Problems and Solutions on Engineering Mathematics - Paper Example

Include the equations or formulas you used.

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Explain, in words or with mathematical steps, how you arrived at your answers. You do not have to submit sketches, but you may find that drawing parts of the problem on scratch paper can help you understand the problem.

Include all relevant units (such as miles or cubic inches) in your final answers.

Maine Lobster Direct in Portland, Maine, hires a contractor to ship its goods to Harrys Restaurant of Manhattan, Kansas, by a refrigerated truck. The driving route is 1,608 miles. Providing a proper shipping environment is vital so the lobsters can arrive at their destination alive.

Assuming the driver does not stop and drives at an average speed of 65 miles per hour, approximately how many hours will the trip take? Round to one decimal place. How long is that in whole minutes? Calculate the minutes from your rounded hours answer.

Distance = 1, 608 miles

Speed = 65 miles per hour

According to Anderberg (2014), to obtain the number of hours that the driver will take at the given speed, the following formula is used;

Time taken=DistanceSpeedHence, the driver takes = 1,608 miles /65 miles per hour = 24.7 hours. Considering that 60 minutes make an hour, and then converting the time in minutes by multiplying with 60, it implies that the driver will take 24.7 x 60 = 1, 484 minutes for the journey.

Lobsters cannot survive more than 30 hours in refrigeration. How many half-hour breaks can the driver take and still deliver the lobsters alive?

A halfhour break implies taking 30 minutes at every break session. There are 1484 minutes that the driver is expected to arrive at the destination. Therefore, the number of breaks expected will be as follows:

Half hour break = total travelling time/ breaking time

= 1484 minutes / 30 minutes

= 49

This implies the driver will take 49 halfhour breaks before reaching the destination.

Each shipment of lobsters is packed into a crate (a rectangular prism) that measures 22 inches long, 17 inches wide and 13 inches high. For the trucking company to bill you accurately, you must report certain calculations of the crates size with the correct units. Determine:

The area of the base

Assuming figure 1 below is the crate (a rectangular prism) being used in shipping the crates:

To obtain the area of the base, the following formula can be used (Erwin et al., 2015);

Base Area=Length x Width= 22 inches x 17 inches

= 374 inches2

The perimeter of the base

To obtain the perimeter of the base, the following formula is used;

Base Perimeter=2xLength+Width= 2 x (22 + 17)

= 78 inches

The volume of the crate

According to Erwin et al., (2015), the formula for volume of a cuboid-shaped object such as the crate is obtained using the formula below:

Volume=Length x Width x Height= 22 inches x 13 inches x 17 inches

= 4862 inches3

The lobsters must all be packed in the same orientation (with all the heads are facing the same direction) to travel safely. Assume that each lobster requires a rectangular space that is 10 inches in length, 5 inches at its widest, and 3 inches high. Refer to the diagram below to see how one lobster would be positioned in a crate.

Given the orientation requirements, how many lobsters can fit along the 22-inch length of the crate?

To obtain the number of lobsters that would fit along a 22inch length, it requires dividing the length of the crate by the length of a single lobster as follows;

Number of lobsters along the length of crate=Length ofcrateLength of lobster= 22inches / 10inches

= 2.2 2 lobsters

How much space in the crate does one lobster take?

To get the size of the space taken by one lobster implies that the space at the base, on the wide size and on the height is calculated. This brings the volume concept of the lobster which is calculated using the following formula (Erwin et al., 2015);

Volume=Base area x heightBase area is calculated by taking the length by width of the lobsters, that is,

Base area = 10 inches by 5 inches = 50 inches2

Then, volume = 50 inches2 x 3 inches

= 1500 inches3

Therefore, the space taken by a single lobster is 150 inches3.

Consider how you determined how many lobsters can fit along the length of the crate. How many lobsters can be packed in one crate the same way as in the diagram?Hint: Draw on scratch paper a sketch of several lobsters (rectangles) in the crate, noting the dimensions for each lobster and the crate. This should tell you how to structure the problem.

Since lobsters are solid components that would not be broken down, the full item number that can be arranged along the length of the crate are 2.

The crate weight limit is 25 kilograms. The contents of your crate weigh 50 pounds. Is the crate safe? Why or why not?

Based on the metrics of unit conversion: 1Pound= 0.453592 kilograms

Given that 50 pounds is the weight of crate content, this is equivalent to;

=50x 0.453592= 22.6796kilograms

The 22.6796 kilograms is within the accepted limit of the crate which carries a maximum load of 25 kilograms. The crate is thus safe.

To make sure the lobsters are cool but not frozen, you need to keep their temperature between 32 and 40 degrees Fahrenheit while they are being shipped. However, your driver, Igor, is from Europe, where they use Celsius instead of Fahrenheit. Please provide these temperatures in Celsius for Igor and round to the nearest degree.

Conversion of Degrees Fahrenheit to Degrees Celsius obeys the formula below:

T(0C) = (T(0F) - 32) 5/9

In the case of 32 and 40 degrees Fahrenheit, the following are the degrees in Celsius for Igor to use:

32oF=0oC

40oF= 4.44444 Which can be approximated to 4oC

References

Anderberg, M. R. (2014). Cluster analysis for applications: probability and mathematical statistics: a series of monographs and textbooks (Vol. 19). Academic press.

Erwin, K., Herbert, K., & Edward, N. J. (2015). Advanced engineering mathematics.