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simple mat 177 queastions, plz show every step of each queastions clearly, thanks
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Explanation & Answer
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1. Scientific Notation and Percent. (Based on the ideas in Objective 1 and Objective 4.) (6
points)
Two percent of Jennie’s skin cells were burned when she escaped from a fire. If 3.7 × 1010 of
her skin cells were burned then, how many skin cells were not burned?
Sol: Let x be the total number of skin cells.
As given that 2% of total skin cells are burnt skin cells which are, 3.7 × 1010 . So,
2% 𝑜𝑓 𝑥 = 3.7 × 1010
2
(𝑥) = 3.7 × 1010
100
2𝑥 = 3.7 × 1010 × 100
2𝑥 = 3.7 × 1010+2
2𝑥 = 3.7 × 1012
3.7 × 1012
𝑥=
2
𝑥=
3.7
× 1012
2
𝑥 = 1.85 × 1012
The total number of skin cells is 1.85 × 1012 . Now the number of skin cells that are not burnt
is
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑜𝑡 𝑏𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠 = 𝑇𝑜𝑡𝑎𝑙 − 𝐵𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑜𝑡 𝑏𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠 = 1.85 × 1012 − 3.7 × 1010
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑛𝑜𝑡 𝑏𝑢𝑟𝑛𝑡 𝑐𝑒𝑙𝑙𝑠 = 1.813 × 1012
Hence.
2. Solving for a variable in terms of other variables. (From Objective 4.)
A. [4 pts] The equation for the future value of a simple interest investment is given by the
equation 𝐴 = 𝑃 + 𝑃𝑟𝑡. Solve this equation for P, which is the amount of principal (initial
investment) needed.
Sol: Given
𝐴 = 𝑃 + 𝑃𝑟𝑡
Taking P common, we get
𝐴 = 𝑃(1 + 𝑟𝑡)
Now dividing both sides by (1 + 𝑟𝑡), we get
𝐴
𝑃(1 + 𝑟𝑡)
=
(1 + 𝑟𝑡)
(1 + 𝑟𝑡)
𝐴
=𝑃
(1 + 𝑟𝑡)
𝑃=
𝐴
(1 + 𝑟𝑡)
Or
𝑃 = 𝐴(1 + 𝑟𝑡)−1
Hence.
B. [4 pts] The pressure, temperature, and volume of an ideal gas are related by the equation
𝑅=
𝑃𝑉
𝑛𝑇
. Solve this equation for T, which is the temperature in degrees Kelvin.
Sol: Given
𝑅=
𝑃𝑉
𝑛𝑇
Multiplying both sides by T, we get
𝑅×𝑇 =
𝑃𝑉
×𝑇
𝑛𝑇
𝑅𝑇 =
𝑃𝑉
𝑛
Now dividing by R on both sides, we get
𝑃𝑉
𝑅𝑇
= 𝑛
𝑅
𝑅
𝑇=
Hence.
𝑃𝑉
𝑛𝑅
3. (Based on ideas in Objective 2.) 6 points
Xavier and Yifei have been married for exactly 37 years. Yifei is four years older than...