quick check needed (1 Viewer)

[lyounamu]

I am doing some past papers that don't have the solution so I am not sure if I am correct or not.

The letters of the word Circular are printed on separate cards.

1. how many arrangements are possible in a straight line
2. how many arrangements are possible in a circle
3. how many arranges are possible with Cs NOT TOGETHER in a circle

I got 8!/2!2! = 10080, 7!/2!2! = 1260 and 1260 - 6!/2! = 900.

 

[vds700]

I am doing some past papers that don't have the solution so I am not sure if I am correct or not.

The letters of the word Circular are printed on separate cards.

1. how many arrangements are possible in a straight line
2. how many arrangements are possible in a circle
3. how many arranges are possible with Cs NOT TOGETHER in a circle

I got 8!/2!2! = 10080, 7!/2!2! = 1260 and 1260 - 6!/2! = 900.

I thik the first 2 are correct, but with the 3rd one, shouldn't u times the top by 2!, because the 2 C's are together, u can switch them around

Dunno, might be wrong, i suck at perms and combs.

 

[FOB all the way]

i really suck at this but this is how i would think about it
first seat = 1 (put a C here)
second seat = 6 (as the second C can not go there)
third seat = 6 (six letters remaining)
fourth seat = 5
.
.
final seat =1
= 4320 then divide this by 2!2! (as you can switch the C's and R's around)
and you get
1080

but i really suck at these so they are most lickly wrong
please dont crucifi me if they are wrong

 

[hon1hon2hon3]

The first two looks right to me, and for the third one . . . i think it should be the total arrangement minus the total arranagement of Cs TOGETHER, soo u get totally arranagement of Cs not together . . . should thing like 7! - 6!/2! ? something like 4680 i think . .

 

[lyounamu]

The first two looks right to me, and for the third one . . . i think it should be the total arrangement minus the total arranagement of Cs TOGETHER, soo u get totally arranagement of Cs not together . . . should thing like 7! - 6!/2! ? something like 4680 i think . .

If you said the first two look right, why did you just make a contradictory statment there (another highlighted part)?

For the third part, you are referring to the 2nd part. Since the 2nd part is the total number, I just substracted the chance of getting 2 Cs together from that total.

I thik the first 2 are correct, but with the 3rd one, shouldn't u times the top by 2!, because the 2 C's are together, u can switch them around

Dunno, might be wrong, i suck at perms and combs.

Nah, they are same. So it doesn't make any difference as they are exactly same. Combination of CC is equal to another combination of CC.

 

[lyounamu]

I have another question.

What happens if the inverse function and the normal function are exactly same? What are the geometrical significance of that? I just said that they are symmetrical about the y=x. Is there anything more to say?

 

[FOB all the way]

i thouth the only way that the inverse could be the same as the normal only if the inverse was not a function
would you please be able to give an example of where this event occurs

 

[lyounamu]

example:

y = (2x-2)/(x-2)

If you look at the inverse, it will be same as well.

But the domain and range are definitely different for both.

 

[bored of sc]

example:

y = (2x-2)/(x-2)

If you look at the inverse, it will be same as well.

But the domain and range are definitely different for both.

I'll have a go.

With y = (2x-2)/(x-2) domain is all real x except 2, range is all y.

With y = (x-2)/(2x-2) domain is all real x except 1, range is all y.

Am I even remotely on the right track?

 

[shaon0]

I'll have a go.

With y = (2x-2)/(x-2) domain is all real x except 2, range is all y.

With y = (x-2)/(2x-2) domain is all real x except 1, range is all y.

Am I even remotely on the right track?

I think it is.
(x+x-2)/(x-2)
=x/(x-2) + 1
and i think you can get it from there.

 

[lyounamu]

I think it is.
(x+x-2)/(x-2)
=x/(x-2) + 1
and i think you can get it from there.

well, why did you do that? You just made it more complicated. You could just leave the inverse as:

(2x-2)/(x-2) meaning that the inverse and the normal functions are same.

 

[lyounamu]

ok, another questin:

An employer wishes to choose two people for the job. There are 8 applicants where 5 are women and 3 are men.

i) If each applicant is interviewed separately with women being interviewed before any men, find out how many ways this interview can be carried out.

For this question, I just went: 3! x 5! = 720. Please comment on this if you think it is wrong.

ii) If employer chooses two people, what's the probability that at least one of them is a woman.

For this question, I just went: (5C2 x 2C0 + 5C1 x 2C1)/8C2 = 5/7

It will be great if you could say whether you think I am wrong or right. If I am wrong, please provide some working out.

Thanks in advance.

 

[FOB all the way]

looks right to me

 

[lyounamu]

Triangle PQR is an isoceles triangle where PQ = PR = 6 and angle RPQ = @

If the area of PQR increases at the rate of 3 cm^2 per second, determine the rate at which angle RPQ is changing at the instant when the area of triangle PQR is 9 cm^2

Can anyone check if I am right?

Here is my working out too:

A = (6 x 6 x sin @)/2 = 18sin@
dA/d@ = 18cos@
so d@/dA = 1/18cos@

When A = 9, sin@ = 1/2, therefore, @ = pi/6

d@/dt = dA/dt . d@/dA = 3 x 1/18cos@
= 1/6cos@
Sub @ = pi/6 in, so you get:

d@/dt = 0.192450089...

 

[duy.le]

or more exactly sqrt3 / 9

dont leave your answer in approximate form, show that u rely too greatly on your calculator.

 

[lyounamu]

or more exactly sqrt3 / 9

dont leave your answer in approximate form, show that u rely too greatly on your calculator.

Thanks for the tip.

 

[2S1D3]

Triangle PQR is an isoceles triangle where PQ = PR = 6 and angle RPQ = @

If the area of PQR increases at the rate of 3 cm^2 per second, determine the rate at which angle RPQ is changing at the instant when the area of triangle PQR is 9 cm^2

Can anyone check if I am right?

Here is my working out too:

A = (6 x 6 x sin @)/2 = 18sin@
dA/d@ = 18cos@
so d@/dA = 1/18cos@

When A = 9, sin@ = 1/2, therefore, @ = pi/6

d@/dt = dA/dt . d@/dA = 3 x 1/18cos@
= 1/6cos@
Sub @ = pi/6 in, so you get:

d@/dt = 0.192450089...

I had the same exact question in my trials,and yea that does look right, but if the question doesn't say round off to 2 dec. pl. then don't do what you've done, they took marks off in my trials cause I did that