Since a calculator is involved in finding the answer, it makes sense to me to use a calculator capable of adding vectors.
The airplane's ground speed is 158 mph, and its heading is 205.3°.
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A diagram can be helpful. You have enough information to determine two sides of a triangle and the angle between them. This makes using the Law of Cosines feasible for determining the resultant (r) of adding the two vectors.
.. r^2 = 165^2 +15^2 -2*165*15*cos(60°) = 24975
.. r = √24975 ≈ 158.03
Then the angle β between the plane's heading and its actual direction can be found from the Law of Sines
.. β = arcsin(15/158.03*sin(60°)) = 4.7°
Thus the actual direction of the airplane is 210° -4.7° = 205.3°.
The ground speed and course of the plane are 158 mph @ 205.3°.
All of the telephones * all of the telephones minus one (because one is in use)
85 * 84 = 7140 connections
It will take Levi's dad 1.67 hours to wash the car alone.
Step-by-step explanation:
Time taken by Levi to wash car alone = 2.5 hours
Time taken by Levi and his father together = 1 hour
Let,
x be the time taken by Levi's dad.
Levi will contribute 1/2.5 hours and his dad will contribute 1/x to wash the car together.
![\frac{1}{2.5}+\frac{1}{x}=1\\\\\frac{x+2.5}{2.5x}=1\\\\x+2.5=2.5x\\\\2.5=2.5x-x\\\\2.5=1.5x\\\\1.5x=2.5](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2.5%7D%2B%5Cfrac%7B1%7D%7Bx%7D%3D1%5C%5C%5C%5C%5Cfrac%7Bx%2B2.5%7D%7B2.5x%7D%3D1%5C%5C%5C%5Cx%2B2.5%3D2.5x%5C%5C%5C%5C2.5%3D2.5x-x%5C%5C%5C%5C2.5%3D1.5x%5C%5C%5C%5C1.5x%3D2.5)
Dividing both sides by 1.5
![\frac{1.5x}{1.5}=\frac{2.5}{1.5}\\x=1.67](https://tex.z-dn.net/?f=%5Cfrac%7B1.5x%7D%7B1.5%7D%3D%5Cfrac%7B2.5%7D%7B1.5%7D%5C%5Cx%3D1.67)
It will take Levi's dad 1.67 hours to wash the car alone.
Subtract 23.5 from 36.9 which gives you 13.4. The differences in temperature is therefore 13.4