 9)/(x - 3)] has to be found. lim x-->3 [sqrt ( x^2 - 9)/(x - 3)] substituting x = 3, gives the indeterminate form 0/0. => lim x-->3 [sqrt (x - 3)*...

Asked by justinenotes3 on via web

• Math
We need to find lim x --> 2[ (x - 2)/4 - sqrt (4x - x^2)] substituting x = 2 , gives (0/4) - sqrt (8 - 4) => 0 - sqrt 4 => -2 The required limit is -2.

Asked by justinenotes on via web

• Math
The value of lim x--> 1[ (x - 1)/sqrt(2x - x^2 - 1)] has to be found. It can be seen that a direct substitution of x = 1, yields 0/0 which cannot be determined. lim x-->1[ (x - 1)/sqrt(2x -...

Asked by justinenotes2 on via web

• Math
To simplify (8x^2 - 242) / (2x^2 - 25x+77) we have to factorize the numerator and the denominator and cancel any common factors. (8x^2 - 242) / (2x^2 - 25x + 77) => 2(4x^2 - 121) / (2x^2 - 14x -...

Asked by xetaalpha2 on via web

• Math
To simplify (x^2-13x+42) / (14x^2+71x-33) use the following steps: (x^2-13x+42) / (14x^2+71x-33) factorize the denominator and the numerator => (x^2 - 7x - 6x + 42) / (14x^2 + 77x - 6x - 33)...

Asked by xetaalpha on via web

• Math
For a given data set, the range is the difference between the largest value and the smallest value. The mean is the sum of all the values divided by the number of values. The mode is the value that...

Asked by schoolier on via web

• Math
The range for a data set is the difference between the largest value and the smallest value. In the case of the data set set you have provided: 94, 90, 88, 66, 94, 81, 102, 108, 88, the largest...

Asked by schooldump on via web

• Math
Complex numbers are an extension to real numbers and extensively used in many aspects of mathematics relating to fields like engineering, electromagnetism, quantum physics, applied mathematics, and...

Asked by pooyh on via web

• Math
log3 ( x+ 3) + log3 ( x-5) = 2 First we will determine the domain, ==> x+ 3 > 0 and x-5 > 0 ==> x > -3 and x > 5 ==> x > 5 is the domain.......(1) We will use...

Asked by yetty on via web

• Math
An exponential equation is one of the form y = a*b^x, where a is the initial value of y when x = 0 and it increases at a non-linear rate. The value of y increases by the factor b, also called the...

Asked by saaaaah on via web

• Math
To determine the extremes of the function, we'll have to calculate the critical values of the function, that are the roots of the first derivative of f(x). We'll differentiate the function with...

Asked by bulbul on via web

• Math
Sorry, the derivative is dy/dx=1/(cos2x+sin^2x)!

Asked by clovis82 on via web

• Math
We have to find the derivative of f(x) = (2x+1)^2+(2x-2)^2 + 2(4x^2-2x-2) f'(x) = [(2x+1)^2+(2x-2)^2 + 2(4x^2-2x-2)]' f'(x) = [(2x+1)^2]'+[(2x-2)^2]' + [2(4x^2-2x-2)]' Use the chain rule. f'(x) =...

Asked by augenblau on via web

• Math
The vectors AB and CD are perpendicular to each other. In this case the dot product is equal to 0, as cos 90 = 0. The dot product of the vectors AB = (3-2a)*i+(a+1)*j and CD=(2a+1)*i+2*j is also...

Asked by axel12 on via web

• Math
We have to prove : (1/(sin x^2x)+(1/cos^2x)=(tan x+(1/tan x))^2 Take the left hand side 1/(sin x)^2+ 1/(cos x)^2 => ((cos x)^2 + (sin x)^2)/(sin x)^2*(cos x)^2x => 1/(sin x)^2*(cos x)^2x...

Asked by lbawa on via web

• Math
As it is tough to type theta, I will use "y" instead. It is given that :sin(2*pi - y) - sin(pi - y) - cos(3/2pi + y) = 3/2 sin (2*pi - y) = -sin y sin (pi - y) = sin y cos (3*pi/2 + y) = -sin y...

