Maths

Divanhot SG · 2009-05-30T11:54:48+00:00

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Divanhot SG

The numbers from 1 to 49 are arranged in a table shown below.

FireIce SG

table lehhh?

Divanhot SG

Column

1 2 3 4 5 6 7
1 1 2 3 4 5 6 7
2 8 9 10 11 12 13 14
3 15 16 17 18 19 20 21 Rows 4 22 23 24 25 26 27 28
5 29 30 31 32 33 34 35
6 36 37 38 39 40 41 42
7 43 44 45 46 47 48 49

N X

M

(a) find the sum of the 7 numbers in the shaded BOLD diagonal.

(b) express x in terms of n where x is the number in the nth row and 1st column.

(d) express the sum S of the 7 numbers in terms of m and n.

(e) if S=714, find the value of n.

Forbiddensinner SG

table lehhh?

He is new here, give him sometime.

And to TS, what is the question?

Divanhot SG

hi all pls click on the link to get the photo image of the question just taken, the questions are as below (a) to (e) as reposted by moderator eagle(thanks! bro)

much help kindly appreciated. i'm not good at guessing number patterns, any tips? :>

eagle SG

Repost:

The numbers from 1 to 49 are arranged in a table shown below.

(a) find the sum of the 7 numbers in the shaded BOLD diagonal.

(b) express x in terms of n where x is the number in the nth row and 1st column.

(d) express the sum S of the 7 numbers in terms of m and n.

(e) if S=714, find the value of n.

Forbiddensinner SG

Repost:

The numbers from 1 to 49 are arranged in a table shown below.

(a) find the sum of the 7 numbers in the shaded BOLD diagonal.

(b) express x in terms of n where x is the number in the nth row and 1st column.

(d) express the sum S of the 7 numbers in terms of m and n.

(e) if S=714, find the value of n.

Don't just repost, help to solve!

Currently stuck at (d), need some sweets to get my brain moving again.

(a) 175

(b) x = 1 + 7 (n-1)

eagle SG

busy writing some summary notes for solving common potentiometer questions in H2 Physics la

You sure can do one, jiayou

dkcx SG

Stuck at d as well...

Divanhot SG

hey bro forbiddensinner, thanks for yr reply.

was thinking it will be great how you can derive the formula for (b) and (c)

Forbiddensinner SG

hey bro forbiddensinner, thanks for yr reply.

was thinking it will be great how you can derive the formula for (b) and (c)

For ( b ) and ( c ), it is mostly just observation-based.

The 1st thing you will have to notice is that the numbers are plus 7 as it move down the row.

Since the 1st no. in column 1 is 1, we take it as a base constant, and then we add 7 ( n - 1 ), where n is the row, to it. The same goes for each and every column.

eagle SG

Stuck at d as well...

Ok, I chu ma

actually can just express in terms of m

Sum of 7 numbers = (m-24) + (m-16) + (m-8) + m + (m+8) + (m+16) + (m+24) = 7m

And then using this, can solve for e

Divanhot SG

Here's another question b4 i go sleep:

Susan stands at edge of cliff, throws a ball upwards. The height of ball above top of cliff in h metres is

h= 8t-5t^2

Q: Susan throws 2nd ball, in exactly same way, 4s after she throws the 1st .

Find how far apart the 2 balls are, 1s after the 2nd ball is thrown.

Forbiddensinner SG

Ok, I chu ma

actually can just express in terms of m

Sum of 7 numbers = (m-24) + (m-16) + (m-8) + m + (m+8) + (m+16) + (m+24) = 7m

And then using this, can solve for e

I got something like summation of m + n - 4 from 1 to 7.

Any ideas on how to simplfy it?

eagle SG

I got something like summation of m + n - 4 from 1 to 7.

Any ideas on how to simplfy it?

no need so chim ma

the number m is at the centre of the 7 numbers

so is 7m lor

So if express in terms of n, then sum will be using part c's answer
Sum = 7 (4 + 7 (n-1))

so part e will be
714 = 7 (4 + 7 (n-1))
4 + 7n - 7 = 102
n = 15

Forbiddensinner SG

Here's another question b4 i go sleep:

Susan stands at edge of cliff, throws a ball upwards. The height of ball above top of cliff in h metres is

h= 8t-5t^2

Q: Susan throws 2nd ball, in exactly same way, 4s after she throws the 1st .

Find how far apart the 2 balls are, 1s after the 2nd ball is thrown.

height of 1st ball = 8(5) - 5(5)^2 = 40 - 125 = -85m, meaning it is 85m below cliff.

height of 2nd ball = 8(1) - 5(1)^2 = 8 - 5 = 3m, meaning it is 3m above cliff.

distance apart = 85m + 3m = 88m

Forbiddensinner SG

no need so chim ma

the number m is at the centre of the 7 numbers

so is 7m lor

So if express in terms of n, then sum will be using part c's answer
Sum = 7 (4 + 7 (n-1))

so part e will be
714 = 7 (4 + 7 (n-1))
4 + 7n - 7 = 102
n = 15

Thanks to you, I see the light.

But the question is quite misleading.

What they want is an expression in S and m, followed by another in S and n.

Divanhot SG

hi, wonder how come for part (d), we can use 25 as base reference point. m is not equal to 25 right? they r only in same column 4

eagle SG

hey bro eagle, i dun understand answer to part (d)

how u get S= 7m. can u illustrate examples to show this, thanks

Here it is :D

Sum of 7 numbers = (m-24) + (m-16) + (m-8) + m + (m+8) + (m+16) + (m+24) = 7m

Try and see the pattern

Hint: In your table, m = 25

Divanhot SG

hi bro eagle, i dun understand how we can assume m=25, cuz i thought m is a number in the 4 column but in nth row.

i can c if we use 25 as base reference, we get S=7m= 7*25=175