Answer:
2r (1 + √3)
Step-by-step explanation:
Circle O₁ is tangent to AB. Let's call the point of intersection point D. If we draw a radius from the center O₁ to D, we know this forms a right angle.
△ABC is an equilateral triangle, so we know m∠A = 60°. If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.
So △DAO₁ is a 30-60-90 triangle. We can find the length AD:
AD = r √3
Now on the other side, circle O₃ is tangent to AB. Let's call the point of intersection point E. We know it's the same triangle we found earlier, so:
EB = r √3
And finally, we can draw a rectangle connecting O₁, O₃, E, and D. The distance between O₁ and O₃ is 2r, so:
DE = 2r.
Therefore:
AB = r√3 + 2r + r√3
AB = 2r√3 + 2r
AB = 2r (1 + √3)
Here's a graph showing the steps. Hopefully this helps, let me know if you have questions!
desmos.com/calculator/hgaonfzxsm
Answer:
Step-by-step explanation:
Point-slope form: y - y1 = m(x - x1)
Slope: 
Point: (3, 2) = (x1, y1)
To write the equation in point-slope form, we need to know the values of the slope and one point. Since we've already been given those values, all we have to do is input them into the equation:
y - y1 = m(x - x1)
The equation in point-slope form is:
A.) 5 layers with 48 balls in each layer would equal 250 balls in the box
(5x48=250)
B.) 15 layers with 48 balls in each layer would equal 720
(15x48=720)
Answer:
x ≤ 15
Step-by-step explanation:
25x + 225 ≤ 600
Subtract 225 from both sides and get
25x ≤ 375
Divide 25 from both sides and you´ll get
x ≤ 15
