數學問題 20點急用

2013-11-26 2:48 am

1(a) A cube measures 2cm x 2cm x 2cm is dropped into a cylindrical jar of internal radius 4cm. the original water level is 6cm . find the new water level?

1(b)if the height of the cylindrical jar is 7cm, how many cubes can be dropped into the jar that no water will be spilled off?

2.if 5,x,y,320 are in geometric progression,find x and y

3.the expenditure ($E) of holding a birthday party is partly constant and partly varies directly as the number of guests (n). for 50 guests, the expenditure is $1450, and
for 70 guests,the expenditure is $1790

(a)Express E in terms of 'n'
(b)find the expenditure per head when 100 guests join the party.

4.solve 6x^2+11x-35<0

回答 (1)

用戶40008

2013-11-26 3:23 am

✔ 最佳答案

1a) volume of cube=2 x 2 x 2 cm^3
=8 cm^3
let the increased water level be h
h * pi * 4^2 = 8
h = 1/2 / pi

so the new water level is 6+0.5/pi

1b) let the no of cubes be n
0.5/pi * n <= 1
n <= 2pi
n<= 9.8...
so the no of cubes is 9

2. x/5=y/x
x^2=5y..........(1)
y/x=320/y
y^2=320x ..............(2)
put (1) into (2)
(x^2/5)^2=320x
x^4/25=320x
x^3=8000
x=20
so y=80

3a) E=C+kn
when E=1450, n=50
1450=C+50k .........(1)
when E=1790, n=70
1790=C+70k ..........(2)
(2)-(1)
240=20k
k=12
put k into (1)
1450=C+600
C=850
so E=850+12n

3b) E=850+12(100)
=2050

4. 6x^2+11x-35=0
(3x-5)(2x+7)=0
x=5/3 or -7/2

👍 0 👎 0