Asked by pawilai on via web

• Math
The vectors u = m*i + (m+1)*j and v = 3*i + 5*j are collinear. This is possible if m / (m+1) = 3/5 m / (m+1) = 3/5 => 5m = 3(m + 1) => 5m = 3m + 3 => 2m = 3 => m = 3/2 The value of m = 3/2

Asked by loochy on via web

• Math
To simplify 8i/(2 - 2i) we have to convert the denominator to a real number. This can be done by multiplying it and the numerator by the complex conjugate or 2 + 2i 8i/(2 - 2i) => 8i(2 + 2i)/(2...

Asked by sauerrahm on via web

• Math
The derivative of y is given as dy/dx = sqrt(-4x^2+8x+12) y' = sqrt [ -4x^2+8x+12] => 2*sqrt [-x^2 + 2x + 3] => 2*sqrt [ -(x^2 - 2x + 1) + 4] => 2*sqrt [ -(x - 1)^2 + 4] y = Int[ y' dx]...

Asked by siteulove on via web

• Math
We have to find the anti derivative of f(x)*cos x , where f(x) = ln(1 + (sin x)^2) Int [ f(x)*cos x dx] => Int [ ln(1 + (sin x)^2) * cos x dx] let sin x = y dy = cos x dx => Int [ ln(1 + y^2)...

Asked by sensitiv on via web

• Math
We need to find the indefinite integral of f(x)=3x^2+12x+18 Int [ f(x) dx ] => Int [ 3x^2+12x+18 dx ] => Int [ 3x^2 dx ] + Int[12x dx] + Int[ 18 dx ] => 3*x^3 / 3 + 12x^2 / 2 + 18x + C...

Asked by orlovolga on via web

• Math
The function f(x)=(x^2+2)^4 can be differentiated using the chain rule. According to the chain rule for f(x) = h(g(x)) f'(x) = h'(g(x))*g'(x) f(x) = (x^2+2)^4 take g(x) = x^2 + 2, h(x) = x^4 f'(x)...

Asked by greycake on via web

• Math
The equation that we have to find the solutions of is 4*2^(x^2)/2^(3x)=64 4*2^(x^2)/2^(3x)=64 => 2^(x^2)/2^(3x)=64/4 => 2^(x^2)/2^(3x)=16 => 2^(x^2) = 16*2^(3x) => 2^(x^2) = 2^4*2^(3x)...

Asked by olaf on via web

• Math
Let us find the solution of the equation 3^(2x-6) = 81 3^(2x-6) = 81 => 3^(2x - 6) = 3^4 we can equate the exponent 2x - 6 = 4 => x = 10/2 = 5 The number of elements in the set...

Asked by tarja19 on via web

• Math
We have to find the partial fractions of 2x/(x^2-9) 2x/(x^2-9) => 2x/(x+3)(x - 3) => A/(x + 3) + B/(x - 3) [A(x - 3) + B(x + 3)]/(x + 3)(x - 3) = 2x/(x+3)(x - 3) => Ax - 3A + Bx + 3B = 2x...

Asked by leeaeel on via web

• Math
Let f(x) = y y = sqrt(x - 1) We'll interchange x by y: x = sqrt(y - 1) We'll raise to square both sides, to eliminate the square root: x^2 = y - 1 We'll add 1 both sides, to isolate y: x^2 + 1 =...

Asked by sixpenpencil on via web

• Math
First, we'll re-write the expression of dy/dx, using the negative power rule: (2+cosx)^-1 = 1/(2+cosx) dy/dx = 1/(2+cosx) => dy = dx/(2+cosx) To determine the primitive of the given function dy,...

Asked by sirserie on via web

• Math
First, we'll create the function f(x) = sin x - x*cos x and we'll have to prove that f(x)>0. To study the behavior of the function, namely if it is an increasing or a decreasing function, we'll...

