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
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Answer:</h3>
<h3>
Step-by-step explanation:</h3>
In this question, we're trying to find the probability of it being cloudy and raining.
In this case, we know that:
- Probability of it being cloudy is 30%
- Probability of it raining is 25% (this is necessarily not needed)
- If it's cloud, the probability of it raining is 45%
With the information above, we can find the probability.
We know that from a 100% scale, the chance of it being cloudy is 30%.
We know that if it's cloudy, the chances of raining is 45%
To find the probability of it being cloudy and raining, we would multiply 0.3 (30%) by 0.45 (45%)
Solve:
Your answer would be C). 13.5%
<h3>
I hope this helped you out.</h3><h3>
Good luck on your academics.</h3><h3>
Have a fantastic day!</h3>
It will cost her 1,710 dollars because 10 times 17 is 170 and 170 times 16 is $1,710
Wat r u asking about this problem
The slope is -9/7. I don’t have an explanation because I used an online calculator but that’s the answer in case you don’t have to show work.
