Math at eNotes
http://www.enotes.com/math
The latest questions and answers, from members following Math at eNotes.Fri, 22 Aug 2014 20:15:11 PSTen-usTo prove the relation is the same as proving the identity: `(1 + sin...
http://www.enotes.com/homework-help/show-that-1-sin-x-1-sin-x-1-sin-x-1-sin-x-4-tan-x-470503
To prove the relation is the same as proving the identity: `(1 + sin x)/(1-sin x)-(1 - sin x)/(1 + sin x) = 4 tan x sec x` Now, we can first rewrite the RHS as (using tan x = (sinx)/(cosx) and sec x = 1/cosx): `4*(sin x)/(cos^2x)` On the other hand, the LHS is (putting all with common denominator): `((1+sin x)^2-(1-sin x)^2)/(1-sin^2 x)=4*(sin x)/(1-sin^2 x)=4*(sin x)/(cos^2 x)` . QEDhttp://www.enotes.com/homework-help/show-that-1-sin-x-1-sin-x-1-sin-x-1-sin-x-4-tan-x-470503Fri, 22 Aug 2014 20:15:11 PSTThe equation of the perpendicular bisector of the line segment joining...
http://www.enotes.com/homework-help/what-equation-perpendicular-bisector-line-joining-470507
The equation of the perpendicular bisector of the line segment joining the points (3,2) and (10,4) has to be determined. The slope of a line joining the points (3,2) and (10,4) is (4 - 2)/(10 - 3) = 2/7. As the product of the slope of perpendicular lines is equal to -1, the slope of the required bisector is -7/2. This line passes through the a point lying exactly between the points (3,2) and (10,4) on the line joining them. The coordinates of...http://www.enotes.com/homework-help/what-equation-perpendicular-bisector-line-joining-470507Fri, 22 Aug 2014 19:38:17 PSTWhat is the equation of the perpendicular bisector of the line joining...
http://www.enotes.com/homework-help/what-equation-perpendicular-bisector-line-joining-470507
What is the equation of the perpendicular bisector of the line joining the points (3,2) and (10,4)http://www.enotes.com/homework-help/what-equation-perpendicular-bisector-line-joining-470507#1August 22, 2014, 7:29 pm PSTThe slope of the tangent at any point on a curve y = f(x) is given by...
http://www.enotes.com/homework-help/what-point-curve-y-3x-3-4x-2-8-slope-tangent-0-470505
The slope of the tangent at any point on a curve y = f(x) is given by f'(a) where a is the x-coordinate of the point. In the problem, the curve is defined by the equation y = 3x^3 - 4x^2 + 8. The derivative y' = 9x^2 - 8x. The slope of the tangent is 0 at the solution of the equation y' = 0 => 9x^2 - 8x = 0 => x(9x - 8) = 0 => x = 0 and x = 8/9 At x = 0, y = 8 and at x = 8/9, y = 1688/243. At the points (0, 8) and (8/9,...http://www.enotes.com/homework-help/what-point-curve-y-3x-3-4x-2-8-slope-tangent-0-470505Fri, 22 Aug 2014 19:18:33 PSTAt what point on the curve y = 3x^3 - 4x^2 + 8 is the slope of the...
http://www.enotes.com/homework-help/what-point-curve-y-3x-3-4x-2-8-slope-tangent-0-470505
At what point on the curve y = 3x^3 - 4x^2 + 8 is the slope of the tangent 0.http://www.enotes.com/homework-help/what-point-curve-y-3x-3-4x-2-8-slope-tangent-0-470505#2August 22, 2014, 7:10 pm PSTA quartic equation of the form `ax^4 + bx^3 + cx^2 + dx + e = 0` has 4...
http://www.enotes.com/homework-help/give-an-equation-with-roots-2-3-1-1-470504
A quartic equation of the form `ax^4 + bx^3 + cx^2 + dx + e = 0` has 4 roots. These can be real, complex, equal or different depending on what the value of a, b, c, d and e is. Complex roots of a quartic equation are always complex conjugate pairs as the coefficients of x are real. There are an infinite number of equations with roots 2, 3, 1-i and 1+i. The simplest of these is: (x - 2)(x - 3)(x - 1 + i)(x - 1 - i) = 0 => (x^2 - 2x - 3x +...http://www.enotes.com/homework-help/give-an-equation-with-roots-2-3-1-1-470504Fri, 22 Aug 2014 18:57:03 PSTGive an equation with roots 2, 3, 1 - i and 1 + i.
http://www.enotes.com/homework-help/give-an-equation-with-roots-2-3-1-1-470504
Give an equation with roots 2, 3, 1 - i and 1 + i.http://www.enotes.com/homework-help/give-an-equation-with-roots-2-3-1-1-470504#3August 22, 2014, 6:47 pm PSTThe trigonometric identity `(1 + sin x)/(1-sin x)-(1 - sin x)/(1 + sin...
