anonymous
  • anonymous
the kilopascal is a unit of measure for atmospheric pressure. suppose the atmospheric air pressure at sea level is about 103 kilopascals. for every 1000-m increase in altitude, the pressure decreases about 11.1%. what is the approximate pressure at an altitude of 3000m? .... Apparently the answer is 72, but how do I get 72?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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ganeshie8
  • ganeshie8
`pressure decreases by 11.1% for every 1000 m increase in altitude` that means, pressure drops to 100-11.1 = 88.9% for every 1 km increase in altitude, yes ?
ganeshie8
  • ganeshie8
what is 88.9% of 103 ?
anonymous
  • anonymous
where did you get 100 from?

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ganeshie8
  • ganeshie8
that is a very good question !
ganeshie8
  • ganeshie8
before answering that, let me ask you a small question
ganeshie8
  • ganeshie8
suppose there are 100 students in your class and 11 of them are wearing red dress. here is the question : how many students are "not" wearing red dress ?
anonymous
  • anonymous
89
ganeshie8
  • ganeshie8
Excellent!
ganeshie8
  • ganeshie8
cent means 100 percent means per 100
ganeshie8
  • ganeshie8
11% means 11 per every 100
asib1214
  • asib1214
or every 100
ganeshie8
  • ganeshie8
`pressure decreases by 11.1% for every 1000 m increase in altitude`
ganeshie8
  • ganeshie8
if 11.1% of pressure is lost, how much is still there ?
anonymous
  • anonymous
from 100 or 1000?
ganeshie8
  • ganeshie8
percent always refers to 100
anonymous
  • anonymous
88.9
ganeshie8
  • ganeshie8
So you do see that the pressure reduces to 88.9% for every 1000 m increase in altitude
ganeshie8
  • ganeshie8
Since the pressure is 103 at sea level, it should be 88.9% of 103 at a height of 1000m
ganeshie8
  • ganeshie8
what is 88.9% of 103 ?
anonymous
  • anonymous
9156.7? "of" means multiplication, right?
asib1214
  • asib1214
91.56
anonymous
  • anonymous
how did you get 91.56
asib1214
  • asib1214
88.9/100 X 103KPa
anonymous
  • anonymous
i multiplied 88.9 and 103 together, and i got 9156.7
ganeshie8
  • ganeshie8
"of" means "multiplication" yes
asib1214
  • asib1214
as ganshie said, it's 88.9% "percent" and percent means out of 100. or 88.9/100
ganeshie8
  • ganeshie8
but calculating percentages is a bit tricky, you need to think a bit... simply multiplying two numbers doesn't give you the percent
ganeshie8
  • ganeshie8
I suggest you watch this quick video first https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/percent-intro-pre-alg/v/finding-percentages-example
anonymous
  • anonymous
oh wait, isn't there the rule with moving the decimal two places to the.. right? or left? or maybe thats for something else
asib1214
  • asib1214
ganshie before you go....|dw:1450334114131:dw|
asib1214
  • asib1214
this is how i wanted to solw with one blow...idk if it's even close to write...LOL
ganeshie8
  • ganeshie8
that looks good, but we need to take the percent 3 times right ?
ganeshie8
  • ganeshie8
@jasconut yes... 88.9% of 103 is calculated as shown by asib earlier : 88.9/100 * 103 = ?
ganeshie8
  • ganeshie8
88.9% of 103 changes to 88.9/100 * 103
ganeshie8
  • ganeshie8
notice that we're replacing % by 1/100
anonymous
  • anonymous
ohhh
ganeshie8
  • ganeshie8
`pressure at sea level` : 103 `pressure at 1000m height` : 88.9/100 * 103 = ?
anonymous
  • anonymous
91.567
ganeshie8
  • ganeshie8
Good! lets climb 1000m more
ganeshie8
  • ganeshie8
`pressure at sea level` : 103 `pressure at 1000m height` : 88.9/100 * 103 = 91.567 `pressure at 2000m height` : 88.9/100 * 91.567 = ?
anonymous
  • anonymous
81.40
ganeshie8
  • ganeshie8
Awesome! you know what to do next ?
anonymous
  • anonymous
88.9/100*81.40, right?
ganeshie8
  • ganeshie8
Yes!
ganeshie8
  • ganeshie8
`pressure at sea level` : 103 `pressure at 1000m height` : 88.9/100 * 103 = 91.567 `pressure at 2000m height` : 88.9/100 * 91.567 = 81.4 `pressure at 3000m height` : 88.9/100 * 81.40 = ?
anonymous
  • anonymous
72.36
ganeshie8
  • ganeshie8
Yep! we could also do it at one shot : `pressure at 3000m height` = 103*(0.889)^3
asib1214
  • asib1214
ganshie before you go, could you please put it in mathematical form for me please?!?!?!?
anonymous
  • anonymous
72.36! Thank you so much! Especially doing it step by step for me, thank you
asib1214
  • asib1214
like in one equation....
ganeshie8
  • ganeshie8
np :) brace yourself, you took time to understand these and really you did great!
ganeshie8
  • ganeshie8
@asib1214 it is an exponential decay function right ?
asib1214
  • asib1214
yes :)
ganeshie8
  • ganeshie8
pressure at an altutude of \(h \) kilometers is given by : \[p(h) = 103\left(1 - \dfrac{11.1}{100}\right)^h\]
ganeshie8
  • ganeshie8
that should do right?
asib1214
  • asib1214
cuz initially i thought it's a linear trend, so you go up, 11.1% of 103 KPA drops...but no your right i did it on a piece of paere....Thanks I LOVE YOU!!
ganeshie8
  • ganeshie8
np :) most events in nature are exponential.... very rarely do you see linear growth/decay...
asib1214
  • asib1214
yah your right...Thank you so much!!1 MASTER :")

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