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herothing
11-12-10, 18:42
I have a few maths questions which i can't do. Since the 'search' funcition has been disabled i'm creating a new thread for this, since i can't find the homework thread.
Pleae help me answer these questions with the working out, i don'tunderstand any of them.

1. Two Squares, each of a side length 1+ √2 units, overlap. The overlapping region is a regular octagon.
What is the area in square units.
A: 1+ √2 B: 1+ 2√2 C: 2+√2 D: 2+2√2 E: 2+3√2

2 A taxi firm needs a memorable phone number. They want a number which has a maximum of two differet digits. Their phne must start with the digit 3 and be 6 digits long. How many numbers are possible?

A: 288 B:280 C:279 D:226 E:225

3. Shahbaz thinks of an integer 'N', such that the difference beteen √N and7 is less than 1. How many possibilities are there for N?

A: 13 B: 14 C: 26 D: 27 E: 28


Thanks for your help guys :)

kthnxbai
11-12-10, 18:51
Ok, well for the first one you should try drawing it out, that usually helps.
In order for the overlap to form a regular octagon, the squares would be positioned at the same centre point, but with one rotated 45 degrees...

The second one, the phone number will have the general structure of 3333xx, where x is any number between 0 and 9... and then you can have any permutation of that number, with any amount of 3s or xs within 6 digits

And for the last one, if you want sqrtN to be within +- 1 of 7, you take the square of 6 and the square of 8, and those are your limits for N
well, is it less than or equal to? or strictly less than 1????
because if it's strictly less than 1, you need to discount the upper and lower bounds (so take 2 away from the answer you get)
I'm explaining that badly....

herothing
11-12-10, 18:56
I sort of understand how to do the first one, but still not getting the other 2 :p
And the question just say's 'less than 1'

kthnxbai
11-12-10, 19:01
Ok, well have you studied permutations and combinations at all??? cause that's what the second one is on...

Like I could do it for you, but that's not help...

Basically, say you have the letters A B and C... but you can have them in any order
So all the possible combinations of these letters are:
ABC
ACB
BAC
BCA
CAB
CBA

(I might be forgetting some, but you get the idea)
So, for the phone number, you want something like 3xxxxx
sorry, i got that wrong originally....
So, you have all the possible combinations of 3 and x to make 6 digits multiplied by 10 (due to the possible values for x)

tbh I might still have that wrong... the method is right, but you need to figure out what you need the number to be


http://www.mathsisfun.com/combinatorics/combinations-permutations.html
theres a bit more explaining combinations and permutations there....most scientific calculators have a function for calculating combs and perms
ok, so for the last one....

you want the difference of root N and 7 to be less than 1

So, you want the root of N to be between 6 and 8... so N can be anything from 6 squared (36) to the square of 8(64)... however, since you want it to be less than 1, you have to discount both 36 and 64... giving you 26 possible values

herothing
11-12-10, 19:25
Still not understanding that permutation and combination one :(
Also i have 1 more which needs doing, although it has a diagram.

4. The diagram shows a pattern of 8 equal shaded square inside a circle of area 'pi' square units. What is the area (in square units) of the shaded region?

A: 1 and 1/3 B: 1 and 3/5 C: 1 and 2/3 D: 1 and 7/9 E: 2

Heres the diagram, sorry for the low resolution.
http://i55.************/r7632e.jpg

By the way, these questions are part of a maths challenge i've been set to do, some of these things i havent learned yet...