1. For x^2 - 4xy + 4y^2 + x -12y - 10 = 0
a) Calculate the values for y when x=6
b) Find y'
c) Find an equation for y explicitly in terms of x. [Hint: Quadratic Formula]
d) Determine whether or not this relation is a function.
I dont understand any of this and I have a quiz tomorrow :*( please help
a) Calculate the values for y when x=6
b) Find y'
c) Find an equation for y explicitly in terms of x. [Hint: Quadratic Formula]
d) Determine whether or not this relation is a function.
I dont understand any of this and I have a quiz tomorrow :*( please help
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1. For x^2 - 4xy + 4y^2 + x -12y - 10 = 0
a) Calculate the values for y when x=6
36-24y +4y^2+6-12y-10=0
4y^2-36y+32 =0
Y^2-9y+8=0
(y-8)(y-1)=0
Y=8 or 1
b) Find y' implicitly:
2x + (-4x*y') + (-4y)+ 8y *y' +1 -12*y'=0
Y' [ -4x+8y-12] = -2x+4y-1
Y' = (-2x+4y-1)/ (-4x+8y-12)
c) Find an equation for y explicitly in terms of x. [Hint: Quadratic Formula]
Regroup terms : y^2 , y, non-y
4y^2 -(4x+12)y+ (x^2+x-10)=0
Apply quadratic formula:
A=4; B= -(4x+12); C= (x^2+x-10)
Y=[ (4x+12)+/- sqr[ (4x+12)^2-4(4)(x^2+x-10)] /8
d) Determine whether or not this relation is a function.
No, because of the +/-, which gives two y values for each x
Hoping this helps!
a) Calculate the values for y when x=6
36-24y +4y^2+6-12y-10=0
4y^2-36y+32 =0
Y^2-9y+8=0
(y-8)(y-1)=0
Y=8 or 1
b) Find y' implicitly:
2x + (-4x*y') + (-4y)+ 8y *y' +1 -12*y'=0
Y' [ -4x+8y-12] = -2x+4y-1
Y' = (-2x+4y-1)/ (-4x+8y-12)
c) Find an equation for y explicitly in terms of x. [Hint: Quadratic Formula]
Regroup terms : y^2 , y, non-y
4y^2 -(4x+12)y+ (x^2+x-10)=0
Apply quadratic formula:
A=4; B= -(4x+12); C= (x^2+x-10)
Y=[ (4x+12)+/- sqr[ (4x+12)^2-4(4)(x^2+x-10)] /8
d) Determine whether or not this relation is a function.
No, because of the +/-, which gives two y values for each x
Hoping this helps!