0
What is it that you want done with that equation? The equation alone is not a question.
3y + x2 = 5x - 4
Do you want to know what kind of curve that equation describes? It's a parabola with a maximum y value and no minimum.
Do you want to solve it for y?
y = -(x2 - 5x + 4) / 3
Do you want to solve for x?
x2 - 5x = -3y - 4
x2 - 5x + (5/2)2 = -3y - 4 + (5/2)2
(x - 5/2)2 = -12y/4 - 16/4 + 25/4
(x - 5/2)2 = (9 - 12y)/4
x - 5/2 = ± √(9 - 12y) / 2
x = [5 ± √(9 - 12y)] / 2
Do you want the rate of change of y with respect to x?
dy/dx = (-2x + 5)/3
Do you want to know the vertex of the parabola? Solve its derivative for y:
0 = (-2x + 5) / 3
-2x + 5 = 0
x = 5/2
Then plug that x back into the original equation to find the y coordinate:
y = -(x2 - 5x + 4) / 3
y = -([5/2]2 - 5[5/2] + 4) / 3
y = -(25/4 - 25/2 + 4)/3
y = -25/12 + 50/12 - 16/12
y = 3/4
So the parabola's vertex is at the point (5/2, 3/4)
Do you want the rate of change of x with respect to y?
x = [5 ± √(9 - 12y)] / 2
x = 5/2 ± 1/2(9 - 12y)1/2
dx/dy = ± 1/4(9 - 12y)-1/2 (-12)
dx/dy = ± 3 / √(9 - 12y)
Do you want the indefinite integral of y with respect to x?
∫ -(x2 - 5x + 4) / 3 dx
= -1/3 ∫(x2 - 5x + 4) dx
= -1/3(x3/3 - 5x2/2 + 4x) + C
= -1/3(2x3/6 - 15x2/6 + 24x/6) + C
= -x/18(2x2 - 15x + 25) + C
= -x/18(2x2 - 10x - 5x + 25) + C
= -x(2x - 5)(x - 5)/18 + C
If you were looking for some other answer regarding the given equation, then I would recommend expressing your question a little more clearly.
Wiki User
∙ 10y ago
Add your answer:
Earn +20 pts
X2 plus 3xy - 18y2 equals?
(x + 6y)(x - 3y)
What is the vertex of the function y equals x2 plus 6x-5?
x = -3y = -14
What is the expntents of x5 - 3x4 plus x2 - 4 plus 5x4 plus 3x2 plus 2x plus 1?
x^5+2x^4+4x^2+2x-3
What is a factor of x3 plus 27y3?
x3+27y3 = (x+3y) · (x2-3xy+9y2)
X2 plus 6x plus 8 equals?
The quadratic expression x2+6x+8 when factorised equals (x+2)(x+4)
X2 plus 3xy - 18y2 equals?
(x + 6y)(x - 3y)
What is the vertex of the function y equals x2 plus 6x-5?
x = -3y = -14
4x8 plus 5x4 - 2x3 plus x2 - 1?
103
How do you solve this problem it just says solve x2 plus 3y equals 7 3x plus y2 equals 3?
x2 + 3y = 7 3x + y2 = 3 3y = x2 + 7 y2 = -3x + 3 y = x2/3 + 7/3 y = ± √(-3x + 3) If you draw the graphs of y = x2/3 + 7/3 and y = ± √(-3x + 3) in a graphing calculator, you will see that they don't intersect, so that the system of the given equations has not a solution.
Is 3y equals x2-8 linear?
yes.
How many terms are in x2 - 10xy plus 3y plus y2 - 1?
5
What does x2 plus x2 equals?
x2 + x2 = 2x2
How do you simplify x2 plus 6xy - 27y2?
By factorisation: x2 + 6xy - 27y2 = (x + 9y)(x - 3y).
Factor X2 plus 2XY - 15Y2?
(x + 5y)(x - 3y)
What is is X plus 3y equals 6 and 2x plus y equals -8?
x + 3y = 62x + y = -8Solve by substitution:x + 3y = 6 subtract 3y to both sidesx = 6 - 3y2x + y = -8 substitute 6 - 3y for x2(6 - 3y) + y = -812 - 6y + y = -812 - 5y = -8 subtract 12 to both sides-5y = -20 divide by -5 to both sidesy = 4x = 6 - 3yx = 6 - 3(4) = 6 - 12x = -6Thus, the solution of the system is (-6, 4).
What is the expntents of x5 - 3x4 plus x2 - 4 plus 5x4 plus 3x2 plus 2x plus 1?
x^5+2x^4+4x^2+2x-3
What is a factor of x3 plus 27y3?
x3+27y3 = (x+3y) · (x2-3xy+9y2)
