Math Equations Questions

Assignment Part 1: Solve the following absolute value equations a. |𝑥 + 1| − 5 = 6 b. |4𝑥 − 1| ≤ 12 c. |3𝑥 − 7| ≥ 8 d. 3 + |𝑥 + 5| > 13 e. |𝑥 − 6| − 4 < 12 f. |𝑥 + 9| < −7 Part 2: I. For the following exercises, use the below figure to find the desired quantities. a. sin 𝛽 = b. cos 𝛼 = c. tan 𝛽 = II. Use the sine rule to find the missing value (𝑥) III. Use the cosine rule to find the missing value (𝑥) Part 3: a. Solve 4𝑒 3𝑥 + 7 = 15 b. Solve ln(3𝑥 − 6) = ln (𝑥 + 6) c. Write the following in one single logarithmic problem d. Convert (√3, − 1 ) from cartesian to polar 3 ln(5𝑥 + 2) + ln(3𝑥 − 7) − 2ln (3𝑥 + 5) e. Use the law to simplify 𝑙𝑛 (3𝑥+5)2 √𝑥−7 (5𝑥+3)3 2𝜋 f. Convert (2, 3 ) from polar to cartesian