4
y = sin(x+y) cos( x + y )[(1 + y')] = y' cos(x + y ) + y'cos(x + y ) = y' y'-y'cos( x+ y) = cos( x + y ) y'[1-cos(x+y)]= cos(x+y) y'= [cos(x+y)]/ [1-cos(x+y)]
y = square root of x y = x(1/2) y' = (1/2)x(1/2 - 1) y' = (1/2)x(-1/2) y' = (1/2)(square root of x)
X - Y^2 = 1 - Y^2 = - X + 1 Y^2 = X - 1 Y = (+/-) sqrt(X - 1) now, X is represented as a function of Y. Function values are generally Y values.
(x + y) / (x-1 + y-1) = (x + y) divided by ( 1/x + 1/y)Multiply numerator and denominator by 'xy' :xy (x + y) / (y + x)Then the whole thing falls apart, and we're left with:xy
(y * x) - y = y * (x - 1)
x+y=1 x=1-y or y=1-x or if you fill that in 1-y+y=1 1 = 1 or 1-x+x = 1 1 = 1
If you mean: y = x - a/x Then: y = x - ax-1 y' = 1 + ax-2 y' = 1 + a/x2 If you mean: y = (x - a)/x Then: y = 1 - ax-1 y' = ax-2 y' = a/x2
The assertion in the question is false. The result of a multiplication depends on the values. Given two numbers X and Y, if X < 0 and if Y < 0 then X*Y is greater than either; if X > 1 and if Y > 1 then X*Y is greater than either; if X < 0 and if Y > 1 then X*Y is smaller than either; if X > 1 and if Y < 0 then X*Y is smaller than either; if 0 < X < 1 and if 0 < Y < 1 then X*Y is smaller than either; If X < 0 and if 0 < Y < 1 then X*Y is greater than X but smaller than Y; If 0 < X < 1 and if Y > 1 then X*Y is greater than X but smaller than Y; If 0 < X < 1 and if Y < 0 then X*Y is smaller than X but greater than Y; If X > 1 and if 0 < Y < 1 then X*Y is smaller than X but greater than Y.
In the equations Y=X-1 and Y=-X+1, the solution is (1,0)
(x-y) + (xy - 1) = (x - 1)(y + 1)
(x + y) / (x-1 + y-1) = (x + y) divided by ( 1/x + 1/y)Multiply numerator and denominator by 'xy' :xy (x + y) / (y + x)Then the whole thing falls apart, and we're left with:xy
x y = x y Transposing x to the Left Hand Side will give us x y − x = y x ⋅ ( y − 1 ) = y ( x was a common factor on the Left Hand Side) Dividing both sides by ( −1) (Assuming y≠1) , we get x=yy−1
0
4
97 x 3 is the same as 97 + 97 + 97 if that helps you understand how multiplication works, 97 x 3 = 291
You can multiply each side of the multiplicative inverse equation by the other inverse to show that any two multiplicative inverses are equal. Here it is more formally. Theorem: For all x in R, there exists y in R s.t. x * y = 1. If there is a y' in R such that x * y' = 1, then y = y'. Proof: - Start with x * y = 1. - y * x = 1 (commutative) - (y * x) * y' = 1 * y' = y' - y * (x * y') = y' (associative) - y * 1 = y' (because x*y' = 1) - y = y'