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:
The distance the Bensons had traveled from their home 
hours after picking up their grand parents 292.5 miles
Step-by-step explanation:
The given equation for the distance the Benson family traveled from their home can be presented as follows;
d = 55·t + 100
Where;
d = The total distance that the Benson family has traveled from their home after traveling 100 miles to pick up their grandparents
t = The time duration the Benson family have been traveled from their grandparents home on the way to their vacation
To find how far from their home the Bensons will be after 3 1/2 hours of driving with their grand parents, we substitute t with 3 1/2 hours or 3.5 hours as follows;
d = 55·t + 100
When t = hours, we get;
Therefore, the distance the Bensons had traveled from their home hours after picking up their grand parents = 292.5 miles.
Answer:
-2.5
Step-by-step explanation:
Plugged into calculator
From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.
Using pythagoras theorem,
and
Angle θ is given by
Given that a = 4 units, b = 5 units, and c = 9 units, thus
To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
Given that x is a point on line segment AB, this means that x is a positive number less than 5.
Thus
Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.
Answer:
The same person does that to me and i heard to NOT mess with those link because they can find our address or something
Step-by-step explanation:
