University:
Morehouse College
Course:
HMTH 105 | College Algebra 1
Academic year:

2024
Views:

71

Pages:

2
Author:

Reynaldo Wong

Question 1 Determine whether the set have a subset relationship. Are the two sets disjoint or equivalent? Do the sets intersect? 𝑅 = { right triangles } R={right triangles}, 𝑂 = { obtuse triangles } O={obtuse triangles} Answer 1 A right triangle has a right angle and two acute angles, and an obtuse triangle has an obtuse angle and two acute angles. So, an obtuse triangle can never be a right triangle and vice versa. Thus, 𝑅 R and 𝑂 O are disjoint sets. Question 2 Find the length of the leg of the triangle 45-45-90 with a long hypotenuse of 25 inches. Answer 1 In a 45°-45°-90° triangle, the length of the hypotenuse is 2 2 2 2 times each leg. If 𝑥 x is the leg length, then we can write: 25 = 𝑥 2 25=x 2 𝑥 = 25 2 x= 2 25 𝑥 = 25 2 2 x= 2 25 2 Question 3 In quadrant I, draw a right triangle with one leg on the x-axis and its hypotenuse on the terminal side of drawn in standard position. If sin ⁡ 𝜃 = 7 25 sinθ= 25 7 , then what is the value of 𝜃 θ? Answer 1 Let opp = 7 opp=7 and hyp = 25 hyp=25. Solve for adj adj (adjacent side) using the Pythagorean Theorem: opp 2 + adj 2 = hyp 2 opp 2 +adj 2 =hyp 2 7 2 + adj 2 = 2 5 2 7 2 +adj 2 =25 2 49 + adj 2 = 625 49+adj 2 =625 adj 2 = 576 adj 2 =576 adj = 24 adj=24 The tangent is positive in quadrant I: tan ⁡ 𝜃 = opp adj = 7 24 tanθ= adj opp = 24 7 Question 4 Calculate the tension 𝐹 𝑇 F T in the wire that supports the 30 kg beam shown in the picture, and the force 𝐹 𝑊 F W exerted by the wall on the beam (give magnitude and direction). Answer 1 Weight = 𝑚 𝑔 = 30 ⋅ 9.8 = 294 N Weight=mg=30⋅9.8=294N 𝑇 = 294 2 ⋅ sin ⁡ 40 ≈ 94.5 N T= 2⋅sin40 294 ≈94.5N Question 5 The drawing shows a uniform electric field that points in the negative y direction; the magnitude of the field is 5300 N/C. Determine the electric potential difference (a) 𝑉 𝐵 − 𝑉 𝐴 V B −V A between points A and B, (b) 𝑉 𝐶 − 𝑉 𝐵 V C −V B between points B and C, and (c) 𝑉 𝐴 − 𝑉 𝐵 V A −V B between points C and A. 𝐴 − 𝐶 A−C is 10.0 cm, 𝑏 − 𝑐 b−c is 8.0 cm, 𝑎 − 𝑏 a−b is 6.0 cm. They are all in a right triangle shape, with angle 𝑏 b having the 90 degree angle, and electric potential is pointing down. This is problem 56 in 7th edition. Answer 1 a) 𝑉 𝐵 𝐴 = 𝐸 ⋅ 𝑑 = 0 V BA =E⋅d=0 b) 𝑉 𝐶 𝐵 = 𝐸 ⋅ 𝑑 = 5300 ⋅ 0.08 = 424 V V CB =E⋅d=5300⋅0.08=424V c) 𝑉 𝐴 𝐵 = 𝐸 ⋅ cos ⁡ 4 5 ∘ ⋅ 𝑑 = 374.76 V V AB =E⋅cos45 ∘ ⋅d=374.76V