The curve with the equation given below is called a kampyle of Eudoxus. Find the equation of the tangent line to this curve at the point (-1, 2). y2 = 5x4 − x2

y= (-9/2)*x-5/2  or  2y+9x+5=0

Step-by-step explanation:

given the following equation

y² = 5*x⁴ - x²

we can take the derivative with respect to x in both sides to get the slope of the tangent line , and knowing that y=f(x) we can apply the chain rule , therefore

d(y²)/dx = d(5*x⁴ - x²)/dx

2*y*dy/dx = 5*4*x³ - 2*x

dy/dx = (10*x³-x)/y

replacing values (x=-1,y=2)

m=dy/dx = (10*(-1)³-(-1))/2 = -9/2

now from the equation of the line

y= m*x+h

we know that (x=-1,y=2) belongs also to the line since it is tangent to the curve, thus

2= (-9/2)*(-1) + h

h = 2 - 9/2 = (-5/2)

thus

y= (-9/2)*x-5/2

or

2y+9x+5=0

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

none.

step-by-step explanation:

m

1

=

5

m1=5

b

=

−

1

b=-1

find the slope and y-intercept of the second equation.

tap for more

m

2

=

0

m2=0

b

=

−

6

b=-6

compare the slopes

m

m of the two equations.

m

1

=

5

,

m

2

=

0

m1=5,m2=0

compare the two slopes in the decimal form. if the slopes are equal, then the lines are parallel. if the slopes are not equal, then the lines are not parallel.

m

1

=

5

,

m

2

=

0

m1=5,m2=0