http://www.enotes.com/homework-help/show-that-1-sin-x-1-sin-x-1-sin-x-1-sin-x-4-tan-x-470503
The trigonometric identity `(1 + sin x)/(1-sin x)-(1 - sin x)/(1 + sin x) = 4 tan x sec x ` has to be proved. Start with the left hand side: `(1 + sin x)/(1-sin x)-(1 - sin x)/(1 + sin x)` Multiply to get a common denominator = `((1 + sin x)(1 + sin x) - (1 - sin x)(1 - sin x))/((1-sin x)(1 + sin x))` = `((1 + sin x)^2 - (1 - sin x)^2)/((1-sin x)(1 + sin x))` = `(1 + sin^2x + 2*sin x - 1 - sin^2x + 2*sin x)/((1-sin x)(1 + sin x))` = `(4*sin...http://www.enotes.com/homework-help/show-that-1-sin-x-1-sin-x-1-sin-x-1-sin-x-4-tan-x-470503#4Fri, 22 Aug 2014 17:59:02 PSTShow that (1 + sin x)/(1-sin x)-(1 - sin x)/(1 + sin x) = 4 tan x sec x
http://www.enotes.com/homework-help/show-that-1-sin-x-1-sin-x-1-sin-x-1-sin-x-4-tan-x-470503
Show that (1 + sin x)/(1-sin x)-(1 - sin x)/(1 + sin x) = 4 tan x sec xhttp://www.enotes.com/homework-help/show-that-1-sin-x-1-sin-x-1-sin-x-1-sin-x-4-tan-x-470503#5August 22, 2014, 5:52 pm PSTFirst, look at the expression that you have to evaluate for the...
http://www.enotes.com/homework-help/what-value-sin-x-cos-x-2-sin-x-cos-x-2-x-30-x-60-470499
First, look at the expression that you have to evaluate for the different values of x. It is possible to simplify `(sin x - cos x)^2 + (sin x + cos x)^2` as follows: `(sin x - cos x)^2 + (sin x + cos x)^2` Use the fact `(a - b)^2 = a^2 + b^2 - 2ab` and `(a+b)^2 = a^2+b^2 +2ab` = `sin^2 x + cos^2x - 2*cos x*sin x + sin^2 x + cos^2x + 2*cos x*sin x` Use the identity `sin^2x + cos^2x = 1` = `1 - 2*cos x*sin x + 1 + 2*cos x*sin x` = 2 The value of...http://www.enotes.com/homework-help/what-value-sin-x-cos-x-2-sin-x-cos-x-2-x-30-x-60-470499Fri, 22 Aug 2014 15:20:52 PSTWhat is the value of (sin x - cos x)^2 + (sin x + cos x)^2 for x = 30...
http://www.enotes.com/homework-help/what-value-sin-x-cos-x-2-sin-x-cos-x-2-x-30-x-60-470499
What is the value of (sin x - cos x)^2 + (sin x + cos x)^2 for x = 30 and for x = 60 degrees.http://www.enotes.com/homework-help/what-value-sin-x-cos-x-2-sin-x-cos-x-2-x-30-x-60-470499#6August 22, 2014, 3:03 pm PSTThe trigonometric identity `tan x + cos x/(1+sin x) = 1/cos x` has to be...
http://www.enotes.com/homework-help/prove-tan-x-cos-x-1-sin-x-1-cos-x-470498
The trigonometric identity `tan x + cos x/(1+sin x) = 1/cos x` has to be proved. Start with the left hand side. `tan x + cos x/(1+sin x)` = `sin x/cos x + cos x/(1+sin x)` = `(sin x*(1+sin x) + cos x*cos x)/(cos x*(1+sin x))` = `(sin x + sin^2x + cos^2x)/(cos x*(1+sin x))` Use the fact `sin^2x+cos^2x = 1` = `(sin x + 1)/(cos x*(1+sin x))` = `1/(cos x)` This proves `tan x + cos x/(1+sin x) = 1/cos x`http://www.enotes.com/homework-help/prove-tan-x-cos-x-1-sin-x-1-cos-x-470498Fri, 22 Aug 2014 15:00:39 PSTProve tan x + cos x/(1+sin x) = 1/cos x
http://www.enotes.com/homework-help/prove-tan-x-cos-x-1-sin-x-1-cos-x-470498
Prove tan x + cos x/(1+sin x) = 1/cos xhttp://www.enotes.com/homework-help/prove-tan-x-cos-x-1-sin-x-1-cos-x-470498#7August 22, 2014, 2:47 pm PSTOops. Sorry educators, the second equation was x+2y+3z=18. I wanted to...
http://www.enotes.com/homework-help/solve-3x-2y-z-10-z-2y-3z-18-x-y-z-3-by-elimination-470496
Oops. Sorry educators, the second equation was x+2y+3z=18. I wanted to edit the question but there was no option to do that. http://www.enotes.com/homework-help/solve-3x-2y-z-10-z-2y-3z-18-x-y-z-3-by-elimination-470496Fri, 22 Aug 2014 08:57:45 PSTDear justaguide, I think you misread the Q on the 2nd equation. It is z...
http://www.enotes.com/homework-help/solve-3x-2y-z-10-z-2y-3z-18-x-y-z-3-by-elimination-470496
Dear justaguide, I think you misread the Q on the 2nd equation. It is z + 2y + 3z = 18 whereas you wrote X + 2y + 3z = 18.http://www.enotes.com/homework-help/solve-3x-2y-z-10-z-2y-3z-18-x-y-z-3-by-elimination-470496#8Fri, 22 Aug 2014 07:32:02 PST