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
Answer:
Part (a)
Buying of land would be smart thought if the net present estimation of advantage is at any rate equal to or more prominent than the present estimation of cost of land.
Net present estimation of land = 
= $1,825,592.54
The expense of land is anyway $2,000,000. The net present expense of land is more noteworthy than the advantages. Subsequently it isn't a good thought to purchase the land.
Part (b)
The maximum sum that ought to be paid ought to be equivalent to the net present estimation of advantages, for example $1,825,592.54.
Part (c)
If the entertainment benefits increment by 3 years then the net present estimation of advantages for a long time would be:
= ![\frac{100,000 * [ 1 - (1.03/1.05)^{50} ] }{(0.05-0.03)}](https://tex.z-dn.net/?f=%5Cfrac%7B100%2C000%20%2A%20%5B%201%20-%20%281.03%2F1.05%29%5E%7B50%7D%20%20%5D%20%7D%7B%280.05-0.03%29%7D)
=$3088535.28
The land should be purchased since the present estimation of advantages is more prominent than cost.
Answer:
trial balance
Explanation:
Based on the information provided within the question it can be said that in this scenario Audrey will prepare a trial balance. This refers to an extensive list detailing all the general ledger accounts that can be found within the ledger of a business, each of which will reveal the name and balance of that account. This is what Audrey is preparing and is one of the main tasks completed by accounting departments.
Answer:
$33.50
Explanation:
we can use the perpetual growth model to determine the price of the stock
the firm's stock price = ($1.25 x 1.15)/1.11 + ($1.25 x 1.15²)/1.11² + ($1.25 x 1.15³)/1.11³ + [($1.25 x 1.15³ x 1.06)/(11% - 6%)]/1.11³
the stock price in 3 years = ($1.25 x 1.15³ x 1.06)/(11% - 6%) = $40.30
the firm's stock price = ($1.25 x 1.15)/1.11 + ($1.25 x 1.15²)/1.11² + ($1.25 x 1.15³)/1.11³ + $40.30/1.11³ = $1.30 + $1.34 + $1.39 + $29.47 = $33.50
Answer:
9%
Explanation:
The first step is to understand the relevant terms in the question
Average Cost of New Capital
The cost of capital represents a required return rate (in percentage) an organisation or an individual ( in the case of John) will need to make a capital project advantageous, worthwhile or profitable.
In the case of John, the Average Cost of New Capital is 9%
MARR - Minimum Acceptable Rate of Return
This rate also in percentage represents the lowest or minimum rate of return a business or an individual is able to accept in order to start a given project. It is usually based on the risk of the project as well as the alternate benefit foregone if other projects were accepted.
It is also called the Hurdle rate, or the cutoff rate.
John's MARR is 18%
Based on these,
John's Net rate of return is calculated as follows
Minimum Acceptable Rate of Return - Average Cost of the New Capital
= 18% - 9% = 9%
