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Andre45 [30]
3 years ago
10

Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position

. a(t) = 2 i + 6t j + 12t2 k, v(0) = i, r(0) = 7 j − 4 k
Business
1 answer:
Murljashka [212]3 years ago
8 0

Answer:

v(t) = (2t + 1)i + 3t²j + 4t³k

r(t) = (t² + t)i + (t³ + 7)j + (t⁴ - 4)k

Explanation:

a(t) = 2i + 6tj + 12t²k

v(t) = ∫a(t)dt

     = ∫(2i + 6tj + 12t²k)dt

     = 2ti + (6t²/2)j + (12t³/3)k + c

     = 2ti + 3t²j + 4t³k + c

v(0) = i

    i = 0i + 0j + 0k + c

    c = i

∴ v(t) = 2ti + 3t²j + 4t³k + i

v(t) = (2t + 1)i + 3t²j + 4t³k

r(t) = ∫ v(t)dt

    = i ∫ (2t + 1)dt + 3j ∫ t²dt + 4k ∫ t³dt

    = i (2t²/2 + t) + 3j(t³/3) + 4k(t⁴/4) + d

    = i (t² + t) + jt³ + t⁴k + d

r(0) = 7j - 4k

0i + 0j + 0k + d = 7j - 4k

d = 7j - 4k

∴ r(t) = (t² + t)i + t³j + t⁴k + 7j - 4k

r(t) = (t² + t)i + (t³ + 7)j + (t⁴ - 4)k

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Answer:

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Explanation:

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<em>One of the most important goals financial management has is to maximize the stakeholders' wealth.</em>

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The answer is: Stock markets reflect all available information about the value of stocks

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Efficient market hypothesis (EMH) is an investment theory about stock markets where the price of stocks is always the fair market value of the stocks. It argues that it is impossible for someone to determine when stocks are either undervalued or overvalued. So all the technical and fundamental analysis techniques are useless.

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Ben says that "an increase in the tax on beer will raise its price." Holly argues that "taxes should be increased on beer becaus
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B. Holly's statement is normative, but Ben's is positive.

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Positive statements are based on objective deduction of what is, or was. It is based on facts. Ben's comment "an increase in the tax on beer will raise its price", is an example of positive statement.

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For a stock to be in equilibrium, that is, for there to be no long-term pressure for its price to depart from its current level,
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Answer:

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Answer:

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the loan's interest rate is missing, so I looked for a similar question and found that it is 6%

present value = monthly payment x annuity factor

monthly payment = present value / annuity factor

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8 0
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