Using C++, write a program to calculate the height and velocity of a ball thrown upward at a user-specified height and speed in 10 seconds. Position (h) and velocity (v) of the ball as a function of time are given by the equations: h(t) =(1/2)gt² + v₀t + h₀ v(t) = gt + v₀

Design an O(nlogn) algorithm that takes two arrays A and B (not necessarily sorted) of size n of real numbers and a value v. The algorithm returns i and j if there exist i and j such that A[i] + B[j] = v and no otherwise. Describe your algorithm in English and give its time analysis.

Implement function get_contact(contacts, name) that returns a string. The contacts and the name parameter are both type string. This function checks for the name string in the contacts string and returns that person’s contact information. If the person is not found, the function returns, “name not in contact”. Assume input is always valid. Assume the same name is not repeated in contacts.

[You may use split(), range(), len() ONLY and no other built-in function or method]

Examples:

              contacts = “Frank 703-222-2222 Sue 703-111-1111 Jane 703-333-3333”

              name = “Sue”

              print(get_contact(contacts, name))

              returns:

              703-111-1111

              name = “Sam”

print(get_contact(contacts, name))

              returns:

              name not in contact

Implement function get_contact(contacts, name) that returns a string. The contacts and the name parameter are both type string. This function checks for the name string in the contacts string and returns that person’s contact information. If the person is not found, the function returns, “name not in contact”. Assume input is always valid. Assume the same name is not repeated in contacts.

[You may use split(), range(), len() ONLY and no other built-in function or method]

Examples:

              contacts = “Frank 703-222-2222 Sue 703-111-1111 Jane 703-333-3333”

              name = “Sue”

              print(get_contact(contacts, name))

              returns:

              703-111-1111

              name = “Sam”

print(get_contact(contacts, name))

              returns:

              name not in contact

Problems:

The Diamond Glitter Company is in the process of preparing its financial statements for 2016. Assume that no entries for depreciation have been recorded in 2016. The following information related to depreciation of fixed assets is provided to you.

1. The company purchased equipment on January 2, 2013, for $165000. At that time, the equipment had an estimated useful life of 7 years with a $25000 salvage value. The equipment is depreciated on a straight-line basis. On January 2, 2016, as a result of additional information, the company determined that the equipment has a remaining useful life of 3 years with a $15000 salvage value.

2. During 2016, the company changed from the double-declining-balance method for its building to the straight-line method. The building originally cost $625000. It had a useful life of 10 years and a salvage value of $50000. The following computations present depreciation on both bases for 2014 and 2015. 2015 2014 Straight-line $ 57,500 $ 57,500 Declining-balance $ 92,000 $ 115,000

3. The company purchased a machine on July 1, 2014, at a cost of $450000. The machine has a salvage value of $25000 and a useful life of 10 years. The company's bookkeeper recorded straight-line depreciation in 2014 and 2015 but failed to consider the salvage value. Ignore Tax effect.

4. The company has failed to accrue sales commissions payable at the end of each of the last 2 years, as follows. December 31, 2015 $ 5,400 December 31, 2016 $ 4,600

5. In reviewing the December 31, 2015, inventory, the company discovered errors in its inventory-taking procedures that have caused inventories for the last 3 years to be incorrect, as follows. The company has already made an entry that established the incorrect December 31, 2016, inventory amount.

December 31, 2014 Understated $ 32,000

December 31, 2015 Understated $ 51,000

December 31, 2016 Overstated $ 9,500

6. At December 31, 2016, the company decided to change to the straight-line depreciation method on its retail display equipment from double-declining-balance. The equipment had an original cost of $250000 when purchased on January 1, 2015. It has a salvage value of 0 and a 8-year useful life. Depreciation expense recorded prior to 2016 under the double-declining-balance method was $62,500. The company has already recorded 2016 depreciation expense of $46,875 using the double-declining-balance method.

7. Before the current year, the company accounted for its income from long-term construction contracts on the completed-contract basis. Early this year, the company changed to the percentage-of-completion basis for accounting purposes, but continues to use the completed-contract method for tax purposes. Income for the current year has been recorded using the new method. Prior year tax effects must be considered. The following information is available.

Pretax Income

              Percentage-of-Completion      Completed-Contract

Prior to 2016       $320,000                        $180,000

2016                     $140,000                       $120,000

Required:

Prepare the journal entries necessary at December 31, 2016 to record the corrections and changes made to date related to the information provided. The books are still open for 2016. The income tax rate is 35%. The company has not yet recorded its 2016 income tax expense and payable amounts so current-year tax effects may be ignored.

The merry-go-round rotates counterclockwise with a constant angular speed u. The distance between the horse on the merry-go-round and the rotational center is r.

(a) Find the position of the horse x and its velocity v, v(t) = d/dt x(t), as vector-functions of time.

(b) Find the acceleration of the horse, a(t) = d^2/dt^2 x(t), as a vector-function of time. What is its direction (in comparison with the direction of x)?

Now the same horse has a non-constant angular speed u(t) (the merry-go- round still rotates counterclockwise).

(c) Find the position of the horse x and its velocity v, v(t) = d/dt x(t), as functions of time.

(d) Find the acceleration of the horse, a(t) = d^2/dt^2 x(t), as a function of time.

(e) What is the direction of a(t) at the moment when the merry-go-round starts to rotate?

1. The parking orbit of an Earth satellite has apogee and perigee altitudes of 850 km and 250 km, respectively (this orbit is sometimes referred to as an 850 km x 250 km orbit). (a) Determine the delta v required to circularize the orbit using a single-impulse burn at perigee. What is the period of the resulting circular orbit? Sketch the two orbits, indicating the point where the impulsive burn occurs. (b) Determine the delta v required to circularize the orbit using a single-impulse burn at apogee. What is the period of the resulting circular orbit? Sketch the two orbits, indicating the point where the impulsive burn occurs. (c) Compare parts (a) and (b); which is the least “expensive”. (d) Determine the delta v required to escape from the perigee of the parking orbit. (e) Determine the delta v required to escape from the apogee of the parking orbit. (f) Compare parts (c) and (d); which is the least “expensive.”

1. Given the data below (spread plate counts in CFUs/mL and OD reads for S. aureus) create a graph of time v. CFUs/mL, time v. OD = 600nm and OD = 600nm v. CFUs/mL (2 pts). Then calculate the growth rate and the generation time for this organism. (1 pt) Turn in images of your graphs and show your calculation work.

2. Say we create a graph of OD = 600nm v. CFUs/mL for S. aureus… What is the OD = 600 nm reading measuring? And are there any factors that could affect the results from assuming that a particular OD corresponds with a specific bacterial concentration? (1 pt)

Sheets of aluminum from a supplier have a thickness that is normally distributed with a mean of 50 mm and a standard deviation of 4 mm (call this random variable X). Your company compresses the aluminum with a tool that is normally distributed with a mean of 20 mm and a standard deviation of 3 mm (call this random variable Y). You are interested in the random variable V = X – Y, the random variable V is the final aluminum thickness.

1. What is the probability that the outputted aluminum (that is, V), will be between 25 mm and 32 mm?

2. What is the probability that the outputted aluminum (that is, V), will be between 26.5 mm and 33.5 mm?

3. If the company had the choice between compressing aluminum to between 25-32 mm or 26.5-33.5 mm, then which is preferred (or neither)?

4. In one or two sentences, why is one preferred (if either) over the other [continuation of 3.3]; if neither are preferred, then why?