• Math
Given the lines: ax + by + c = 0 We need to determine the x and y intercepts and the gradient. The x-intercept is when the line meets the x-axis. Then, y= 0 ==> ax + c = 0 ==> x = -c/a Then...

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1. Simplify (a^2b^0c)^0 Anything to raised to the zero is equal to one, so the answer here is 1. 2. Simplify x^{-2}y^3 We can write x^{-2} as \frac{1}{x^2} ,so this simplifies to...

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Zeller's algorithm is  h=(q+|__((m+1)26)/10__|+Y+|__Y/4__|+|__C/4__|-2C) mod 7 Where q is the date of the month m is the month (March=3, April=4, ... January=13, February=14) Y is the year of the...

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2(X-Y)^2 - 9(X-Y)Z - 5Z^2 = 0 Multiply by -1 both sides. ==> 5z^2 +9(x-y)z -2(x-y)^2 = 0 Let (x-y)= A ==> 5z^2 +9Az- 2A^2 = 0 ==> (5z +A)(z-2A) = 0 ==> (5z+(x-y))(z-2(x-y)) =...

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f(x)=2(x^2-1)^3 f'(x)=2*3(x^2-1)^2(2x)=12x(x^2-1)^2 f''(x)=12(x^2-1)^2+12x(2)(x^2-1)(2x) =12(x^2-1)^2+48x^2(x^2-1) =60x^4-72x^2+12 As a check, expand the binomial and then take the...

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a_1 = -3  a_(k+1)=a_k^2 a_2 = a_1^2 = (-3)^2 = 9 a_3 = a_2^2 = (9)^2 = 81 a_4 = a_3^2 = (81)^2 = 6561 a_5 = a_4^2 = (6561)^2 = 43046721 So the answer is -3, 8, 81, 6561, 43046721

• Math
f(x)= x^3 -5x^2 +6x +3 We know that the slope of the tangent line is the derivative at the point of tendency. But we know that the tangent line is horizontal. Then, the slope is 0. ==>...

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The vertex of the quadratic function f(x)=ax^2+bx+c is (-1, 7) and it passes through the point (-3, -9). The function can be written as f(x) = a(x + 1)^2 + 7 => a(x^2 + 2x + 1) + 7 => ax^2 +...

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3x^4 +2x^3 -9x^2 -12x -4 = 0 We will factor x^3 from the first 2 terms and -1 from the last three terms. x^3(3x+2) - (9x^2 +12x +4) = 0 Now we know that (9x^2 + 12x +4) is a complete...

• Math
When 5000 is loaned at an interest rate of 10% per annum compounded annually, the principal increases every year by an amount equal to the interest earned on the principal in the last period. The...

• Math
We have to determine 75/61 + 42/18 75/61 + 42/18 First equate the denominator of both the terms (75*18)/(61*18) + (42*61)/(61*18) => 1350/(61*18) + 2562/(61*18) => 3912/(61*18) =>...

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Find the slope of the line through the points (-2,5) and (1,4). m=(y_2-y_1)/(x_2-x_1)=(5-4)/(-2-1)=-1/3

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I will assume that the base of the tissue is a square with the length of the side is 8.5 and the height is 7.7 First we will find the volume: ==> V = L X W X H = 8.5 X 8.3 X 7.7 = 556.325 cubic...

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Find the vertical asymptotes for f(x)=(x+8)/(x^2-100) . Note that vertical asymptotes occur when a function with no common factors in the numerator and denominator has a factor that causes a...

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6x^5 -51x^3 -27x  First we will factor 3x . ==gt 3x( 2x^4 -17x^2 -9)  Now we will factor the quadratic equation. ==gt 3x(2x^2 +1)(x^2-9)  ==gt 3x(2x^2+1)(x-3)(x+3)

• Math
Given the expression: 27x^3 + 216 We need to solve for x. ==> 27x^3 + 216 = 0 We know that: (a^3 + b^3)= (a+b)(a^2- ab + b^2) (27x^3 + 216)= ((3x)^3 + 6^3)  ==gt a = 3x ==gt b= 6  ==gt...

