
Math
Given the parabola f(x) = 3x^2 + 3x 5 Since the coefficient of x^2 is negative, then the function has a maximum point. First we will differentiate f(x). ==> f'(x) = 6x + 3 = 0 ==> x = 1/2...

Math
Given the quadratic equation: 3x^2  4x + 3 = 0 We will use the quadratic formula to solve for x. ==> x = [ b + sqrt(b^24ac)]/2a ==> a = 3 b= 4 c= 3 ==> x1= [...

Math
I would love to help you with this question, but I just can't seem to make sense out of it. I think you've worded the question incorrectly? Two people meet eachother, right? How many ways can...

Math
The sine and cosine functions are periodic with a periodicity equal to 2*pi. For any angle x, sin x = sin (x + n*2*pi) and cos x = (cos x + n*2*pi) with n being any integer. sin (x + 2*pi) = sin x...

Math
To reset the TI85 factory settings you would have to use the following keystrokes: 2nd + F3 F1 F4 F3 is used to indicate that you want to reset. F1 is to choose everything and F4 is to choose yes...

Math
You did not post a question. Please revise your post so that someone may assist you. :)

Math
The turning point of a curve is the point where the first derivative of the equation is equal to 0. Here the function either stops decreasing or stops increasing. For the given function y = x^2 ...

Math
I guess you have asked this question with reference to which of the most commonly used and widely understood measures of central tendency the mean, medium and mode should be used. For the data...

Math
From the information given, there are two paperweights which are hemispherical in shape. The smaller one has a volume of 5 cubic inches and the larger has dimensions four times as large as the...

Math
Area of the triangle = (1/2)absinC = (1/2) 1.3*2.4*sin30 = 0.78 sq uinits.

Math
sinA < 0 for 180 degr < A < 360 deg. CotA > 0 for 180 deg < A < 270 deg. => Angle A is in 3rd quad.

Math
Given the quadratic equation: 2x^2  5x + 1 = 0 We will use the quadratic formula to find the roots. ==> x = [ b + sqrt(b^2  4ac)]/2a ==> a = 2 b= 5 c = 1 ==> x1= [ 5 +...

Math
f(x) = sin2x + cosx We need to find f(pi/2) We will substitute with x= pi/2 ==> f(pi/2) = sin(2*pi/2) + cos (pi/2) = sin(pi) + cos(pi/2) = 0 + 0 = 0 Then...

Math
Given that : sinA = 0.3 cosB = 0.8 Then we conclude that the angle C= 60 degree. Then the hypotenuse is AB But we know that sinA = opposite / hypotenuse= BC/AB ==> BC/AB = 0.3 ......(1) sinB =...

Math
The equation to be solved is x(x40)(3x+2)= 240 x(x40)(3x+2)= 240 => (x^2  40x)(3x + 2) = 240 => 3x^3  120x^2 + 2x^2  80x = 240 => 3x^3 198x^2  80x = 240 => 3x^3 198x^2  80x ...

Math
The value of 2a  3b = 6 We expression we have to find the sum of is (5 2a + 3b)+(5 2a + 3b)^2+...+(5  2a + 3b)^500 (5 2a + 3b)+(5 2a + 3b)^2+...+(5  2a + 3b)^500 => (5 (2a  3b))+(5 (2a...

Math
The roots of a quadratic equation ax^2 + bx + c = 0 are equal to x1 = [b + sqrt (b^2  4ac)]/2a and x2 = [b  sqrt (b^2  4ac)]/2a Here the equation we have is 5x^2 = 8x + 2 => 5x^2  8x  2 =...

Math
We need the result of : 2x/(x^24)3/(x2)(x+2)+2/(x+2) 2x/(x^24)3/(x2)(x+2)+2/(x+2) first make the denominator the same for all the terms => 2x/(x 2)(x + 2)  3/(x2)(x+2) + 2(x ...

Math
The equation of the circle given is: x^2+y^2+6y4x=36 x^2+y^2+6y4x=36 => x^2  4x + 4 + y^2 + 6y + 9 = 36 + 4 + 9 => (x  2)^2 + (y + 3)^2 = 7^2 This is the general form of the equation of a...

