Answer:
Step-by-step explanation:
A jar contains 0.75 liter of blackberry juice and 0.60 liter of blueberry juice. Patrick poured 0.25 liter of guava juice into t
1 answer:
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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°
A = 35.7°
B = 67.6°
C = 76.7°
cosine law
A = 35.723697
sine law for the rest of the angles
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°
Answer:
The distance between them after 1 hour and 30 minutes will be of 63.64 miles.
Step-by-step explanation:
This question can be solved using the Pythagorean Theorem.
Both cars travel at a constant speed of 30 miles per hour. So, after 1 hour and 30 minutes, which is 1 and a half hour, they will have traveled 30*1.5 = 45 miles.
The distance between them is the hypotenuse of a right triangle, in which the sides are 45. So
The distance between them after 1 hour and 30 minutes will be of 63.64 miles.
The recommended daily amount of fiber is 30 grams.
Step-by-step explanation:
Quantity of fiber in one cup = 12 grams
It is 40% of our daily recommended amount.
Let,
x be the quantity of fiber recommended daily.
40% of x = 12
Dividing both sides by 0.4
The recommended daily amount of fiber is 30 grams.
Keywords: percentage, division
Learn more about percentages at:
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