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Algebraic manipulation (q8 2022 paper 1)

I think I am quite close to the answer but for some reason I just cant convert it to the right form, please someone helpIMG_4649.jpgScreenshot 2023-06-04 1.11.34 PM.png
(edited 1 year ago)

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Original post by leoishush
I think I am quite close to the answer but for some reason I just cant convert it to the right form, please someone help

Can't follow that at all - which part is this?
Original post by leoishush
I think I am quite close to the answer but for some reason I just cant convert it to the right form, please someone help


You're trying to find where dV/dt= 0. If you look at what you got when you differentiate and think about setting it to 0, it's natural to rewrite it as f(t) = g(t) for two fairly obvious functions f,g. Then think about how you can reduce one side to just be t.
(edited 1 year ago)
Original post by leoishush
I think I am quite close to the answer but for some reason I just cant convert it to the right form, please someone help


After your first two lines of working, you need to set dv/dt = 0, then rearrange to arrive at the given expression.
Reply 4
Original post by leoishush
I think I am quite close to the answer but for some reason I just cant convert it to the right form, please someone helpIMG_4649.jpgScreenshot 2023-06-04 1.11.34 PM.png

I can't follow what you've done, but when you get to the 2nd line (correct) I would advise setting that to 0 and multiplying by t+1 to clear the horrible fraction. Then rearrange from there.
Original post by davros
I can't follow what you've done, but when you get to the 2nd line (correct) I would advise setting that to 0 and multiplying by t+1 to clear the horrible fraction. Then rearrange from there.


Original post by leoishush
I think I am quite close to the answer but for some reason I just cant convert it to the right form, please someone helpIMG_4649.jpgScreenshot 2023-06-04 1.11.34 PM.png

Still need help?
Original post by mathsstudent222
let me know if u cant followit

Please observe the forum posting guidelines (sticky) - hints not full solutions - and remove your full solution.
Reply 7
Hi everyone thank you so much for your responses! I know a lot of you are confused as to what I have done after the second line. Here's what I did:
- 3rd line: divided everything by 0.4 ln (t+1)
- 4th line: factored out 0.5 in the fraction to get (25-t) in the numerator
- 5th line : cancelled out the 0.4

Many people have said to equal the equation to 0- I have already done that I just didn't make that obvious on the whiteboard (my bad)

This is for part b btw and I am really struggling to rearrange the equation for the required form
Reply 8
Original post by mathsstudent222
I posted solution but daddy moderator deleted it


ahhhhh oh well. I have seen the solution to it on youtube but I was wondering if I would get anywhere with the way I have done it ? I don't understand where I have went wrong
Original post by leoishush
ahhhhh oh well. I have seen the solution to it on youtube but I was wondering if I would get anywhere with the way I have done it ? I don't understand where I have went wrong


You're not necessarily wrong, but you have headed off in a slightly strange direction. What I would suggest is:

* Go back to line 2
* Start the line with "0 =" rather than just "="
* Concentrate on making "t" the subject of the equation
Original post by leoishush
ahhhhh oh well. I have seen the solution to it on youtube but I was wondering if I would get anywhere with the way I have done it ? I don't understand where I have went wrong


If I was doing it I would have worked back from the answer 1 step and tried to prove
(t+1) (1 + ln(t+1)) = 26

You dont seem to set dv/dt to zero. If you did youd get
0.4 ln(t+1) = (10 - 0.4t) / (t+1)
It should be straightforward to get the above answer by multiplying through and rearranging?
Original post by mqb2766
If I was doing it I would have worked back from the answer 1 step and tried to prove
(t+1) (1 + ln(t+1)) = 26

You dont seem to set dv/dt to zero. If you did youd get
0.4 ln(t+1) = (10 - 0.4t) / (t+1)
It should be straightforward to get the above answer by multiplying through and rearrangin

ahhhh right. I have now tried doing that but for some reason i am still not getting the right answer
(line 3 I cancelled out the 0.4, line 4 I swapped t+1and ln(t+1)IMG_4650.jpg
I would have multiplied through, but add zero = 1 - 1 to the numerator should get you about there?
Original post by mqb2766
I would have multiplied through, but add zero = 1 - 1 to the numerator should get you about there?


sorry i am confused
Original post by leoishush
sorry i am confused


Multiply through and add 1 - 1 to the right gives
(t+1) ln(t+1) = 26 - t - 1
....
Original post by mqb2766
Multiply through and add 1 - 1 to the right gives
(t+1) ln(t+1) = 26 - t - 1
....

for some reason I am still stuck with 25 in my working
Original post by leoishush
for some reason I am still stuck with 25 in my working


Multiply through you get
(t+1)ln(t+1) = 25 - t
you want 26, you also want a factor t+1 on the right. So add 0 = 1 - 1 to the right to get
(t+1)ln(t+1) = 25 + 1 - t - 1 = 26 - (t+1)
take the (t+1) on the right over, factorise and divide ...

For me there were a few ways to proceed but to rearrange the desired relationship as in the previous post, then notice that
10/0.4 = 25
and we needed 26 and an extra t+1 factor pretty much got it done.
(edited 1 year ago)
Original post by mqb2766
Multiply through you get
(t+1)ln(t+1) = 25 - t
you want 26, you also want a factor t+1 on the right. So add 0 = 1 - 1 to the right to get
(t+1)ln(t+1) = 25 + 1 - t - 1 = 26 - (t+1)
take the (t+1) on the right over, factorise and divide ...

For me there were a few ways to proceed but to rearrange the desired relationship as in the previous post, then notice that
10/0.4 = 25
and we needed 26 and an extra t+1 factor pretty much got it done.


ohhhhhhhh thank you so much!
Original post by leoishush
ohhhhhhhh thank you so much!


For questions like this, if necessary try and work back a step or two. As there was t on both sides of the desired relationship, for me it indicated that multiplying through back from the final solution and just think what bits you have and how to rearrange / factorise them was important before really putting pen to paper.
(edited 1 year ago)
Original post by mqb2766
For questions like this, if necessary try and work back a step or two. As there was t on both sides of the desired relationship, for me it indicated that multiplying through back from the final solution and just think what bits you have and how to rearrange / factorise them was important before really putting pen to paper.


Ok thank you!

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