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:
The answer is t>0
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2<3t−2
Step 1: Flip the equation.
3t−2>−2
Step 2: Add 2 to both sides.
3t−2+2>−2+2
3t>0
Step 3: Divide both sides by 3.
3t
/3 > 0/3
<em><u>t>0
</u></em>
To find the common factors between two numbers, you must first break the numbers down into factors, and then find all common factors.
Let's break down 88.
88: 2 x 44, 4 x 22, 8 x 11.
Now let's break down 24.
24: 2 x 12, 3 x 8, 4 x 6.
Now that we've factored both numbers, let's select all the common factors.
Common factors:
1, 2, 4, 8.
I hope this helps!
Answer:
The revenue will be recognized on the June 25th
Step-by-step explanation:
Data provided in the question:
Date on which the order for 500 cupcakes was received is <u>June 1st</u>
Date on which the order for 500 cupcakes was delivered is <u>June 25th</u>
Date on which the deposit of $50 was received is June 5th
Date on which the remaining $450 was received is June 30th
Now,
Revenue is always recognized as and when revenue generated and order completes.
Therefore,
In the given question, the order was delivered on June 25th
Hence,
The revenue will be recognized on the June 25th
Answer:
Step-by-step explanation:
![\sf 3a^5-18a^3+6a^2\\\\HCF = 3a^2\\\\Take \ 3a^2 \ common\\\\= 3a^2(a^3-6a+2)\\\\\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Csf%203a%5E5-18a%5E3%2B6a%5E2%5C%5C%5C%5CHCF%20%3D%203a%5E2%5C%5C%5C%5CTake%20%5C%203a%5E2%20%5C%20common%5C%5C%5C%5C%3D%203a%5E2%28a%5E3-6a%2B2%29%5C%5C%5C%5C%5Crule%5B225%5D%7B225%7D%7B2%7D)
Hope this helped!
<h3>~AH1807</h3>
