You are not logged in.
Pages: 1
thank you very much, this helped a lot.
but for question 2, i understand how the shapes are pentagon and hexagon, but i'm struggling to find how many of each type there is.
the answers at the back of the book give the following
1.
i) 60
ii) 20{3}+12{5}
2.
i)/ii) 12 pentagons and 30 hexagons
iii) 80V 120E
if possible, i would like to know how can i get to these answers please.
I was reading through an old math book, and at the end of the chapter about Euler's formula (V-E+F=2) there was a Mini Challenge. If anyone could help me solve it it would be much appreciated.
1) A rhombic triacontahedron is a polyhedron with 30 congruent faces which are rhombuses, and 2 types of vertices. At vertice type 1, 3 rhombuses meet and the angles are all obtuse. At vertice type 2, 5 rhombuses meet and the angles are all acute.
i) How many edges are there and
ii) How many vertices of each type?
2) A new semi-regular polyhedron is formed by suitably truncating all the vertices of type 2 of the rhombic triacontahedron. In this case all the vertices have the same number of edges meeting at them but there are two types of faces.
i) Describe the types of faces
ii) How how many of each type there are
iii) Give the number of vertices and edges.
Help would be very much appreciated.
Thank you.
after a few pages of scribbling(aka. used a calculator) i think i've got it:
f(5)=2349
f(20)=308489
f(99)=44357941
is this right?
thank you for the reply but i reworded the question slightly, the original question was simply asking for f(5), f(20) and f(99), it doesn't ask for a general formula, i just thought it might have been easier to work out. looks like i was wrong...
given when:
x=1, f(x)=5
x=2, f(x)=35
x=3, f(x)=245
x=4, f(x)=921
express f(x) in terms of x.
i am extremly sorry for this, i did not realize this was from a competition. (I live in Peru) my friend from the UK sent me these problems and asked me to see if i can do them, when i realized i had no idea how to do them, i thought it was a bit embarrasing and asked for help here. i have not sent any of the answers back so he won't be getting an unfair advantage.
again, very sorry for this
mathsyperson: thank you very much, i think i get it now
but can anyone help me out with 3 and 4? i got a hint from my friend for 3, it's: ((x^n)-(y^n)) = (x-y)(x^(n-1)+....+y^(n-1))
i've got no idea what that formula means unfortunately
as for 4, i've got no idea as to even how to approach that question....
thank you very much, but does anyone have any more insight on 3, 4, and 5?
1. Show that if a rectangle, which is twice as long as it is broad, can fit diagonally into a square, then it can also fit into the square with its sides parallel to the sides of the square. Also, prove this is not true if the rectangle is three times as long as it is wide.
2. A queue of slow moving traffic is 5 miles long. It takes 15 minutes to pass a particular road sign. A police car takes a total of 20 minutes driving at constant speed to travel from the back of the queue to the front and return to the back. How fast does the police car travel?
3. In 1946, an American numerologist, Prof. W, predicted the downfall of the USA in the year 2141 based on what he called a profound mathematical discovery depending on the following expression:
1492^n - 1770^n - 1863^n + 2141^n
He spent many months calculating the value of this for n = 1, 2, 3 and so on up to 1945 and found the remarkable fact that the result was always divisible by 1946. Since the years 1492, 1770 and 1863 are all important in American history, he claimed that 2141 would also be significant - hence his prediction.
Show how he could have saved himself months of work.
4. A circle of radius 15cm intersects another circle of radius 20cm at right angles. What is the difference of the areas of the non-overlapping portions? Hence, what is the sum of the areas of the non-overlapping portions?
5. Show that the square of any interger leaves a remainder of 0, 1, 4, or 7 when divided by 9.
Use this to establish the following condition that a number which is a perfect square must satisfy the following:
for a number that is a perfect square, add up its digits to form a second number. If that number has more than one digit, add up its digits to form a third number. Continue until you obtain a single digit number. That final number must be 1, 4, 7 or 9.
Quick responses will be appreciated.
I don't quite understand how u got that.
This was in my maths exam today, I just counldn't get it...
A cyclist and a runner start off simultaneously around a racetrack each going at a constant speed in the same direction. The cyclist completes one lap and then catches up with the runner. Instantly the cyclist turns around and heads back at the same speed to the starting point where he meets the runner who has just finished his first lap. Find the ratio of their speeds.
Please help...
Pages: 1