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(y^3-64)/(3y^2 -17y +20) First we will factor the numerator and denominator. ==> We know that (a^3-b^3)= (a-b)(a^2+ab+b^2)  ==gt (y^3-64)= (y-4)(y^2 +4y +16)  ==> Now we will factor...

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3a(x+5)= 114 given that a = 4 ==> 3*4 (x+5)= 114 ==> 12(x+5)= 114 Now we will divide by 12. ==> (x+5)= 114/12 = 19/2= 9.5 ==> x = 9.5 -5= 4.5 ==> x = 4.5

• Math
-(3+i) + (7-3i)= We will expand brackets. ==> -3 -i + 7 - 3i = Now we will combine like terms. ==> (-3+7) + (-i-3i) = ==> 4 + (-4i) Then, the final form of the complex number is as...

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If you have 11 counters you can only form 1 array: 1x11. With ten counters, you can form a 1x10 array, as well as a 2x5 array. Thus even though 11>10, you can form more arrays with ten counters...

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The figure shows that the height of the cylinder is equal to the diameter of the sphere. The volume of the cylinder is V = Area of the base*height The base of cylinder is a circle. The radius of...

• Math
You need to find the coefficient n if f = (x+1)g. Replacing f and g by the corresponding equations yields: x^3-nx+1 = (x+1)(x^2-x+1) You need to open the brackets to the right side: x^3- n x+1 =...

• Math
A tribonacci sequence can be defined as t_n=t_(n-1)+t_(n-2)+t_(n-3) for n>4 or as a,b,c,a+b+c,a+2b+2c,2a+3b+4c,... Here we have 5,11,_,_,_,_,_,260,... Let the third element be x; then the...

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You need to solve the integral int (xdx)/(x+1) Adding and subtracting 1 to numerator yields: int ((x + 1 - 1)dx)/(x+1) = int ((x+1)dx)/(x+1) -int dx/(x+1) int (xdx)/(x+1) =int dx - ln |x+1| +...

• Math
You need to know that the rational number pi expresses the relation between the circumference and the diameter of a circle. I suggest you to try the following experiment. Calculate the...

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You should come up with the following substitution such that: e^x = t =gt e^x dx = dt . If you change the variable, you should calculate the limits of integration. x = 0 =gt e^0 = 1 = t  x =...

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The given equation is: Ax = C-By ==> By = -Ax + C In order to rewrite in the slope form, we need to isolate y on one side and determine the coefficient of x which is the slope. ==> To isolate...

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d/dx log x^2 Chain rule: d(inside)*d(outside with inside unchanged) 2x*1/(x^2ln10) =2/(xln10) ----------- Alternatively you could have used a log rule to pop the 2 out front in the...

• Math
It is given that: 2x^3+3x^3y^2 = 4y^2+1. To determine (dy)/(dx) use implicit differentiation. (2x^3+3x^3y^2)' = (4y^2+1)' => 6x^2 + 3x^3*2y*(dy)/(dx) + 9x^2*y^2 = 8y*(dy)/(dx) =>...

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7x^3 + 2x^2 +28x + 8 = 0  First we will re-arrange terms. (7x^3 + 28x) + (2x^2 + 8) = 0  Now we will facotor each terms. Factor 7x from the first two terms and 2 from the last two terms....

• Math
The solution of the given linear equations is: x/14 - 1/2 = -1/7 => x/14 = -1/7 + 1/2 => x/14 = (7-2)/14 => x = 5 (4/5)x + 3 = 2x - 3/5 => 2x - (4/5)x = 3 + 3/5 => 1.2x...

• Math
f(x) = 6 is a horizontal line through y = 6. Since it has a slope of zero, the function is not increasing or decreasing. It is a constant function.

