Final Exam Answer Sheet

1 MATH 108 Final Exam Answer Sheet This exam is worth 240 points. Questions 1 - 20 are each worth 5 points; do not show your work. Questions 21 – 27 are each worth 20 points; show your work to earn full credit. Write answers on the appropriate numbered blank. For questions 21 – 27 you can insert additional lines or delete lines as needed. See rubric for grading details. Leave answers in exact form unless otherwise directed to approximate the results. Write all fractions in lowest form. Round decimals to hundredths unless otherwise directed to round. Write answers using positive exponents except when using scientific notation. Simplify all radicals and rationalize the denominators. Applied problems should have the variables identified (Let x =), an equation, and the units (degree, inches, $, etc.) for full credit. Do not post the exam in the assignment folder. Post only your Answer Sheet in the assignment folder. Questions 1 – 10: Fill-in-the-blank, do not show work. Questions 11 – 20: Multiple choice, select the letter of the one alternative that best completes the statement or answers the question. Check that the answers are all letters (A, B, C, D, or E) and not a value, do not show work. 1.) 𝐴 = 66.95° , 𝐶 = 53.05° , c=14.76km 11.) E 2.) 𝑎 52 = 94 12.) C 3.) − √6 −√2 4 13.) E 4.) 120/119 14.) A 5.) ___________________ 15.) C 6.) 𝜋/2 16.) C 7.) 15.07° 17.) D 8.) 45 18.) E 9.) = 161 19.) B 10.) ? = −4(? − 1) 2 + 7 20.) B

2 SHORT ANSWER. Show your detailed work. The following questions are each worth 20 points. Applied problems that have the variable(s) identified (Let x =) will earn +1 point. Final exam grade cannot exceed 240 points. 21.) Verify: 22.) answer: __________ Show work and post graph here: Vertex : (1,7) Directrix: y=113/16 23.) answer: __________ Show work and post graph here:

4 { ? = ? + 4.40 ? + ? = ? + 15.58 ? + ? + ? = 53.42 Substitute E1 y= z +4.40 on E2 x + z =y+15.58 X + z = y +15.58 X + z = z +4.40 + 15.58 X + z = z +19.98 X = -z + z + 19.98 X = 19.98 Average amount spent on flowers $19.98 Now that we have found x, we are going to find the value of z by substituting on E3 X +y + z = 53.42 19.98 + z +4.40 + z = 53.42 Z + z +19.98 +4.40 = 53.42 2z + 24.38 = 53.42 -24.38 + 2z +24.38 = 53.42 -24.38 2z = 29.04 Z = 29.04/ 2 Z = 14.52 Average amount spent on gift cards $14.52 Now we can substitute on E1 to find the value of y Y = z + 4.40 Y = 14.52 +4.40 Y= 18.92 Average amount spent on jewelry $18.92 25.) answer: The work done towing the trailer is 700,000 foot-pounds Show work here: Data:

5 Force to tow the boat from the barn to the dock = 1400 pounds Displacement = 500 foot Work done = ? To find the work done we ’ re using theorem 11.28 work as a dot product 𝑊 = 𝐹 ⃗ . ?? ⃗⃗⃗⃗⃗⃗⃗⃗ = ‖𝐹 ⃗ ‖‖?? ⃗⃗⃗⃗⃗⃗ ‖ cos 𝜃 Where W = work done, F = force applied , PQ= the vector, 𝜃 = angle between F and PQ 𝜃 = 1 because is assumed that the force is applied in the direction of the motion So, we get that: W = 1400 pounds * 500 foot * 1 = 700, 000 foot-pounds 26.) answer: __________ 27.) answer: The angle of inclination is ≈ 3.43° Show work here: 120 ft 2000 feet To solve this, we can use tanθ = ???????? 𝑎??????? We have that straight road = 120 feet Road = 2000 feet tan 𝜃 = 120 2000 = 3 50 To find the angle we apply inverse of tangent tan −1 ( 3 50 ) = 3.43°