Hi there!
We can calculate dy/dx using implicit differentiation:
xy + y² = 6
Differentiate both sides. Remember to use the Product Rule for the "xy" term:
(1)y + x(dy/dx) + 2y(dy/dx) = 0
Move y to the opposite side:
x(dy/dx) + 2y(dy/dx) = -y
Factor out dy/dx:
dy/dx(x + 2y) = -y
Divide both sides by x + 2y:
dy/dx = -y/x + 2y
We need both x and y to find dy/dx, so plug in the given value of x into the original equation:
-1(y) + y² = 6
-y + y² = 6
y² - y - 6 = 0
(y - 3)(y + 2) = 0
Thus, y = -2 and 3.
We can calculate dy/dx at each point:
At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.
At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.
72:80
9:10
Divide 72 and 80 by 8 to simplify it and get the ratio
Answer:
f(x)=x^2
Step-by-step explanation:
if you wanted have a function where both of the robot's arms are in the air the function could be x to the power of any even number such f(x)=x^2, f(x)=x^4, f(x)=x^6, or even f(x)=x^10. And you could still do the same transformations with these equations.
If the line segment point is D(-5, 10) and E(a,b) and the midpoint of the segment is F(13, -2) that mean
DE= 2*DF
You can directly find the distance of AC
Xdf= Xf-Xd= 13 - (-5)= 18
Ydf= Yf - Yd= -2 - 10= -12
Then add the distance of AB( which is 2*AC) to point D
Xe= a = Xd + 2*Xdf
a= -5 +2*18= 31
Ye= b = Yd + 2Yf
b= 10+ 2*-12= -14
<span>absolute difference between a and b:
|b-a|= </span>|-14-31|= 45
Direct variation is when one variable changes the other changes in proportion of the first, therefore all the above
