Applying the Law of Cosines, the distance across the lake is: 2.1 miles.
<h3>What is the Law of Cosines?</h3>
Law of Cosines is given as: c² = a² + b² - 2(a)(b)cos(C).
The diagram showing the measurements along the ground is in the attachment below.
Given:
- a = 2.82 miles
- b = 3.11 miles
- C = 40.3°
- c = distance across the lake.
Applying the Law of Cosines, we have:
c² = 2.82² + 3.11² - 2(2.82)(3.11)cos(40.3)
c² = 4.25
c = √4.25
c = 2.1 miles
Thus, applying the Law of Cosines, the distance across the lake is: 2.1 miles.
Learn more about Law of Cosines on:
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Answer:
0
Step-by-step explanation:
∫ sin²(x) cos(x) dx
If u = sin(x), then du = cos(x) dx.
∫ u² du
⅓ u³ + C
⅓ sin³(x) + C
Evaluate between x=0 and x=π.
⅓ sin³(π) − ⅓ sin³(0)
0
Answer:
The answer is below
Step-by-step explanation:
Let us assume that the age of Greg's brother (Gabe) is x years, and let Greg's age by y years. Since Greg is 10 years older than his brother gabe, then:
y = x + 10 (1)
Also. Greg is 3 times as old as Gabe, hence:
y = 3x (2)
From equation 1 and equation 2:
y = x + 10 = 3x
Hence:
3x = x + 10
Subtracting x from both sides gives:
3x - x = x + 10 - x
2x = 10
Dividing by 2:
2x/2 = 10/2
x = 5 years
y = x + 10 = 5 + 10 = 15 years
Therefore Gabe is 5 years old and Greg is 15 years old
The slope of XY is the same as the slope of AB because AB is parallel to XY and parallel lines have the same slope.
