Basically, the equator is like the x-axis of the world and the prime meridian is like the y-axis. You locate places by distances from these lines.
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:
18+12.125π units²
Step-by-step explanation:
The diameter of the semicircle can be found by the use Pythagoras theorem.
Δx²+Δy²=d²
Δx=3--1=4
Δy=3--6=9
d²=4²+9²
d=√(16+81)
Area=πr²/2
=π×(√(16+81)/2)²÷2
=[π×(97)/4]/2
=97π/8
=18+12.125π units²
97π/8 is equivalent to 18+12.125π units²
