# applications Homework Help

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• applications
The information provided by enunciation is that the elements of the set, have to respect the constraint |x-2|=<3 We'll re-write the constraint using the absolute value property: |x-2|=<3...

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• applications
To compute the left side expression, we'll expand the squares, using the formulas: (a+b)^2 = a^2 + 2ab + b^2 (a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+ac+bc) (x+y)^2 = x^2 + 2xy + y^2 (x+y+1)^2 = x^2 +...

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• applications
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• applications
The intervals are sets of real numbers. Examples: The open interval (-a;b) is the set of real numbers x that have the property: -a < x < b All the real numbers located between -a and b,...

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• applications
We'll recall the identities that helps us to complete the given squares: (a+b)^2 = a^2 + 2ab + b^2 (a-b)^2 = a^2 - 2ab + b^2 We'll complete the first square x^2-14x+_ We'll identify a^2 = x^2 =>...

Asked by jeuxdesfou on via web

• applications
We'll factor the numerator and denominator by x^n*y^n:x^n*y^n(x^3n - y^3n)/x^n*y^n(y^2n - x^2n)We'll reduce and we'll get:(x^3n - y^3n)/(y^2n - x^2n)We'll write the numerator using the formula of...

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• applications
We know that the values of x are positive in the 1st and the 4th quadrants.We also know that the values of y are negative in the 3rd and the 4th quadrants.We notice that the 4th quadrant...

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• applications
6x-1>6-x We'll subtract 6-b both sides: 6x - 1 - 6 + x > 0 We'll combine like terms: 7x - 7 > 0 We'll factorize by 7: 7(x-1)>0 We'll divide by 7: x-1>0 x>1 The range of possible...

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• applications
The value of discriminant is evaluated applying the formula: delta = b^2 - 4ac We'll identify a,b,c: 6y^2 - 2y - 3 = 0 a = 6 b = -2 c = -3 We'll substitute the coefficients in the formula of...

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• applications
Any function is determined when it's coefficients are known. y = f(x) = mx + n Therefore, in order to determine the linear function, we'll have to calculate the coefficients m and n. Since the...

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• applications
We'll establish the conditions of existence of logarithms: (b+2)^2>0 The perfect square is always positive, for any value of b. log (b+2)^2- 2log b = log 3 We'll shift 2log b to the right: log...

Asked by insuland0 on via web

• applications
We'll re-write the given expression: 2*24/2(x+1) = 2(x+3) We'll reduce: 24/(x+1) = 2(x+3) We must multiply both sides by the denominator x+1. 24(x + 1)/ (x + 1) = 2(x+3)(x+1) We'll reduce and we'll...

Asked by fab10 on via web

• applications
Let the numbers be x and y: x - y = 28 x = 28 + y x^2 + y^2 = (28+y)^2 + y^2 We'll expand the square: 784 + 56y + y^2 + y^2 We'll combine the like terms and we'll re-arrange the terms: 2y^2 + 56y +...

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• applications
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• applications
We'll calculate Sn (x) for x = 1. Sn (x) = 1 + 2*1 + 3*1 + .... + n*1 Since the expression above represents the sum of the first natural n terms, we'll replace it by the formula: Sn (1) = n(n+1)/2...

Asked by latimer on via web

• applications
We'll eliminate z from the equation (2) and (3). x + 2y = 10 (1) 9y – 3z = - 6 (2) 6x – 5z = 2 (3) To eliminate z from (2) and (3), we'll multiply (2) by 5 and (3) by -3: 45y – 15z = - 30...

Asked by catbyshe on via web

• applications
We'll put the equation of the lines in the general form: ax + by + c = 0 The first equation is: 7x-2y-17=0 The second equation is: 14x-9y-24=0 We'll form the system: 7x-2y-17=0 We'll add 17 both...

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• applications
To calculate the modulus of the complex number z, we'll re-write the given complex number z. Since it is not allowed to keep a complex number to denominator, we'll multiply the ratio by the...

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• applications
We'll calculate the inverse function for the given functions. Let f(x) = y: y = -x We'll multiply by -1 and we'll get: x = -y f^-1(x) = -x So f(x) = f^-1(x) for f^-1(x) = -x. We'll get the inverse...

