Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
Answer:
<em>x = 2</em>
Step-by-step explanation:
<u>Exponential Equations</u>
Solve:
Separate each exponential:
Operating:
Multiplying by 5:
Rearranging:
Recall that:
Calling
Factoring:
There are two possible solutions:
y=25
y=-50
Since
y cannot be negative, thus:
The solution is:
x = 2
1: 5 2: 9 or 10
For question 1 we can round 115 to 100, 5x100 is 500 which is closer to 545 than 7x100 = 700.
I prefer to use fractions for some irrational numbers.
For example, 1/3 is equal to an infinite 0.3333333333333333...
Answer:
19.1 feet
Step-by-step explanation:
This forms a right triangle
use the pythagorean theorem
a^2 + b^2 = c^2
a^2 + 6^2 = 20^2
a^2 + 36 = 400
a^2 = 364
a = 19.0787840283
Rounded
19.1 feet
