Math 121
Assignment #1
Mr. Jacobs
Page 14
45)
Simplify
(3𝑚4 )3 (2𝑚−5 )4 → (33 𝑚12 )(24 𝑚−20 ) → (27)(16)(𝑚−8 ) → 432⁄ 8
𝑚
50)
Simplify
(
79)
125𝑝12 𝑞−14 𝑟 22
25𝑝8 𝑞 6 𝑟 −15
−4
)
25𝑝8 𝑞6 𝑟 −15
4
𝑞 20
4
→ (125𝑝12 𝑞−14 𝑟 22 ) → (5𝑝4 𝑟 37) →
𝑞 80⁄
625𝑝16 𝑟 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 𝐴𝑈 ′ 𝑠
1 𝐴𝑈
=
93,000,000 𝑚𝑖𝑙𝑒𝑠
𝑥 𝑚𝑖𝑙𝑒𝑠
→ 𝐶𝑟𝑜𝑠𝑠 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 → 1𝑥 = 39 × 93,000,000
3,627,000,000 𝑚𝑖𝑙𝑒𝑠 → 3.627 × 109 𝑚𝑖𝑙𝑒𝑠
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 𝐿𝑌
3.26 𝐿𝑌
5.88×1012 𝑚𝑖𝑙𝑒𝑠
= 𝑥 𝑚𝑖𝑙𝑒𝑠 → 𝐶𝑟𝑜𝑠𝑠 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑦 → 1𝑥 = 1.91688 × 1013 𝑚𝑖𝑙𝑒𝑠
1 𝑃𝑎𝑟𝑠𝑒𝑐 = 1.91688 × 1013 𝑚𝑖𝑙𝑒𝑠
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
𝑟
𝐴 = 𝑃(1 + 𝑛)𝑛𝑡 = (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
𝑟
𝐴 = 𝑃(1 + 𝑛)𝑛𝑡 = (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.
(2𝑥 + 3𝑦 + 𝑧 − 7) + (4𝑥 − 2𝑦 − 𝑧 + 8) + (−3𝑥 + 𝑦 − 2𝑧 − 4) →
2𝑥 + 4𝑥 − 3𝑥 + 3𝑦 − 2𝑦 + 𝑦 + 𝑧 − 𝑧 − 2𝑧 − 7 + 8 − 4 → 𝟑𝒙 + 𝟐𝒚 − 𝟐𝒛 − 𝟑
13)
Perform the operations indicated.
(𝑎 − 𝑏)(2𝑎3 − 𝑎𝑏 + 3𝑏 2 ) →
𝑎(2𝑎3 ) + 𝑎(−𝑎𝑏) + 𝑎(3𝑏 2 ) − 𝑏(2𝑎3 ) − 𝑏(−𝑎𝑏) − 𝑏(3𝑏 2 ) →
2𝑎3 − 𝑎2 𝑏 + 3𝑎𝑏 2 − 2𝑎3 𝑏 + 𝑎𝑏 2 − 3𝑏 3 → 𝟐𝒂𝟑 − 𝟐𝒂𝟑 𝒃 − 𝒂𝟐 𝒃 + 𝟒𝒂𝒃𝟐 − 𝟑𝒃𝟑
32)
Perform the operations indicated.
(4𝑥 2 − 5𝑦)2 → (4𝑥 2 − 5𝑦)(4𝑥 2 − 5𝑦) →
4𝑥 2 (4𝑥 2 ) + 4𝑥 2 (−5𝑦) − 5𝑦(4𝑥 2 ) − 5𝑦(−5𝑦) → 16𝑥 4 − 20𝑥 2 𝑦 − 20𝑥 2 𝑦 + 25𝑦 2 →
16𝑥 4 − 40𝑥 2 𝑦 + 25𝑦 2
40)
Perform the operations indicated.
(5𝑥 + 2𝑦 + 3)(5𝑥 + 2𝑦 − 3)
5𝑥(5𝑥) + 5𝑥(2𝑦) + 5𝑥(−3) + 2𝑦(5𝑥) + 2𝑦(2𝑦) + 2𝑦(−3) + 3(5𝑥) + 3(2𝑦) − 9
25𝑥 2 + 10𝑥𝑦 − 15𝑥 + 10𝑥𝑦 + 4𝑦 2 − 6𝑦 + 15𝑥 + 6𝑦 − 9
25𝑥 2 + 4𝑦 2 + 20𝑥𝑦 − 9