• Math
Consider the function f(x)=1/x . As x tends to 0, the function increases without bound, so Wallis argues that as x crosses the y-axis the function continues increasing; thus these numbers are...

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The function y = |x| . For values of x < 0, y = -x and for values of x >= 0, y = x . The graph of the function y = |x| is: The graph intersects the x-axis at the point (0, 0).

• Math
The function f(x) = (x^2 + 6x - 9)/(x - 6) The vertical asymptotes correspond to the roots of the denominator, x = 6 The function does not have a horizontal asymptote as the degree of the...

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You should notice that your problem involves rational exponents, hence you need to remember that the fifth root means one fifth power such that: root(5)(1215) = (1215)^(1/5) Notice that the...

• Math
Find the sum of a 6-term geometric series if a_1=19 and a_6=319333 The sum of a finite geometric series is S_n=a_1((1-r^n)/(1-r)) for r!=1 . We have a_1=19 and n=6 , so we need to find...

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200000=100000(1+0.12)^N 2=(1.12)^N Solving for an exponent... time to break out the logs! log 2 = log (1.12^N) = N log 1.12 Did you remember that log rule? logA^x=xlogA N = log 2 / log 1.12 =...

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Since they need the scenery in half the time, it will require twice as many people. We can set this up to calculate the number of people as well 4 people * 6 days = x people * 3 days x = 8 people

• Math
You need to remember that arcsin(sin x) = x , hence you may write the equation in terms of x such that: 0.25 = x + x/2 =gt 1/4 = x + x/2 You need to bring the terms to a common denominator such...

• Math
Given the points (-2,5) and (3,4) First we will find the slope. ==> m= (y2-y1)/(x2-x1)= (5-4)/(-2-3)= 1/-5 = -1/5 Now we will find the equation of the line . ==> y-y1 = m (x-x1) ==> y- 4 =...

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Let the number that 6 is 98% of be X. X*(98/100) = 6 => X = 600/98 => X = 300/49 6 is 98% of 300/49

• Math
The local maximum point of the expression x^3 - 6x^2 + 8 for values of x lying in [-2, 2] can be determined by solving (x^3 - 6x^2 + 8)' = 0. The result x = c must lie in [-2, 2] and the value of...

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Let the quadratic equation be: f(x)= ax^2 + bx + c let x1, and x2 be the roots: Then we know that: x1+ x2= -b/a x1*x2= c/a Given that the roots are: x1= 5+sqrt2*i  x2= 5-sqrt2*i ==gt x1+...

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Think of it as y=x^2+6x^(-1) Then (dy)/(dx)=2x-6/(x^2) by power rule. Now we must solve 2x=6/x^2 2x^3=6 x^3=3 x=root(3)(3)

• Math
(^3sqrt(x) sqrt(x^5))/sqrt(25x^16)  (x^(1/3)(x^(5/2)))/(5x^8) x^(1/3+5/2) / (5x^8) ==> (x^(17/6))/(5x^8) ==> (1/5) x^(17/6 - 8) ==> (1/5)x^(-31/6) ==> 1/(5x^(31/6))...

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The solution of |x^2 + 3x + 8| = 6 has to be determined |x^2 + 3x + 8| = 6 => x^2 + 3x + 8 = 6 and x^2 + 3x + 8 = -6 => x^2 + 3x + 2 = 0 and x^2 + 3x + 14 = 0 x^2 + 3x + 2 = 0 => x^2 + 2x...

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P= Ae^(rt) Given the initial amount is A= 7500 Also, given the rate r= 4.3% = 0.043 We need to find the time (t) needed in order for the money to double. ==> Then A = 2A = 2*7500 = 15000 ==>...

The expression sqrt 45 + (20/ sqrt 5) has to be expressed in the form k*sqrt 5 , where k is an integer. sqrt 45 + (20/ sqrt 5) => sqrt 45 + (4*5/ sqrt 5) => sqrt 45 + (4*sqrt 5)...