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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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juin [17]

Answer:

$7,692.31

Explanation:

Given;

Cost of non-residential real property = $300,000

Purchased in March 2018.

Useful life of non-residential real property = 39 years

Annual Depreciation = cost/useful life

                                   = $300,000/ 39

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Stanley's 2019 depreciation on the property amounts to $7,692.31.

8 0
3 years ago
Pepper Corporation owns 75 percent of Salt Company's voting shares. During 20X8, Pepper produced 50,000 chairs at a cost of $79
muminat

Answer:

Please see below

Explanation:

Given that:

Number of chairs sold = 35,000

Cost per chair $79

The cost of goods sold that must be eliminated from the consolidated

= Number of chairs sold × Cost per chair

= 35,000 × $90

= $2,765,000

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4 0
3 years ago
A special agent is authorized to:
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<span>c. handle all of the principal's affairs in one or more areas
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Industrial work in the factory resulted in ________ compared to work as a skilled artisan.
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Computing investing cash flows
mel-nik [20]

Answer: Please refer to Explanation

Explanation:

The Cash Flow Statement was created to ensure that businesses would know just how much hard cash they actually have. This Statement is therefore different from others in that in only records cash when it has been received and/or disbursed thus making it easier for a company to know how much cash it has.

The Investing Section of the Cashflow statement deals with fixed assets as well as transactions involving securities and bonds of other entities as those are investments.

When cash is spent on these transactions it is a Cash Outflow and is therefore subtracted.

When cash is received from such transactions it is considered a cash inflow and is added.

Effects of Above Transactions.

Sold a Truck for $11,200. This will INCREASE the Investing Cash Flow by $11,200.

Sold a Machine for $8,200. This will INCREASE the Investing Cash Flow by $8,200.

Purchased stock investments for $17,600 cash. This will DECREASE the Investing Cash Flow by -$17,600 as it was a cash Outflow.

The Investing Section of the Cash Flow Statement will look like,

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7 0
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