
Math
Given the equation: x^3+ x^2 + x +1 = 0 We need to find x values that satisfies the equation. First we will simplify by factoring. We will factor x^2 from the first two terms. ==> x^2 ( x+1) +...

Math
Given the volume of the cylinder is v= 234 The height = 12 We need to find the surface area. First we will need to find the radius. We know that the volume if given by : v= r^2*pi*h where r is the...

Math
Let x be the number of people attends. Let the revenue be y. Let the initial revenue when 120 people attend is 30*120 = 3600 y= people attend * price y= (120+x)*(30 1.5*(x/10)] y= (120+x) * ( 30...

Math
The system is consisted of 4 variables and 4 equations as follow: Let the variables be x,y,z, and u ==> 6x +2y z 5u = 25 ==> x +7z +3u = 7 ==> x y 10z +6u = 23 ==> 8y + z 11u = 21

Math
f(x) = 8x +4 Given that f(a) = 1.6 We need to find the values of a. We will substitute with x= a into the function f(x). ==> f(a) = 8a +4 = 1.6 Now we will solve for a. ==> 8a = 1.6 4 =...

Math
Given the formula: V = C(1r)^t v is the values c is the original cost = 40,000 r is the rate = 8% = 0.08 t is the number of years Given the information above, we need to find t such that v=...

Math
Given f(x) = 6x+4 We need to find the values of a such that f(a) = 1.3 We will substitute with x=a into the equation. ==> f(a) = 6a +4 But given that f(a) = 1.3 ==> f(a) = 6a+4 = 1.3 Now...

Math
A=P (1+r)^t A = Value of CD P = original amount= 1000 r = the rate = 3% = 0.03 t= time We need to find t such that A is doubled ==> A = 2*1000 = 2000 Now we will substitute. ==> 2000 =...

Math
We have to simplify (e^x  e^x)^7 (e^x  e^x)^7 => (e^x  1/(e^x))^7 => [(e^x * e^x  1)/(e^x)]^7 => (e^x * e^x  1)^7/(e^x)^7 => (e^2x  1)^7 / e^7x We could expand the numerator...

Math
First, we'll move all the powers of 7 to the right side of the equal sign. 2^x + 2^(x+1) + 2^(x+2) = 7^x + 7^(x+1)+7^(x+2) Now, we'll apply the property of exponentials: a^(b+c) = a^b*a^c According...

Math
We'll expand the binomial and we'll get: (1+x)^6 = a0 + a1*x + a2*x^2 + ... + a6*x^6 a0,a1,a2,...,a6 are the coefficients of polynomial. The sum of even coefficients is: a0 + a2 + a4 + a6 We know...

Math
Since a1,a2,...,an are the terms of an A.P., we'll apply the rule of finding each term of the arithmetical sequence: a2 = a1 + d => a2 a1 = d a3 = a1 + 2d => a3  a1 = 2d...

Math
Well rewrite 4^(2x+1) = 4^2x*4 and 6^(x+2) = 6^x*6^2 We'll rewrite the entire expression: 3^x*4^2x*4 = 6^x*6^2 We'll write 6^x = 2^x*3^x 3^x*4^2x*4 = 2^x*3^x*36 We'll divide by 4*3^x: 4^2x =...

Math
The formula for the surface area of the cone is the following: SA = area of the base + area of the cone. Area of the base = r^2 * pi Area of the cone = r*s*pi ( r is the radius of the base and s...

Math
Only values of a which are greater than or equal to 0 will make the expression inside the absolute symbol (that is a) negative. Therefore, for the property a = a to be meaningful, a must be...

Math
You have to remember that the number of solutions of an equation is equal to the highest power of the variable. A linear variable has 1 solution; a quadratic equation has 2 solutions, etc. The...

Math
When the tire rotates 400 r/ m , then the distance the tire travels in one minute = 400 * circumference of the tire for 1 minute ==> D = 400 * C...............(1) Now we will calculate the...

Math
You want the value of x for which sin x  cos x = 0. Why are you taking the cases where cos x = 1, sin x = 0, etc. Instead, solve for x. sin x  cos x = 0 => sin x = cos x => sin x / cos x =...

Math
You have to solve x = sin x If you have a look at the graph of the sine function you see that it starts from the point (0,0). At this point the value of the sin function is zero and the value of x...

Math
We have the functions: f(x)=x, g(x)=6x8 and h(x) = 4x. We have to find u= fo(gof)/h. u = fo(gof)/h => u = fo[(g(f(x))/ h(x)] => u = fo[(6x  8) / (4  x)] => u = (6x  8)/ (4 ...

Math
The equation 2*lg(x1) = lg (ax3) has two equal roots. 2*lg(x1) = lg (ax3) => lg ( x1)^2 = lg (ax  3) taking the antilog of both the sides => (x  1)^2 = ax  3 => x^2  2x + 1 = ax ...

Math
The equation of the line between the points (6, 3) and (3, 4) is y – 3 = (x – 6)[(4 – 3)/(3 – 6)] => y – 3 = (x – 6)*( 1/3) The slope of the line is (1/3). The equation of the line...

Math
Law 1: log x + log y = log (x*y) Example: log 2 + log 5 = log (2*5) = log 10 = 1 Law 2: log x  log y = log x/y Example: log 100  log 10 = log 100/10 = log 10 = 1 Law 3: log x^a = a* log x...

Math
The slope of the tangent to a curve f(x) is the value of the first derivative of the curve for the appropriate x. Here we have x^2 + y^2 = 34 Differentiating both the sides 2x + 2y (dy/dx) = 0...

