Answer:
It will take 3.2 hours for 8 inches of snow to fall.
Step-by-step explanation:
You can solve this be going "backwards".
You have 2.5 inches of snow falling per hour for x hours until you get 8 inches of snow, which can be represented like this:
2.5x=8 From here you being to solve by isolating x on one side of the equation. You would divide both sides by 2.5 to do this
2.5x=8
/2.5 /2.5
8 divided by 2.5 is 3.2 and you then get
x=3.2
It takes 3.2 hours for 8 inches of snow to fall
Answer:
48 minutes
Step-by-step explanation:
Given that:
Time taken by Janet = 3 hours
Janet's rate = 1/3 job / hour
Time taken by Garry = 2 hours
Garry's rate = 1/2
Rate of working together :
1/3 + 1/2 = (2 + 3) /6 = 5/6 job/hour
If Janet works for one hour before Garry joins ;
1/3 of the job has been done by Janet
1 - 1/3 = 2/3 of the job left
Hence to finish the job together, it will take :
Fraction of JOB left ÷ rate of working together
(2/3 ÷ 5/6)
= 2 /3 * 6/5
= 12 / 15
= 4 / 5 hours
To minutes
(4/5) * 60
= 240/5
= 48 minutes
Answer:
199ft2
Step-by-step explanation:
area) H*W
(16ft×20ft)-(11ft×11ft)
=320ft2-121ft2
<h3>=199ft2</h3>
<em>ft</em><em> </em><em>square</em><em> </em><em>=</em><em>ft</em><em>2</em>
Answer: point E
Step-by-step explanation:
Your answers are
A = 35.7°
B = 67.6°
C = 76.7°
cosine law
![a^2 = b^2 + c^2 -2bc \cos A \\ -2bc \cos A = a^2 - b^2 - c^2 \\ \\ \cos A = \dfrac{a^2 - b^2 - c^2}{-2bc} \\ \\ A = \cos^{-1}\left[ \dfrac{a^2 - b^2 - c^2}{-2bc} \right] \\ \\ A = \cos^{-1}\left[ \dfrac{12^2 - 19^2 - 20^2}{-2(19)(20)} \right] \\ \\ A = 35.723697](https://tex.z-dn.net/?f=a%5E2%20%3D%20b%5E2%20%2B%20c%5E2%20-2bc%20%5Ccos%20A%20%5C%5C%0A-2bc%20%5Ccos%20A%20%3D%20a%5E2%20-%20b%5E2%20-%20c%5E2%20%5C%5C%20%5C%5C%0A%5Ccos%20A%20%3D%20%5Cdfrac%7Ba%5E2%20-%20b%5E2%20-%20c%5E2%7D%7B-2bc%7D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%20%5Cdfrac%7Ba%5E2%20-%20b%5E2%20-%20c%5E2%7D%7B-2bc%7D%20%5Cright%5D%20%5C%5C%20%5C%5C%0AA%20%3D%20%5Ccos%5E%7B-1%7D%5Cleft%5B%20%5Cdfrac%7B12%5E2%20-%2019%5E2%20-%2020%5E2%7D%7B-2%2819%29%2820%29%7D%20%5Cright%5D%20%20%5C%5C%20%5C%5C%0AA%20%3D%2035.723697)
A = 35.723697
sine law for the rest of the angles
![\displaystyle \frac{\sin B}{b} = \frac{\sin A}{a} \\ \\ \sin B = \frac{b \sin A}{a} \\ \\ B = \sin^{-1} \left[ \frac{b \sin A}{a} \right] \\ \\ B = \sin^{-1} \left[ \frac{19 \sin 35.723697 }{12} \right] \\ \\ B \approx 67.58886795](https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%20%3D%20%5Cfrac%7B%5Csin%20A%7D%7Ba%7D%20%5C%5C%20%5C%5C%0A%5Csin%20B%20%3D%20%5Cfrac%7Bb%20%5Csin%20A%7D%7Ba%7D%20%5C%5C%20%5C%5C%0AB%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7Bb%20%5Csin%20A%7D%7Ba%7D%20%20%5Cright%5D%20%5C%5C%20%5C%5C%0AB%20%3D%20%5Csin%5E%7B-1%7D%20%5Cleft%5B%20%5Cfrac%7B19%20%5Csin%2035.723697%20%7D%7B12%7D%20%20%5Cright%5D%20%20%5C%5C%20%5C%5C%0AB%20%5Capprox%2067.58886795)
B = 67.58886795
All angles in triangle sum to 180 so find C with that
A + B + C = 180
C = 180 - A - B
C = 180 - 35.723697 - 67.58886795
C = 76.7°
