If the center of a circle is (1, 1), and it has a radius of 5, which is another point on the circle?

Step-by-step explanation:

The equation of this circle is:

(x - 1)² + (y - 1)² = 5²

Just supposing we choose x = 2.  What's the corresponding y-value?

Actually, there are two unique y-values for each x value.

Let x = 2 in (x - 1)² + (y - 1)² = 5².  Then:

(2 - 1)² + (y - 1)² = 5², or

   1²      + (y - 1)² = 25

Solving for (y - 1)², we get  (y - 1)² = 25 - 4, or 24.

Taking the square root of both sides:

y - 1 = ±√24, so that y = 1 ±√24,

This simplifies to y = 1 ± 2√6.

Therefore, if x = 2, y has two values:

(2, 1+2√6) and

(2, 1-2√6

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west