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°.
12 31/100 is the mixed fraction because in a decimal all the numbers to the left are whole numbers and all the numbers to the right are numbers that are part of a whole. Just like in a mixed fraction there is a whole number and a fraction in a mixed number. Since 12 is in the left it is the whole number and since 31 is to the right and in the place value 31 is ending in the hundredths place so that's why the fraction is, 31/100. That's how you came to know that 12 31/100 is the fraction for 12.31.
6 · e^(4x - 2) = 3
e^(4x - 2) = .5
ln e^(4x - 2) = ln (.5)
4x - 2 = ln (.5)
4x = ln (.5) + 2
x = (ln (.5) + 2)/4
x = 0.3267
x ≈ 0.327
Answer: B
-15+5x= 20
5x= 35
x= 7
20= -15+5x
35= 5x
7 = x
Answer:
D
Step-by-step explanation:
The area (A) of an equilateral triangle is calculated as
A =
← s is length of a side
Here s = 12, thus
A = 
= 
= 36
→ D