MAT 116 Week 6 CONCEPT APPLICATION



MAT 117 Week 6 CONCEPT APPLICATION

Answer the following questions. Use Equation Editor or MathType when writing mathematical expressions or equations. Points will be deducted if a math editor is not used to properly format your work. First, download and save this file to your hard drive by selecting Save As from the File menu. Save with the filename: yourLastnameFirstnameMat117Week6CA. Click the 3rd column to enter your work, the rows will automatically expand as you enter text. Attach your completed document and post to the Assignments Section on eCampus.

|# | |Show your work and final answer in this column. |- Pts |+ Pts |

| | |Include units when applicable. | | |

|1a |A slow-pitch softball diamond is actually a square. |Use the Pythagorean Theorem: | |3 |

| |The distance from home plate to 1st base is 65 feet. |[pic] | | |

| |How far is it from home plate to 2nd base? Give exact |[pic] | | |

| |answer. |c = √8450 | | |

| | |c = 65 √2 feet | | |

|1b |Give the approximate distance to 3 decimal places. |Using a calculator: | |3 |

| | |c = 91.924 feet | | |

|2 |In the northern states of the U.S. during the winter months, residents are concerned about the wind chill factor. | |0 |0 |

| |If the wind speeds are greater than 4 mph it feels colder than the actual temperature because the wind enhances | | | |

| |the loss of heat from the skin. The formula for finding the wind chill temperature is [pic] | | | |

| |where T is the actual temperature in Fahrenheit, and V is the wind speed in miles per hour. | | | |

|2a |Find the wind chill temperature if the actual |Plug in the values of T = -5 and V = 35: | |4 |

| |temperature is [pic]and the wind speed is 35 mph. |W = 91.4-(91.4-(-5))*(0.478+0.301√35-0.02(35)) | | |

| | |W = -58.86 degrees F | | |

|3 |Construction utilizes the Pythagorean Theorem in many instances to insure a “square” structure. In laying out the| |0 |0 |

| |footers or corners of any building the concept of a 3-4-5 right triangle is applied. | | | |

|3a |Name two more dimensions of a right triangle that will |Multiply the dimensions by 2: | |3 |

| |also yield a square corner. |6-8-10 | | |

| | |Or multiply by 3: | | |

| | |9-12-15 | | |

|4 |The diameter size of the carburetor’s opening, D(p), in mm, where p is the number of rpm’s at which the engine | |0 |0 |

| |achieves peak performance is given by the function [pic] for an engine with a displacement of 2.8L | | | |

|4a |If the carburetor’s opening is 81 mm, what are the |Plug in D(p) = 81: | |3 |

| |rpm’s of peak engine power? |81 = 0.75√2.8p | | |

| | |Divide by 0.75: | | |

| | |108 = √2.8p | | |

| | |Square it: | | |

| | |11664 = 2.8p | | |

| | |Divide by 2.8: | | |

| | |p = 4165.71 rpm | | |

|4b |If 4480 rpm’s is peak engine performance, what is the |Plug in p = 4480: | |4 |

| |diameter of the carburetor’s opening? |D(p) = 0.75√2.8(4480) | | |

| | |= 84 mm | | |

|5 |Police investigating an auto accident use the length of a skid mark to determine the vehicle’s speed, using the | |0 |0 |

| |formula, [pic], where r is the car’s rate of speed and L is the length of the skid mark in feet. | | | |

|5a |Find the rate of speed of a car that left a 150 feet |Plug in L = 150: | |3 |

| |skid mark. Round to the nearest whole number. |r = 2√5(150) | | |

| | |r = 55 mph | | |

|5b |Solve the formula for L. |Divide by 2: | |4 |

| | |[pic] | | |

| | |Square: | | |

| | |[pic] | | |

| | |Divide by 5: | | |

| | |[pic] | | |

|5c |Find the length of a skid mark made by a vehicle |Plug in r = 65: | |3 |

| |traveling at 65 mph. |[pic] | | |

| | |L = 211.25 feet | | |

|6 |The formula [pic] can be use to find the period (T in seconds, the time it takes a pendulum to complete one cycle)| |0 |0 |

| |of a pendulum that is L cm long. | | | |

|6a |Rewrite this formula using rational exponents. |A square root is like a ½ power: | |4 |

| | |[pic] | | |

|6b |Solve the formula for L. |Divide by [pic] | |4 |

| | |[pic] | | |

| | |Square: | | |

| | |[pic] | | |

| | |Multiply by 480: | | |

| | |[pic] | | |

| | |Totals | | |

| |Post according to directions (Filename & Worksheet Attachment). | | |1 |

| |Use a math editor to type all math text. | | |1 |

| | |10% deduction per each day late. | | |

| |Comments: |Score | | |

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