Math
We'll substitute x by 2 and we'll get: lim (lnxln2)/(x2 x) = lim (ln 2  ln 2)/(2  4) lim (lnxln2)/(x2 x) = 0/2 =0 But this is the value of the limit of the function, if and only if the...

Math
We have to prove that (1+2(sin a)(cos a))/(12(sin^2 a)=(cos a+sin a)/(cos asin a) Starting from the left hand side (1+2(sin a)(cos a))/(12(sin a)^2) replace 1 with (sin a)^2 + (cos a)^2 =>...

Math
Let's denote the number of students as S. 5/7 of them are boys. If we denote the number of boys as B, B = (5/7)*S The rest of the students are girls. This is equal to (1  5/7)*S = (2/7)*S As the...

Math
ln t =  ln 2 We will preview the properties of the logarithm equations. We know that: ln a^b = b*ln a Then we will rewrite the equation.  ln 2 = 1 * ln 2 = ln 2^1 = ln (1/2) ==> ln t = ln...

Math
x^2 + 6x + 6 = 3 + (x+3)^2 To prove, we will start form the left side and prove the right sides. First we will complete the square. ==> (x^2 + 6x +6) We will add and subtract( x's...

Math
We have to prove that 3+1/(x+1) has a unique solution. 3+1/(x+1) => [3(x +1) + 1] / (x+1) => [3x + 3 + 1] / (x +1) => [3x + 4] / (x + 1) We see that the maximum power of x in the function...

Math
We have to solve the inequation x/2 >= 1 + 4/x x/2 >= 1 + 4/x => x >= 2 + 8/x If we assume that x >=0, we can multiply both the sides of the inequation with x without changing the...

Math
To calculate cosine, using adjacent dided by hypotenuse. Tangent is opposite over adjacent. opposite =10 adjacent = 24 So you are missing hypotenuse. In a right triangle, c is the hypotenuse....

Math
The answer to this question is that the Arctic Wolf is 40 kg. and the bobcat is 8 kg. You can set up the equation as 1/5 X + X =48kg. Next, multiply 1/5 X by 5 to make it a whole number, or X....

Math
We have the function f(x) = sqrt x + a. At x= 16, the tangent to to the function is y = mx + 2 The slope of the tangent to the function f(x) = sqrt x + a at x = 16 is m. f'(x) = (1/2)/ sqrt x =>...

Math
We have f(x) = (x + 8)^2. We have to find the equation of the tangent to the graph at the point where x = 2. The slope of the tangent drawn to a graph f(x) at the point (x, f(x)) is the value of...

Math
We'll start using the condition from enunciation that the binomial coefficients of the given expansion are in arithmetical progression. Since it is not indicated what are the terms, we'll suppose...

Math
We have to prove: sin^4(theta)  cos^4(theta) = sin^2(theta)  cos^2(theta) First let's write the terms in a standard form and use x instead of theta. So we have to prove (sin x)^4  (cos x)^4 =...

Math
We have the length of the sides of the triangle given as 4 ,5 and 8. Let us denote the sides as a = 4, b = 5 and c= 8. The angles A, B and C are opposite the three sides. The angles of the...

Math
The surface area of a cube of side s is given by 6*s^2 . Here the surface area is 486 m^2 6*s^2 = 486 => s^2 = 486 / 6 => s = sqrt 81 => s = 9 The diagonal length of a cube of side 9 is...

Math
You have given that the card has an interest free period of 32 days. The man spends $32000 using his card and pays back $20000 within 32 days, the rest is paid after 45 days. He incurs an interest...

Math
The sides of the triangular park are of 80 m , 100 m and 120 m. The area of the park can be calculated using Heron’s formula which gives the area as sqrt [s*(s – a)(s – b)(s – c)] where a,...

Math
f(x) = (x2)/(2x3) To find the derivative, we will use the quotient rule. Let f(x) = u/v such that: u= x2 ==> u' = 1 v= (2x3) ==> v' = 2 Then we know that: f'(x) = [ u'*v  u*v']/ v^2...

Math
Given the point (a,2) and the point (3a,5). We need to find the distance in terms of a. We will use the distance between two points formula to calculate. ==> We know that : D = sqrt[ (x1x2)^2...

Math
Let the distance both cars travels before they meet is D. The time need to for car 1 is T1 The car needed for car 2 is T2 But car 2 leaves 30 minutes ( 0.5 h) after car 1 ==> T2 = T1  0.5...

Math
2 5*l 2x3 l < 7 First we will need to isolate the absolute values on the left side. Let us subtract 2 from both sides. ==> 5*l2x3l < 5 Now we will divide by 5 and reverse the...

Math
Given the right angle triangle at B is ABC such that: AB = 6 BC= 7 Then the hypotenuse is AC Now we will calculate the length of the hypotenuse. ==> AC^2 = AB^2 + BC^2 ==> AC^2 = 6^2 + 7^2 =...

Math
Let the length of the rectangle be L and the width is W. Given that the length is twice the width. ==> L = 2*W ............(1) Also, given that the area of the rectangle is 98. ==> L*W = 98...

Math
We are given the equation of the line 2xy+2 = 0 We will rewrite into the slope form. ==> y= 2x+2 ..........(1) Also, given the equation of the curve g(x) = x^2 3x 7 We need to find the...

Math
Given the curve p(x) = (x2)(3x1) We need to find the integral of p(x) between 0 and 1 First we will simplify and open the brackets. ==> p(x) = 3x^2 x 6x +2 ==> p(x) = 3x^2 7x +2 Now we...

Math
Given the systems: 2a = b..........(1) a 3b = 12 ..........(2) We need to solve for a and b. We will use the substitution method to solve. We will substitue (1) into (2) ==> a  3b = 12 ==>...