Asked by luna9219 on via web

• applications
This is like having two equations. One is 2x - 3 = 7 and the other is -(2x - 3) = 7 Which is the same as -2x + 3 = 7 So now we have to solve both equations. 2x - 3 = 7 2x = 10 x = 5 And -2x + 3 =...

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• applications
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• applications
Let x and x+1 be the two consecutive numbers. We know, from enunciation that the sum of their squares is 61: x^2 + (x+1)^2 = 61 We'll expand the square using the formula: (a+b)^2 = a^2 + 2ab + b^2...

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• applications
3x - 2 >= 0 3x > =2 x>=2/3 10 - x>=0 x=<10 The interval of admissible values for x is [2/3 ; 10]. Now, we'll solve the equation. We'll multiply both sides by the conjugate of the...

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• applications
We'll start from the given constraint X*Y=Y*X. We know that the product of two matrices is not commutative. Since X is not equal to Y, then, X*Y=Y*X if and only if Y = X^-1 (Y is the inverse of the...

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• applications
BY definition, the tangent line to a graph, at a given point, is the derivative of the given function: dy/dx = -1/x^2 The slope of the tangent line is: m = -1/3^2 m = -1/9 The equation of the line...

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• applications
fof^-1(x) = f(f^-1(x)) = x, by definition Here y = x/4 + 3 The inverse function is found by expressing y in terms of x, x = (y - 3)*4. Now interchange y and x. f^-(x) = (x - 3)*4 fof^-1(x) = f((x -...

Asked by lillyan on via web

• applications
We have to solve 3 log 4 (a-2) = (9/2) for a 3 log(4) (a-2) = (9/2) => log(4) (a-2) = (9/6) => a - 2 = 4^(3/2) => a - 2 = 8 => a = 10 The solution for the equation is a = 10

Asked by undoitu on via web

• applications
Another method to solve x^2 + 3x – 4 = 0 is by factorization. x^2 + 3x – 4 = 0 => x^2 + 4x - x - 4 = 0 => x( x + 4) - 1(x + 4) = 0 => (x - 1)(x + 4) = 0 => x = 1 and x = -4 The...

Asked by nena1993 on via web

• applications
We have to simplify: x/ (1+1/x) + (1/x)/ (x + 1) x/ (1+1/x) + (1/x)/ (x + 1) => x/ ((x+1)/x) + (1/x)/ (x + 1) => x^2/(x + 1) + 1/x(x+1) => (x^3 + 1)/(x + 1)x => (x + 1)(x^2 - x + 1)/(x...

Asked by cartoffried on via web

• applications
The equations to be solved are: x^2 + y^2 = 200 - xy ...(1) x + y = 20 - (xy)^(1/2) ...(2) (2) => (x + y)^2 = (20 - (xy)^(1/2))^2 => x^2 + y^2 + 2xy = 400 + xy - 40(xy)^(1/2) => x^2 + y^2...

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• applications
We have to solve: e^(3x-4) - 1/e^(x-12)=0 e^(3x-4) - 1/e^(x-12)=0 => e^(3x-4) - e^(-(x-12)) = 0 => e^(3x-4) = e^(-(x-12)) take the logarithm to the base e of both the sides => ln(e^(3x-4))...

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• applications
We have to prove: (2x-1)^2-(x-3)^2 = (3x-4)(x+2) Take the left hand side (2x-1)^2-(x-3)^2 Use the relation x^2 - y^2 = (x - y)(x + y) => (2x - 1 - x + 3)(2x - 1 + x - 3) => (x + 2)(3x - 4)...

Asked by raydusol on via web

• applications
We have to find the square of (4+3i) (4+3i)^2 => (4+3i)(4+3i) => 4*4 + 4*3*i + 4*3*i + 3*i*3*i => 16 + 12i + 12i + 9i^2 i^2 = -1 => 16 + 24i - 9 => 7 + 24i The required square is 7 +...

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• applications
The form of the quadratic is ax^2 + bx + c = 0 We'll write the quadratic as a product of linear factors: ax^2 + bx + c = (x - 2/3)(x+4) ax^2 + bx + c = x^2 + 4x - 2x/3 - 8/3 Comparing both sides,...

