Given that the angles of the two sectors are equal, we can find the relationship between the angles, radii, and the lengths of the arc
The length of the arc (S) is given by the formula
![S\text{ = }\frac{\theta}{360}\text{ x 2}\pi\text{ r}](https://tex.z-dn.net/?f=S%5Ctext%7B%20%3D%20%7D%5Cfrac%7B%5Ctheta%7D%7B360%7D%5Ctext%7B%20x%202%7D%5Cpi%5Ctext%7B%20r%7D)
![\text{Since 2}\pi=360^0](https://tex.z-dn.net/?f=%5Ctext%7BSince%202%7D%5Cpi%3D360%5E0)
![S\text{ =}\theta\text{ r}](https://tex.z-dn.net/?f=S%5Ctext%7B%20%3D%7D%5Ctheta%5Ctext%7B%20r%7D)
Then we can make the angle the subject of the formula
![\theta\text{ =}\frac{S}{r}](https://tex.z-dn.net/?f=%5Ctheta%5Ctext%7B%20%3D%7D%5Cfrac%7BS%7D%7Br%7D)
For the first sector
![\begin{gathered} \text{with radius r}_1\text{ and angle }\theta_1 \\ \\ \theta_1\text{ =}\frac{S_1}{r_1} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bwith%20radius%20r%7D_1%5Ctext%7B%20and%20angle%20%7D%5Ctheta_1%20%5C%5C%20%20%5C%5C%20%5Ctheta_1%5Ctext%7B%20%3D%7D%5Cfrac%7BS_1%7D%7Br_1%7D%20%5Cend%7Bgathered%7D)
For the second sector
![\begin{gathered} \text{with radius r}_2\text{ and }\theta_2 \\ \theta_2=\frac{S_2}{r_2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bwith%20radius%20r%7D_2%5Ctext%7B%20and%20%7D%5Ctheta_2%20%5C%5C%20%5Ctheta_2%3D%5Cfrac%7BS_2%7D%7Br_2%7D%20%5Cend%7Bgathered%7D)
![\theta_{1\text{ =}}\text{ }\theta_2\text{ = }\theta\text{ =}\frac{S_1}{r_1}\text{ =}\frac{S_2}{r_2}](https://tex.z-dn.net/?f=%5Ctheta_%7B1%5Ctext%7B%20%3D%7D%7D%5Ctext%7B%20%7D%5Ctheta_2%5Ctext%7B%20%3D%20%7D%5Ctheta%5Ctext%7B%20%3D%7D%5Cfrac%7BS_1%7D%7Br_1%7D%5Ctext%7B%20%3D%7D%5Cfrac%7BS_2%7D%7Br_2%7D)
Simplifying the equation, we will obtain
Sid will pay $76.26 in total including ta and tip.
Step-by-step explanation:
Given,
Cost of Sid's bill = $62.00
Tax rate = 8%
Tip = 15%
Tax amount = 15% of bill
![Tax\ amount=\frac{8}{100}*62.00\\Tax\ amount=0.08*62.00\\Tax\ amount=\$4.96](https://tex.z-dn.net/?f=Tax%5C%20amount%3D%5Cfrac%7B8%7D%7B100%7D%2A62.00%5C%5CTax%5C%20amount%3D0.08%2A62.00%5C%5CTax%5C%20amount%3D%5C%244.96)
As the tip will be on Pre-tax amount, therefore,
Tip amount = 15% of bill
![Tip\ amount=\frac{15}{100}*62.00\\Tip\ amount=0.15*62.00\\Tip\ amount=\$9.30](https://tex.z-dn.net/?f=Tip%5C%20amount%3D%5Cfrac%7B15%7D%7B100%7D%2A62.00%5C%5CTip%5C%20amount%3D0.15%2A62.00%5C%5CTip%5C%20amount%3D%5C%249.30)
Total amount = Bill + Tax amount + Tip amount
Total amount = 62.00 + 4.96 + 9.30 = $76.26
Sid will pay $76.26 in total including ta and tip.
Keywords: addition, percent
Learn more about addition at:
#LearnwithBrainly
Answer:
If he is traveling over 85 miles its cheaper to use company a
Step-by-step explanation:
137-65= 72
72÷0.85= 84.7058823529= 85
So after 85 miles company A is cheaper