In mathematical analysis, Clairaut's equation is a differential equation of the form where f is continuously differentiable. It is a particular case of the Lagrange differential equation
Answer:
r = √13
Step-by-step explanation:
Starting with x^2+y^2+6x-2y+3, group like terms, first x terms and then y terms: x^2 + 6x + y^2 -2y = 3. Please note that there has to be an " = " sign in this equation, and that I have taken the liberty of replacing " +3" with " = 3 ."
We need to "complete the square" of x^2 + 6x. I'll just jump in and do it: Take half of the coefficient of the x term and square it; add, and then subtract, this square from x^2 + 6x: x^2 + 6x + 3^2 - 3^2. Then do the same for y^2 - 2y: y^2 - 2y + 1^2 - 1^2.
Now re-write the perfect square x^2 + 6x + 9 by (x + 3)^2. Then we have x^2 + 6x + 9 - 9; also y^2 - 1y + 1 - 1. Making these replacements:
(x + 3)^2 - 9 + (y - 1)^2 -1 = 3. Move the constants -9 and -1 to the other side of the equation: (x + 3)^2 + (y - 1)^2 = 3 + 9 + 1 = 13
Then the original equation now looks like (x + 3)^2 + (y - 1)^2 = 13, and this 13 is the square of the radius, r: r^2 = 13, so that the radius is r = √13.
Answer:
x=1
Step-by-step explanation:
-5x-16=-10x-11
+10x +10x
5x-16=-11
+16 +16
5x=5
5x/5 = 5/5
x=1
Answer:
Direction
Step-by-step explanation:
Whether the car slows down or speeds up depends on the direction of the force applied, because if Gordon applied the force opposite the direction of the cart's movement, then the cart will slow down. If however, the force is applied in the direction of the carts movement, then the cart will speed up.
Answer:
Substitute the numbers below x by x in the equation given in the middle of the table and that will be the answer for y.
Step-by-step explanation:
For example, x= -1
y= x + 6
y= -1 + 6
y= 5
