Variations

[匿名]

2010-05-13 2:04 am

1.The pressure of a fixed mass of gas varies directly as its absolute temperature and inversely as its volume

If P=100kPa when T=280K and V=0.035m3, find

i.the variation constant

ii.P when T=400K and V=0.032m3

2.The volume of cone varies jointly as the height and the square of radius .Find the percentage change in volume if the radius is increased by

20% and the height is decreased by 40%

3.To hold a tea party , the expenses are partly constant and partly very directly as the number of guests.When there are 50 guests, the expenses is$1850

When there are 150 guests, the expenses are$4350

i.Find the equation represent the relationship between the cost and the number of guests.

ii. Find the cost when there are 200 guests

iii.If there is a budget of $7000, what is maximum number of guests?

4.The expense of running a summer camp is partly varies as the duration and partly varies jointly as the number of students participated and the duration.

If the expense for 60 students for 3 days is $8700 and that for 40 students for 5 days is $10500

i. Express E in terms of n and d

ii.Calculate the expense for 120 students for 6 days

iii. If there are 100 students for 4 days, find the average expense for each student

5.The time taken in a manufacturing process of a product is partly constant and partly varies inversely as the number of workers .

Id 5 workers can finish the process in 39 hours, and 12 workers can finish the proess in 25 hours,

i. Express t in terms of n

ii.How long will it take for 15 workers to finish the process?

iii. If the process must be finished with 20 hours , how many workers are needed

thx~

回答 (1)

STEVIE-G™

2010-05-20 3:32 am

✔ 最佳答案

1i)
P=kT/V (where k is a constant)

P=100kPa when T=280K and V=0.035m3
100*10^3=k(280)/0.035
k=12.5

ii)
P=(12.5)(400)/0.032=156.25kPa

2)
Let h and r be the height and radius respectively
V=khr^2 (where k is a constant)
V'=k[(1-40%)*h][(1+20%)*r]^2
V'=k(0.6h)(1.2r)^2
V'=0.864V

Percentage decreased
=(V-0.864V)/V*100%
=13.6%

3i)
Let E and n be the expense and number of guests respectively
E=a+bn (where a and b are constants)
When there are 50 guests, the expenses is $1850
1850=a+50b...(1)
When there are 150 guests, the expenses are $4350
4350=a+150b...(2)

(2)-(1): b=25
Sub b=25 into (1), a=600
E=600+25n

ii)
E=600+25*200=$5600

iii)
7000=600+25n
n=256

4i)
E=ad+bdn (where a and b are constants)

the expense for 60 students for 3 days is $8700
8700=3a+60*3b
2900=a+180b...(1)

for 40 students for 5 days is $10500
10500=5a+40*5b
2100=a+200b...(2)

(1)-(2): b=-40
Sub b=200/3 into (1), a=10100
E=10100d-40dn

ii)
E=10100*6-40*120*6=$31800

iii)
E=10100*4-40*100*4=$24400
average exp.=24400/100=$244

5i)
t=a+b/n (where a and b are constants)

5 workers can finish the process in 39 hours
39=a+b/5...(1)

12 workers can finish the proess in 25 hours
25=a+b/12...(2)

(1)-(2): b=120
Sub b=120 into (1), a=15
t=15+120/n

ii)
t=15+120/15=23 hours

iii)
20=15+120/n
n=24

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