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• applications
The sum of n terms of an arithmetic series is given as: Sn = 5n^2 - 11n Sn-1 = 5(n - 1)^2 - 11(n - 1) => 5(n^2 + 1 - 2n) - 11n + 11 => 5n^2 + 5 - 10n - 11n + 11 => 5n^2 - 21n + 16 The term...

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• applications
It is given that x = 5*cos t and y = 3*sin t. We have to find the equation of the tangent if t = pi/4 When t = pi/4 , x = 5*(1/sqrt 2) and y = 3/sqrt 2 dx/dt = -5*sin t and dy/dt = 3*cos t dy/dx =...

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• applications
It is given that log(72) 48 = a and log(6) 24 = b a = log(72) 48 = log(6) 48/ log(6) 72 => log(6) (6*8)/log(6) 6*12 => [1 + log(6) 8]/[1 + log(6) 12] => [1 + 3*log(6) 2]/[2 + log(6) 2] b =...

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• applications
To find the derivative dy/dx of y= x^2-5xy+3y^2 implicit differentiation can be used and differentiation carried out in the following way: y= x^2-5xy+3y^2 dy/dx = 2x - 5*x*(dy/dx) - 5y +...

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• applications
We'll write the equation of the ellipse: (x/a)^2 + (y/b)^2 = 1 To put the given equation in this form, we'll divide by 64 both sides: 4x^2 + 16y^2 = 64 4x^2/64 + 16y^2/64 = 64/64 We'll simplify and...

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• applications
We have to find x and y given x(1+2i)+y(2-i)=4+3i x(1+2i)+y(2-i)=4+3i => x + 2xi + 2y - yi = 4 + 3i equate the real and imaginary coefficients x + 2y = 4 and 2x - y = 3 x = 4 - 2y substitute in...

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• applications
According to the fundamental theorem of calculus: Int f(x)dx = F(b) - F(a) for x = a to x = b In this case a = -1 and b = 1 We recall the property of additivity of Integrals: Int (x^3-x)dx = Int...

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• applications
We have to prove that (cospi/4+i*sinpi/4)^2008 is real. cos (pi/4) = 1/sqrt 2 sin (pi/4) = 1/sqrt 2 (cos pi/4 + i*sin pi/4)^2008 => [1/sqrt 2 + i*(1/sqrt 2)]^2008 => [1/sqrt 2 + i*(1/sqrt...

Asked by deuxtoi on via web

• applications
Applying combinatorics we'll get: C(x,2) = x!/2!*(x-2)! But x! = (x-2)!*(x-1)*x 2! = 1*2 = 2 C(x,2) =(x-2)!*(x-1)*x/2!*(x-2)! We'll simplify and we'll get: C(x,2) =(x-1)*x/2 A(x,2) = x!/(x-2)!...

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• applications
We have to find the tangent to the curve y = x^3 - 7x^2 + 14x - 8 at the point where x=1 At x = 1, y = 1 - 7 + 14 - 8 = 0. The slope of the tangent to the curve at x = 1 is the value of y' at x =...

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• applications
We have to solve x + y = 5 ...(1) x^2 + y^2 = 13 ...(2) From (1) x = 5 - y Substituting in (2) (5 - y)^2 + y^2 = 13 => 25 + y^2 - 10y + y^2 = 13 => 2y^2 - 10y + 12 = 0 => y^2 - 5y + 6 = 0...

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• applications
Since the given logarithm does exist, then the base and the argument of logarithm respect the conditions of existence. We'll impose the constraints of existence of logarithms: 1) x+1 > 0 2) x +...

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• applications
The equation given is lg(x+1) - lg 9 = 1 - lg x I assume the base of the logarithm is 10. Use the property that lg a - lg b = lg a/b and 1 = lg 10 lg(x+1) - lg 9 = 1 - lg x => lg(x+1) - lg 9 =...

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• applications
The consecutive terms of a geometric sequence have a common ratio. We have the sequence given by 3 ,a ,b , 24 24/b = b/a = a/3 => 24a = b^2 or a = b^2/24 substitute in b/a = a/3 => 24b/b^2 =...

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• applications
For the triangle ABC AB = 6, B=pi/4, C=pi/6. As the angles of a triangle have a sum of pi. A = 7*pi/12 Use the property sin A/a = sin B/b = sin C/c c = 6, C = pi/6, B = pi/4 and A = 7*pi/12 =>...

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