**Assignment #1**

**Answer each of the following questions. You must ****provide detailed work**** illustrating how you arrived at your solution.**

**Submit your answers to the drop box.**

**Your work may be attached as a Word Document or a PDF File.**

**1)**** ****An open box with a square base (see figure) is to be constructed from 108 square inches of material. The height of the box is 3 inches. What are the dimensions of the box?**

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Surface area = 108 square inches

X*X + 4*a*x = 108

X2 +12x=108

X2 +12x-108=0

Solve the quadratic equation

D=b2-4ac=122 – 4 *1* -108=576

X= (-b±√D)/(2*a)

X=(-12±√576)/(2*1)

X= 6 or -18.

Use the positive value

Dimensions = 6*6*3

**2)**** ****An electric hoist is being used to lift a beam. The diameter of the drum on the hoist is 13 inches, and the beam must be raised 3 feet. Find the number of degrees through which the drum must rotate. Round your answer to nearest whole number. We are given a = 13 and b = 3.**

Circumference = 3

Circumference = (θ/360)* ∏*D

Θ=(360 * Circumference)/( ∏*D)

Θ=(360*3)/(13*22/7)

= 1080/40.857

= 26 degrees

**3)**** ****The hypotenuse of an isosceles right triangle is 4 centimeters long. How long are its sides? Round your answers to two decimal places.**

Isosceles – two equal sides

Assume opposite an adjacent are equal. The angles between hypotenuse and the two are equal.

180-90=90/2=45degrees each.

Cosθ=adj/hyp

Cos 45 = adj/4

Adj = 4 * 0.7071

=2.83cm

**4) A sprinkler on a golf green is set to spray water over a distance of 12 meters and to rotate through an angle of 140°. Find the area of the region. Round your answer to two decimal places.**

Radius = 12M

Sector sprinkled= 140/360

∏ = 22/7

Area=θ/360* ∏ * R2

= 140/360*22/7*12*12

= 176.00M2

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Grading Criteria Assignments
| Maximum Points |
---|---|

Meets or exceeds established assignment criteria
| 40 |

Demonstrates an understanding of lesson concepts
| 20 |

Clearly presents well-reasoned ideas and concepts
| 30 |

Uses proper mechanics, punctuation, sentence structure, and spelling
| 10 |

Total
| 100 |

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