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snow_tiger [21]
2 years ago
6

Question 8: The equation of motion of a particle is

Mathematics
1 answer:
lawyer [7]2 years ago
4 0

Answer:

D) 22\:\text{m/s}^2

Step-by-step explanation:

Acceleration is the derivative of velocity, which is the derivative of position, so we must differentiate the function twice:

Position of Particle: s(t)=t^3-4t^2+2t+8

Velocity of Particle: v(t)=3t^2-8t+2

Acceleration of Particle: a(t)=6t-8

After t=5 seconds, the acceleration of the particle is a(5)=6(5)-8=30-8=22\:\text{m/s}^2

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Interpreting composite functions in the real world The volume of air in a balloon is represented by the function v(r)=4/3 ³, whe
adoni [48]

There are two <em>true</em> statements:

  1. When the function is composed with r, the <em>composite</em> function is V(t) = (1/48) · π · t⁶.
  2. V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.

<h3>How to use composition between two function</h3>

Let be <em>f</em> and <em>g</em> two functions, there is a composition of <em>f</em> with respect to <em>g</em> when the domain of <em>f</em> is equal to the range of <em>g</em>. In this question, the <em>domain</em> variable of the function V(r) is replaced by substitution.

If we know that V(r) = (4/3) · π · r³ and r(t) = (1/4) · t², then the composite function is:

V(t) = (4/3) · π · [(1/4) · t²]³

V(t) = (4/3) · π · (1/64) · t⁶

V(t) = (1/48) · π · t⁶

There are two <em>true</em> statements:

  1. When the function is composed with r, the <em>composite</em> function is V(t) = (1/48) · π · t⁶.
  2. V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.

To learn on composition between functions: brainly.com/question/12007574

#SPJ1

7 0
2 years ago
Simplify (4x − 6) − (3x + 6).
antiseptic1488 [7]

the answer is the first one A


8 0
3 years ago
Read 2 more answers
What number can go into 68 and 100
Sati [7]
One number is 4 Another is 2 I hope this helped
8 0
3 years ago
Read 2 more answers
Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer
k0ka [10]
Alaina has $28 in her account and wants to buy shoes worth $45

So $28-$45=$-17

Her account status will be $ - 17

Hope this helps
3 0
3 years ago
Read 2 more answers
The heaviest dinosaur is estimated to have welghed 2.8 x 10^5 pounds. The average car weighs about 4 x 10^3 pounds.
34kurt

Answer:

  70

Step-by-step explanation:

Apparently, you want the ratio of the weights:

  (dino weight)/(car weight) = (2.8×10^5)/(4×10^3)

  = (2.8/4)×10^(5-3) = 0.7×10^2 = 0.7×100

  = 70

The heaviest dinosaur weighed about 70 times the weight of an average car.

_____

Your calculator can do arithmetic in scientific notation. So can any spreadsheet.

The applicable rule of exponents is ...

  (10^a)/(10^b) = 10^(a-b)

4 0
3 years ago
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