Let x = ea then 1/x = e-a where e is the base of natural logarithms.
Then y = x + 1/x = ea + e-a
So y/2 = (ea + e-a)/2 = cosh(a), the hyperbolic cosine function
a = cosh-1(y/2)
x= exp(cosh-1(y/2))
-6
To solve for y in terms of x, divide both sides of the equation by 2: y = x/2.If x=2y then you have already solved for x.
3(7a - 5b) + 2(4a - 3b) Multiply the contents of each bracket by the number outside it: 21a - 15b + 8a - 6b Bring like terms together: 21a + 8a - 15b - 6b Combine like terms: 29a - 21b This cannot be simplified further.
2x-3x+1 can be simplified (by combining like terms, or terms with the same number/type of variables) to -x+1. This is not an equation, but an "expression," meaning that there is no equals sign, and you cannot solve for x without an equals sign. If, for instance, that entire expression was equal to 7, -x+1=7 -x = 6 x = -6
Note : sin² Φ + cos² Φ = 1 for all real Φ.__________________________________Now, given that : cos² (6y) + sin² (6y) = y + 14∴ 1 = y + 14 ∴differentiating w.r.t. x, ... 0 = (dy/dx) + 0∴ dy/dx = 0 ........... Ans.___________________________________Happy To Help !___________________________________
2 - (y + 2) = 3y Remove brackets: 2 - y - 2 = 3y Combine like terms: 0 = 4y Divide both sides by 4: 0 = y
8kt16=10k
I think I'm answering my own quezstion here but hey. Am I right in saying that (x+0)(x+1) Factorises to x2+ x? I think I am.
-6
To solve for y in terms of x, divide both sides of the equation by 2: y = x/2.If x=2y then you have already solved for x.
Divide all terms by -3 then it will be in slope intercept form
You can combine like terms of p to get 6p. If you are given what p equals you can solve for the completely numerical answer.
9
3(4 - x) - 6(4 - 3x) = 3 Expand the brackets: 12 - 3x - 24 + 18x = 3 [note that -6*(-3x) gives +18x] Combine like terms: -12 + 15x = 3 Add 12 to both sides: 15x = 15 Divide both sides by 15: x = 1.
6a + 5a = -11 Combining like terms: 11a = -11 Dividing by 11: a = -1
3(7a - 5b) + 2(4a - 3b) Multiply the contents of each bracket by the number outside it: 21a - 15b + 8a - 6b Bring like terms together: 21a + 8a - 15b - 6b Combine like terms: 29a - 21b This cannot be simplified further.
2x-3x+1 can be simplified (by combining like terms, or terms with the same number/type of variables) to -x+1. This is not an equation, but an "expression," meaning that there is no equals sign, and you cannot solve for x without an equals sign. If, for instance, that entire expression was equal to 7, -x+1=7 -x = 6 x = -6