X - Y = 2 When X = 3 you have 3 - Y = 2 Moving Y to RHS: 3 = Y + 2 Moving 2 to LHS: 1 = Y
To find the inverse you switch the x and the y and then solve for y. x=2 radical( y + 3) radical(y + 3) = x/2 y+3= (x/2)² y = (x/2)² -3 So the answer is y = (x/2)² -3
5
Prime factor both numbers or expressions and use the factors the number of times it was used the MOST in either number. 6y^3=2*3*y*y*y 18y^4=2*3*3*y*y*y*y 2*3*3*y*y*y*y=18y^4
Explanation: The difference of squares identity can be written: a 2 − b 2 = ( a − b ) ( a b ) The difference of cubes identity can be written: a 3 − b 3 = ( a − b ) ( a 2 a b b 2 ) The sum of cubes identity can be written: a 3 b 3 = ( a b ) ( a 2 − a b b 2 ) So: x 6 − y 6 = ( x 3 ) 2 − ( y 3 ) 2 = ( x 3 − y 3 ) ( x 3 y 3 ) = ( x − y ) ( x 2 x y y 2 ) ( x y ) ( x 2 − x y y 2 ) If we allow Complex coefficients, then this reduces into linear factors: = ( x − y ) ( x − ω y ) ( x − ω 2 y ) ( x y ) ( x ω y ) ( x ω 2 y ) where ω = − 1 2 √ 3 2 i = cos ( 2 π 3 ) sin ( 2 π 3 ) i is the primitive Complex cube root of 1 .
what is y+(2+a)+3
y = 3√x y = 3x^(1/2) y' = 3(1/2)x^(1/2 -1) y'= (3/2)x^(-1/2) y' = 3/[2x^(1/2)] y' = 3/(2√x)
y^2 X y^3 = y^(2 + 3) = y^5 You can only do this if the coefficient 'y' is the same for both terms. Remember y^2 = y X y y^3 = y X y X y Hence y^2 X y^3 = y X y X y X y X y = y^5 Similarly for division/subtraction y^3 / y^2 = y^(3 - 2 ) = y^1 = y The power of '1' is trivial and not normally shown. NB You CANNOT do z^2 X y^3 by adding the indices. z^2 X y^3 is (z^2)*(y^3)
y=3x^2-4x=3 y=3x^2-4x-3 y = ax^2 + bx + c is the parabola y = 3x^2-4x-3 x-coordinate of vertex is -b/2a = -(-4) / (2)(3) = +4 / (2)(3) = 4/6=2/3 y coordinate of the vertex: y = ax^2+bx+c y = 3(2/3)^2-4(2/3)-3 y= 3(4/9) -8/3 -3 y=12/9-8/3-3 = -13/3 Vertex : ( 2/3, , -13/3 )
If you mean y=3x-2, you can solve for x as follows: 3x-2+2 = y+2, x = (y+2)/3 = y/3 + 2/3
let y= xsqrt(x) -1 y= x^(3/2) -1 ---- since xsqrt(x) is the same as x^(3/2) y' = (3/2) x^(3/2-1) y' = (3/2) x^(1/2) y'' = (3/2) (1/2) x^(1/2-1) y'' =(3/2)(1/2) x^(-1/2) y'' = 3/4x^(1/2) y'' = 3 / 4sqrt(x)
(2y-4)/(y+3)=(2-y-2)/(y+3) --> multiply both sides by (y+3) 2y-4=2-y-2 --> 2-2=0 (right hand side) 2y-4=-y --> add y to both sides 3y-4=0 --> add 4 to both sides 3y=4 --> divide both sides by 3 y=4/3
Explanation: The difference of squares identity can be written: a 2 − b 2 = ( a − b ) ( a b ) The difference of cubes identity can be written: a 3 − b 3 = ( a − b ) ( a 2 a b b 2 ) The sum of cubes identity can be written: a 3 b 3 = ( a b ) ( a 2 − a b b 2 ) So: x 6 − y 6 = ( x 3 ) 2 − ( y 3 ) 2 = ( x 3 − y 3 ) ( x 3 y 3 ) = ( x − y ) ( x 2 x y y 2 ) ( x y ) ( x 2 − x y y 2 ) If we allow Complex coefficients, then this reduces into linear factors: = ( x − y ) ( x − ω y ) ( x − ω 2 y ) ( x y ) ( x ω y ) ( x ω 2 y ) where ω = − 1 2 √ 3 2 i = cos ( 2 π 3 ) sin ( 2 π 3 ) i is the primitive Complex cube root of 1 .
To write this algebraically: 7(y^3)|y = 2 Substitute 2 for y: 7(2^3) 2^3 = 8, so substitute 8 for (2^3): 7*8 = 56
2X-Y=3 X+Y=3 ---------- 3X = 6 X=2 2(2)-Y=3 4-Y=3 Y=1 Point of interesection: (2,1).
2x=3-y 2y=12-x y=3-2x 2(3-2x)=12-x 6-4x=12-x -3x=6 x=-2 2(-2)=3-y -4=3-y y=7 x=-2 y=7
y^3 + y^2 - 6 (y+2) (y-3) i think