Asked by realcomplexnr on via web

• Math
First, we'll make the substitution sin x=t (t)^2 - 8*t + 12 = 0 We'll apply quadratic formula t1= [-(-8)+sqrt(64-48)]/2 t1=(8+4)/2 t1=6 sin x=t1 <=> sin x=6 (impossible) Since the range of...

Asked by undoitu on via web

• Math
We'll replace the function cot 45 by it's value 1. To simplify the difference, we'll transform it into a product. We'll have to express the value 1 as being the function cosine of an angle, so...

Asked by jeuxdesfou on via web

• Math
To solve the equation dy/dx = 0, we'll have to differentiate y with respect to x. dy/dx = (11x^4-22x^2+33)' dy/dx = 11*4*x^3 - 22*2*x + 0 dy/dx = 44x^3 - 44x We'll cancel dy/dx: dy/dx = 0 <=>...

Asked by istetz on via web

• Math
First, we'll apply the rule of negative power for the term x^-2: x^-2 = 1/x^2 To get the squares x^2 and (1/x^2), we'll raise to square the expression x- (1/x). If we want to raise to square x-...

Asked by greynose on via web

• Math
We'll determine the possible values of x, for the square root to exist. For this reason, we'll impose the following constraint: the radicand has to be positive or, at least, zero. -2x + 1 >= 0...

Asked by oldcareer on via web

• Math
To evaluate the indefinite integral of f(x)=sin5x*cos3x, we'll apply the formula to transform the product of trigonometric functions into a sum. We'll use the formula: sin a * cos b =...

Asked by leslie29 on via web

• Math
We'll use the binomial raised to cube identity: (a+b)^3 = a^3 + b^3 + 3a*b*(a+b) In this case, a = x1 and b = x2 We'll replace a and b by x1 and x2 and we'll have: (x1+x2)^3 = x1^3 + x2^3 +...

Asked by pengui on via web

• Math
We have to solve: (cos x)^2 - (sin x)^2 + sin x = 0 (cos x)^2 - (sin x)^2 + sin x = 0 substitute (cos x)^2 = 1 - (sin x)^2 => 1 - (sin x)^2 - (sin x)^2 + sin x = 0 => 1 - 2*(sin x)^2 + sin x...

Asked by redsunshine on via web

• Math
Let the terms of a geometric progression be : a1, a2, a3, a4 Given that a3= 1 and the common difference is 1/2. ==> Then we know that: a3 = a1*r^2 1 = a1* (1/2)^2 1= a1/ 4 ==> a1= 4 ==>...

Asked by jojoogel on via web

• Math
Let us assume that the number is x. Then 3 times square x is 3x^2. And we will add 2 times fifth x ==> 3x^2 + 2x/5 = 3x^2 +(2/5)x ==> All divide by (x+7) ==> [(3x^2 + (2/5)x] / (x+7)...

Asked by genieee on via web

• Math
sqrt(x^2 + 3x -5) = x+ 2 First we will square both sides. ==> x^2 + 3x -5 = (x+2)^2 ==> x^2 + 3x -5 = x^2 + 4x +4 ==> 3x -5 = 4x+4 ==>. x = -9 Let us check. ==> sqrt( 81-27-5) =...

Asked by rogeryyo on via web

• Math
Let the first speed be S1 = 55 mph and the time is T1 = 24 min. The second speed is S2= 135 and the time is T2 = 135 min. We need to find the total distance . Let the total diostance be D = D1 +...

• Math
Given that : log a = 12 log b= 3 We need to find the value of the expression : log (a^2*b^3)^6 First we know that log a^b= b*log a. ==> log (a^2*b^3)^6 = 6*log (a^2*b^3) Now we know that log ab...

• Math
log3 (12n-1) - log3 (2x+7) = 2 First we will find the domain. ==> 12n-1 > 0 ==> n> 1/12 ==> 2n+7 > 0 ==> n > -7/2 Then The domain is n > 1/12 .............(1) Now we will...

Asked by zaidzoo on via web