Mathematics Question Thread

[laurenf58]

For Question 2...

Thanks so much!

[RuiAce]

So far, i have a = 1000 x 1.09, r=1.09 and n=22

Not sure if i've got my numbers mixed up or if the textbook has the wrong answer!

Thanks!

[Thebarman]

Hey guys, I'm doing some catchup work right now and I'm struggling with the following questions. Any help would be appreciated.

1. Given log7(2) = 0.36 and log7(5) = 0.86, find log7(35) and log7(98).
The answers were 1.83 and 2.36, respectively.

[RuiAce]

Hey guys, I'm doing some catchup work right now and I'm struggling with the following questions. Any help would be appreciated.

1. Given log7(2) = 0.36 and log7(5) = 0.86, find log7(35) and log7(98).
The answers were 1.83 and 2.36, respectively.

The question (very horribly) made a typo in that log7(5) should be 0.83, not 0.86

[Thebarman]

I didn't even notice the mistake. I'm so sorry about that!

Do you mind also helping me with this question? Use log laws to evaluate log5(50) - log5(2).
There shouldn't be any errors this time 

[RuiAce]

I didn't even notice the mistake. I'm so sorry about that!

Do you mind also helping me with this question? Use log laws to evaluate log5(50) - log5(2).
There shouldn't be any errors this time 

[Thebarman]

Thanks again, this is finally starting to make sense.

Any chance you could also solve this? Find the volume of the solid formed when the curve y=e^(-x) + 1 is rotated about the x-axis from x=1 to x-2

[RuiAce]

Thanks again, this is finally starting to make sense.

Any chance you could also solve this? Find the volume of the solid formed when the curve y=e^(-x) + 1 is rotated about the x-axis from x=1 to x-2

Assuming a typo was made in "x-2"

[Thebarman]

Ah, when I first converted the equation to equal y^2, I had changed the entire equation, rather than just squaring the lot. I tried to integrate your answer from there as a whole, and I got ((e^-x +1)^3)/3. After subbing in the values, I'm still getting a negative answer (-0.37). Not sure where I'm going wrong

[RuiAce]

Ah, when I first converted the equation to equal y^2, I had changed the entire equation, rather than just squaring the lot. I tried to integrate your answer from there as a whole, and I got ((e^-x +1)^3)/3. After subbing in the values, I'm still getting a negative answer (-0.37). Not sure where I'm going wrong

[katnisschung]

Hey hey need help on 2 series questions! Id really appreciate if u could show full working Thanks
58. The limiting sum of the series
1-3t + 9t^2 - 27t^3 +.... is 2/3
Find the value of t

69. A pattern has been created that consists of a series of rectangles with a common centre. The first (innermost) rectangle is 4 units long and 2 units wide. The second rectangle is 2 units longer and 2 units wider than the first rectangle and every other rectangle is 2 units longer and 2 units wider than the previous one. The space between these rectangles is shaded.
The area inside the first rectangle,
A1 units is given by
A1= 4x2
=8
 
A2 is the area between the second and the third rectangle and so on.

A) show that An= 8n
B) find the first term and common difference of the arithmetic series formed by summing these areas

[RuiAce]

Hey hey need help on 2 series questions! Id really appreciate if u could show full working Thanks
58. The limiting sum of the series
1-3t + 9t^2 - 27t^3 +.... is 2/3
Find the value of t

Someone else will get to the second question if they're faster than me, but not too sure what the difficult part was here?

[jamonwindeyer]

69. A pattern has been created that consists of a series of rectangles with a common centre. The first (innermost) rectangle is 4 units long and 2 units wide. The second rectangle is 2 units longer and 2 units wider than the first rectangle and every other rectangle is 2 units longer and 2 units wider than the previous one. The space between these rectangles is shaded.
The area inside the first rectangle,
A1 units is given by
A1= 4x2
=8
 
A2 is the area between the second and the third rectangle and so on.

A) show that An= 8n
B) find the first term and common difference of the arithmetic series formed by summing these areas

Hey! So we know \(A1\), we get \(A2\) by subtracting the area of the smaller rectangle from the larger one (the area in between). So:



Similarly (notice the dimensions both jump by 2 each time):



So the series formed is \(8,16,24...\), which is given by \(A_n=8n\). By inspection, \(a=8\) and \(d=8\) hope it helps!

[phebsh]

Hey there, my teacher said that I should practice trial papers considering they are more difficult than HSC and that I should be aiming for 40% on my trial paper. However, my tutor said to stick to past HSC papers... What do you think?

[RuiAce]

Hey there, my teacher said that I should practice trial papers considering they are more difficult than HSC and that I should be aiming for 40% on my trial paper. However, my tutor said to stick to past HSC papers... What do you think?

I don't actually know why your tutor suggests this. I tutor as well and I agree with your teacher.

Unless your school writes their own past papers and they're literally questions stolen from HSC papers you should be doing trials. Trials best reflect the trials whereas the HSC past papers best reflects the HSC.

(If your school writes their own papers you should keep doing their's though. And if they use company papers you can always ask if they have past papers.)