Heaven and earth will pass away, but my words will never pass away. Matthew 24:35 NIV
6-Review
Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.
- How many triangles are formed with the given information: A = 50˚, a = 70, b = 100?
Solve the triangle with the given information. Round to two decimal places if necessary.
- A = 76˚, B = 17˚, c = 14
- A = 50˚, a = 50, b = 60
- a = 6, b = 9, c = 10
- A = 31˚, b = 21, c = 32
- This triangle has two solutions. Find angle B in the second solution: A = 80˚, a = 69, b = 70.
- Find the area of the triangle with a = 7, b = 13, c = 11. Round to two decimal places.
- Find the component form of a vector with initial point at (10, 13) and terminal point at (0, 17).
- Find a unit vector in the direction of \(\langle 13, 84 \rangle\).
Let \(\overset{\rightharpoonup}{u} = \langle 20, 15 \rangle\) and \(\overset{\rightharpoonup}{v} = \langle -10, 11 \rangle\), find the following.
- \(\overset{\rightharpoonup}{u} + \overset{\rightharpoonup}{v}\)
- \(2\overset{\rightharpoonup}{v}\)
- \(6\overset{\rightharpoonup}{u} - 3\overset{\rightharpoonup}{v}\)
- \(\overset{\rightharpoonup}{u} \cdot \overset{\rightharpoonup}{v}\)
- Find the angle between \(\overset{\rightharpoonup}{u}\) and \(\overset{\rightharpoonup}{v}\).
- Are the vectors \(\langle -2, 4 \rangle\) and \(\langle \frac{1}{2}, -1 \rangle\) orthogonal, parallel, or neither?
- A lawn mower is pushed by exerting a force of 42 pounds on a handle that makes a 30˚ angle with the horizontal ground. Find the work done by pushing the lawn mower 100 feet.
- Write \(z = -9 + 9\sqrt{3}i\) in trigonometric form.
- Write \(z = 25\left(\cos \frac{11π}{6} + i \sin \frac{11π}{6}\right)\) in standard form.
Given m = 10(cos 115˚ + i sin 115˚) and n = 2(cos 25˚ + i sin 25˚), find the following and express your solutions in standard form rounded to two decimal places.
- m ÷ n
- m · n
- n2
- Find the 2nd roots of \(81\left(-\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2}i\right)\). Express your answers in standard form rounded to two decimal places.
Answers
- No triangle
- a = 13.60, b = 4.10, C = 87˚
- B1 = 66.82˚, C1 = 63.18˚, c1 = 58.25; B2 = 113.18˚, C2 = 16.82˚, c2 = 18.88
- A = 36.34˚, B = 62.72˚, C = 80.94˚
- B = 37.69˚, C = 111.31˚, a = 17.69
- 92.46˚
- 38.50
- \(\langle -10, 4 \rangle\)
- \(\langle \frac{13}{85}, \frac{84}{85} \rangle\)
- \(\langle 10, 26 \rangle\)
- \(\langle -20, 22 \rangle\)
- \(\langle 150, 57 \rangle\)
- −35
- 95.40˚
- Parallel
- 3637.31 ft·lbs
- \(18\left(\cos \frac{2π}{3} + i \sin \frac{2π}{3}\right)\)
- \(\frac{25\sqrt{3}}{2} - \frac{25}{2}i\)
- 5i
- −15.32 + 12.86i
- 2.57 + 3.06i
- 3.44 + 8.31i; −3.44 − 8.31i