3u Mathematics Marathon V 1.1 (2 Viewers)

[onebytwo]

next question:
cant find any tough ones, so.....
water is flowing into an inverted cone of base radius 3cm and perpendicular height 7cm, at a rate of 21cm³/s. find the rate at which the surface are of the water is increasing when the depth of the water is 6cm.

 

[BIRUNI]

question: all the letters of the word FACETIOUS are arranged in a line, find the total number of arrangement that contain all the vowels in the order AEIOU but not necessarily together?

Answer:

_ A _ E _ I _ O _ U _

as you can see there are 6 _s

so the first consonant can go in any of the 6 places, the second go to any 7 places, the third consonants go to any 8 places, the forth consonant can go to any 9 places

hence the total number of arrangements is 6.7.8.9=9p4=3024

 

[webby234]

Answer:

_ A _ E _ I _ O _ U _

as you can see there are 6 _s

so the first consonant can go in any of the 6 places, the second go to any 7 places, the third consonants go to any 8 places, the forth consonant can go to any 9 places

hence the total number of arrangements is 6.7.8.9=9p4=3024

Yeah - that was effectively my reasoning. onebytwo's approach was probably quicker.

 

[Lukas1]

Hi everyone - try this one,

"What is the volume generated when the are under y=e^((-x)^2) [e to the (minus x squared)] between x=0 and x=1 is rotated about the y axis?

 

[onebytwo]

that was in some past 4 unit test, but was from 0 to 2