Math
To locate the extreme points of a function you need to take the first derivative and set it equal to zero. The first deravtive tells you where the function changes from increasing to decreasing or...

Math
Let the numbers be A and B. Their product is 6 => A*B = 6 Their sum is twice their product => A + B = 6*2 = 12 We need the value of A^3 + B^3 (A + B)^3 = A^3 + B^3 + 3*A*B*(A + B) => 12^3...

Math
The definite integral of x^2*e^x is required between x = 0 and x = 1. Let's find the indefinite integral first. This requires the use of integration by parts. Int [ x^2*e^x dx] Let u = x^2 => du...

Math
The integral of ( 7x + 2 ) / [ ( x  1 ) ( x + 2 ) ] can be found by first finding the partial fractions of the given expression and then integrating each of the fractions. Let ( 7x + 2 ) / [ ( x ...

Math
The equation to be solved is log(3) x^2 + log(9) x = 2 Use the following properties of logarithms log a^b = b*log a , log a + log b = log a*b and log (b) c = log(a)c / log(a)b log(3) x^2 + log(9) x...

Math
We need to find lim x> inf. [sqrt(x^2 + 5x + 8)  x] sqrt(x^2 + 5x + 8)  x => [sqrt(x^2 + 5x + 8)  x]*[sqrt(x^2 + 5x + 8) + x]/[sqrt(x^2 + 5x + 8) + x] => [sqrt(x^2 + 5x + 8)]^2  x^2...

Math
Given the sides of the right angle triangle are x+ 4, x+ 7, and the hypotenuse is 3x. Then : (3x)^2 = (x+4)^2 + (x+7)^2 ==> 9x^2 = x^2 +8x + 16 + x^2 + 14x + 49 ==> 9x^2 = 2x^2 + 22x + 65...

Math
The dot product between two vectors A = ai + bj + ck and B = a'i + b'j + c'k is given as A*B = AB*cos t, where t is the angle between the vectors A*B is also given as a*a' + b*b' + c*c'...

Math
The function f(x) is defined as f(x) = 0.25x^4 + 3x^3 – 18x^2 +10. The extreme points are the solutions for f'(x) = 0 f'(x) = 4*0.25*x^3 + 9x^2 – 36x 4*0.25*x^3 + 9x^2 – 36x = 0 => x(x^2 +...

Math
We have to show that 2x^3+12x^2+18x+24 = 0 has one real root. I am only proving that there is one real root, not that there is only one real root. The derivative of the function f(x) =...

Math
We have to solve: 81^(x1)  9^(x+1) > 0 81^(x1)  9^(x+1) > 0 => 9^2^(x  1)  9^(x + 1) > 0 => 9^(2x  2)  9^(x + 1) > 0 => 9^(2x  2) > 9^(x + 1) As 9 is a positive...

Math
We need to find the solution for log(x+3)=3log(x3) log(x+3)=3log(x3) => log(x+3)  log(x3) = 3 use log a + log b = log (a*b) => log (x + 3)*(x  3) = 3 => (x + 3)*(x  3) = 10^3 =>...

Math
We'll rewrite the identity, using arcfunctions: arccos x = pi/2  arcsin x We'll shift arcsin x to the left side and we'll get: arccos x + arcsin x = pi/2 It is obvious that for x = 1, we'll get:...

Math
We have to solve (cos x)^2 = 1/2 using difference of squares. (cos x)^2 = 1/2 => (cos x)^2  1/2 = 0 a^2  b^2 = (a  b)*(a + b) => (cos x  1/sqrt 2)(cos x + 1/sqrt 2) = 0 cos x = 1/sqrt 2...

Math
We have to find the partial fractions of (5x+1)/(x^2+x2) First let's factorize the denominator x^2 + x  2 => x^2 + 2x  x  2 => x(x + 2)  1(x + 2) => (x  1)(x + 2) (5x+1)/(x^2+x2) =...

