Answer:
Step-by-step explanation:
Let's say that the two planes travel at point . Without loss of generality, let's say that the first plane travels left and the second plane travels right.
Distance is given by , where
is rate or speed and
is time.
If the first plane travels at a speed of 320 mph and the second plane travels 1.5 times this, the second plane must travel mph.
Using , the first plane must travel:
miles
The second plane must travel:
miles
However, these are the planes' respective distances from point . Since they travelled in opposite directions, the total distance between them is equal to
So, the triangle is equilateral, all its sides are equal⇒
AB=BC=AC=8
In an equilateral triangle, the height is also the median, so it divides the sides into 2 equal parts⇒
AO=OC=8:2=4
by the Pythagorean theorem
Answer: BO=4√3
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The graph which shows the velocity of the particle at any time is attached below.
<h3>How to depict the graph?</h3>The graph is the rate of change of position of an object with respect to time. Velocity is the speed of an object moving in a definite direction.
Velocity is a vector quantity as it has both magnitude and direction. The velocity of a particle is modeled by the function. It is observed that the given velocity function is a cubic function. The attached graph shows the velocity of the particle at any time.
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The value of f(5) is 49.1
Step-by-step explanation:
To find f(x) from f'(x) use the integration
f(x) = ∫ f'(x)
1. Find The integration of f'(x) with the constant term
2. Substitute x by 1 and f(x) by π to find the constant term
3. Write the differential function f(x) and substitute x by 5 to find f(5)
∵ f'(x) = + 6
- Change the root to fraction power
∵ =
∴ f'(x) = + 6
∴ f(x) = ∫ + 6
- In integration add the power by 1 and divide the coefficient by the
new power and insert x with the constant term
∴ f(x) = + 6x + c
- c is the constant of integration
∵
∴ f(x) =
+ 6x + c
- To find c substitute x by 1 and f(x) by π
∴ π =
+ 6(1) + c
∴ π = + 6 + c
∴ π = 6.4 + c
- Subtract 6.4 from both sides
∴ c = - 3.2584
∴ f(x) =
+ 6x - 3.2584
To find f(5) Substitute x by 5
∵ x = 5
∴ f(5) =
+ 6(5) - 3.2584
∴ f(5) = 49.1
The value of f(5) is 49.1
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You can learn more about differentiation in brainly.com/question/4279146
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