Math 121 Assignment #1 Mr. Jacobs Page 14 45) Simplify (3π4 )3 (2π−5 )4 → (33 π12 )(24 π−20 ) → (27)(16)(π−8 ) → 432⁄ 8 π 50) Simplify ( 79) 125π12 π−14 π 22 25π8 π 6 π −15 −4 ) 25π8 π6 π −15 4 π 20 4 → (125π12 π−14 π 22 ) → (5π4 π 37) → π 80⁄ 625π16 π 148 The distance from the Earth to the Sun is defined a 1 Astronomical Unit or AU. It is about 93 million miles. The average distance from Earth to Pluto is 39 AU’s. Find this distance in miles. Set up as a Ratio 39 π΄π ′ π 1 π΄π = 93,000,000 πππππ π₯ πππππ → πΆπππ π ππ’ππ‘ππππ¦ → 1π₯ = 39 × 93,000,000 3,627,000,000 πππππ → 3.627 × 109 πππππ 80) One Parsec is about 3.26 Light Years and 1 Light Year is about 5.88 x 1012 miles. Find the number of miles in 1 Parsec. Set up as a Ratio 1 πΏπ 3.26 πΏπ 5.88×1012 πππππ = π₯ πππππ → πΆπππ π ππ’ππ‘ππππ¦ → 1π₯ = 1.91688 × 1013 πππππ 1 ππππ ππ = 1.91688 × 1013 πππππ 93) Suppose that $2,125.00 is invested at 6.2%, compounded semiannually. How much is in the account at the end of 5 years? P = 2,125 r = 6.2% = 0.062 n = 2 (for Semiannual) t=5 π π΄ = π(1 + π)ππ‘ = (2125)(1 + 0.062 (2)(5) ) 2 There is $2,883.67 in the account. = 2,883.67 Math 121 96) Assignment #1 Mr. Jacobs Suppose that $4,875.00 is invested at 5.8%, compounded quarterly. How much is in the account at the end of 9 years? P = 4,875 r = 5.8% = 0.058 n = 4 (for Quarterly) t=9 π π΄ = π(1 + π)ππ‘ = (4875)(1 + 0.058 (4)(9) ) 4 = 8,185.56 There will be $8,185.56 in the account. Page 20 7) Perform the operations indicated. (2π₯ + 3π¦ + π§ − 7) + (4π₯ − 2π¦ − π§ + 8) + (−3π₯ + π¦ − 2π§ − 4) → 2π₯ + 4π₯ − 3π₯ + 3π¦ − 2π¦ + π¦ + π§ − π§ − 2π§ − 7 + 8 − 4 → ππ + ππ − ππ − π 13) Perform the operations indicated. (π − π)(2π3 − ππ + 3π 2 ) → π(2π3 ) + π(−ππ) + π(3π 2 ) − π(2π3 ) − π(−ππ) − π(3π 2 ) → 2π3 − π2 π + 3ππ 2 − 2π3 π + ππ 2 − 3π 3 → πππ − πππ π − ππ π + ππππ − πππ 32) Perform the operations indicated. (4π₯ 2 − 5π¦)2 → (4π₯ 2 − 5π¦)(4π₯ 2 − 5π¦) → 4π₯ 2 (4π₯ 2 ) + 4π₯ 2 (−5π¦) − 5π¦(4π₯ 2 ) − 5π¦(−5π¦) → 16π₯ 4 − 20π₯ 2 π¦ − 20π₯ 2 π¦ + 25π¦ 2 → 16π₯ 4 − 40π₯ 2 π¦ + 25π¦ 2 40) Perform the operations indicated. (5π₯ + 2π¦ + 3)(5π₯ + 2π¦ − 3) 5π₯(5π₯) + 5π₯(2π¦) + 5π₯(−3) + 2π¦(5π₯) + 2π¦(2π¦) + 2π¦(−3) + 3(5π₯) + 3(2π¦) − 9 25π₯ 2 + 10π₯π¦ − 15π₯ + 10π₯π¦ + 4π¦ 2 − 6π¦ + 15π₯ + 6π¦ − 9 25π₯ 2 + 4π¦ 2 + 20π₯π¦ − 9