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Answers by Anthony B.

1. let h(t) be in the A*sin(bt + c) + M form, where A = amplitude, b = 2π/k, k = 1/f, f = frequency, t = time (in seconds), c = the horizontal translation, and M = the midline. 2. A = the diameter/2 = 7 3. b = 2π/k, k = 1/3 (because the frequency is 3 rev/sec), so b = 2π/(1/3)...

1. let m∠ S = x and the m∠ L = 5x + 12 2. since the two are complementary, we know that their sum equals 90° 3. therefore, (x) + (5x + 12) = 90 4. solve for x: 6x = 78 5. x = 13 6. hence, m∠ S = 13° and m∠ L = 5(13) + 12 = 77°

Let's use this formula: B = A(1+i)n - (P/i)*([1+i]n - 1), where B is the balance after n payments, A is the initial amount of the loan, P is the monthly payment amount, and i is the interest rate compounded monthly.   1. A = 30000, P = 400, i = .06/12 = .005, and n = 2 years*(12...

1. let's use the law of cosines for this :) 2. let a = 70 and b = 175 3. also, 21° is the angle that is opposite to the side of the triangle that we are looking for 4. the law of cosines = c2 = a2 + b2 - 2*a*b*cos(21°) 5. substitute the values in: c2 = (70)2 + (175)2...

1. the angle of elevation formed by the ground and the bottom of the antenna is 62.6° 2. the side opposite to this angle is 1000 3. to find the distance from the building to the point of observation, we do: tan(62.6°) = 1000/a 4. a = 1000/tan(62.6°) ≈ 518.351 5. the angle of...

For the nominative case, use the perspective chart :)   1. first person singular = I 2. second person singular = you 3. third person singular = he, she, or it 4. first person plural = we 5. second person plural = you 6. third person plural = they   The...

Uniform motion (answer)

1. it seems beneficial to use vectors for this problem. (Remember, velocity is a vector, but speed is a magnitude.) 2. let rb = the velocity of Train B and ra = the velocity of Train A. 3. the absolute value of (rb) = the absolute value of (ra) + 15 4. sb, the speed of B, =...