Math
The standard form of (6  2i )/( 4 +14i ) has a real denominator. (6  2i )/( 4 +14i ) multiply numerator and denominator by (4  14i) => (6  2i )(4  14i)/( 4 +14i )(4  14i) => (24  8i ...

Math
We'll decompose the fraction 1/(2n+3)(2n+7) in 2 elementary fractions: 1/(2n+3)(2n+7) = (1/4)[1/(2n+3)  1/(2n+7)] We'll substitute n by 1 and we'll get: s1 = (1/4)*[1/(2+3)  1/(2+7)] = (1/4)(1/5...

Math
We have to solve 8*15^x/5  3*5^(2x1)  9^x = 0 8*15^x/5  3*5^(2x1)  9^x = 0 => 8*15^x/5  3*5^2x/5  3^2^x = 0 => (8/5)*3^x*5^x  (3/5)*5^x^2  3^x^2 = 0 divide by 5^2^x =>...

Math
Let the vector u be ai + bj. u*v = (ai + bj)(6i + 3j) = 6a + 3b = 12 u*w = (ai + bj)(2i + j) = 2a + b = 14 Solve the simultaneous equations 6a + 3b = 12 and 2a + b = 14 We see that the system has...

Math
The expression to be simplified is (sinx + cosx)^2/(1+ 2*sin*x*cos x) (sinx + cosx)^2/(1+ 2*sin*x*cos x) Use (a + b)^2 = a^2 + b^2 + 2*a*b => ((sin x)^2 + (cos x)^2 + 2*sin x*cos x )/(1+...

Math
A sum of n terms of a general geometric progression which has terms such that consecutive terms have a common ratio is given by a*(r^n  1) / (r  1), where a is the first term and r is the common...

Math
We need to find x and y given that 3^(x + y)  243 = 0 and x = 6/y 3^(x + y)  243 = 0 can be written as 3^(x + y) = 243 => 3^(x + y) = 3^5 As the base 3 is common equate the exponent => x +...

Math
We need to find x if 2^(9x15)  1/64 = 0 2^(9x15)  1/64 = 0 move 1/64 to the other side =>2^(9x15) = 1/64 express 1/64 in terms of powers of 2 => 2^(9x15) = 2^(6) as the base is equal...

Math
The function f(x) = (x+7)^1/2 has an inverse if x is positive. Let y = f(x) = (x+7)^1/2 => y^2 = (x + 7) => y^2  7 = x interchange x and y => y = x^2  7 The inverse function of f(x) is...

Math
The bacteria grow at an exponential rate. If there are n g to begin with, after 4 hours there are 2n g. The number of bacteria at any moment of time can be expressed as x(t) = x0*(2)^(t/4)...

Math
l 2t 3 l + 5 = 3t We will subtract 5 from both sides. ==> l 2t 3l = 3t 5 Now we have two cases: 1: (2t3) = 3t 5 ==> t = 2 ..........(1) 2: (2t3) = 3t5 ==> 2t + 3 = 3t 5 ==>...

Math
We have to solve for values of x that satisfy (x^2 3x 4) < 0 (x^2 3x 4) < 0 => x^2  4x + x  4 < 0 => x(x  4) +1(x  4) < 0 => (x + 1)(x  4) < 0 If the above...

Math
Given the sequence of numbers. 3, 7, 23, x, 343, 1367 We need to find the value of x. Then we will need to determine the relation between the terms. Let us determine the differences between each...

Math
The slope of two parallel lines is the same. The equation of the line 2y  4x + 2 = 0 can be written as 2y = 4x  2 => y = 2x  1 this gives the slope of the line as 2 The line we have to find...

Math
If x1 and x2 are roots of f(x) . Then we know that: x1+ x2 = b/a x1*x2 = c/a We will assume that a= 1 ==> x1+ x2 = b ==> x1+ x2= 23i + 2+3i = 4 ==> b= 4 ==> x1*x2 = (23i)(2+3i)= 4...

Math
Let the cost of the pants be P and the cost of the shirts be S. Given that the cost of 2 pants and 5 shirts is 211 ==> 2P + 5S = 211............(1) Also, given that the shirt costs 40 than the...