Mathematics Question Thread

[RuiAce]

Thanks heaps,
THe question was: acceleration of a particle is given by x:=4sin2t. Initially particle is 1m to left of origin and has a velocity of 2m/s. Find the distance travelled in the first 4 seconds.

Are you sure there isn't a minus sign missing? Because the question is uglier but easier without it.

[anotherworld2b]

I hope I am in the right thread this time

I had a feeling that I did the question wrong because I was confused about how to find delta x
I believe I interpreted the responses to my question incorrectly.
I thought that when you are given information about the question having 4 strips/trapeziums/subsections n  becomes 4 +1 when you want to find delta x. Or is n simply 4?
So I assumed to find delta x I had to divide by 5.

I will post future questions in the mathematics (2U) thread. I'm not quite sure how I migrated to this thread

[Opengangs]

I hope I am in the right thread this time

I had a feeling that I did the question wrong because I was confused about how to find delta x
I believe I interpreted the responses to my question incorrectly.
I thought that when you are given information about the question having 4 strips/trapeziums/subsections n  becomes 4 +1 when you want to find delta x. Or is n simply 4?
So I assumed to find delta x I had to divide by 5.

I will post future questions in the mathematics (2U) thread. I'm not quite sure how I migrated to this thread

I answered in the 3U section, but for everyone's sake, I'll answer it again.
When we say "number of subsections or strips", we are merely talking about the interval between the two ending function values. For n strips, there will be n + 1 function values. However, both Simpson's rule and Trapezoidal Rule merely want the interval between two such function values, which is denoted as the sum of the two end points divided by the number of subsections or strips or applications.

This tells us the relative position between two function values, which is the interval they are after.
So, if they ask four function values between 0 and 9, they simply want the change in x (delta x) to be: (0 + 9)/3, since for there to be four such function values, there are only three strips.

[pikachu975]

Hi

How would the graph e^sinx be graphed, with stat points and an indication of what the value is when x = 0, pi, and 2pi?

Should be doable in 2 unit with knowledge of stationary points. Find their nature, find x and y intercepts and plot the points at 0, pi and 2pi then sketch.

[anotherworld2b]

Can I have help with this question please?
I'm not sure what to do

[RuiAce]

Can I have help with this question please?
I'm not sure what to do

What you wrote out so far is correct. Now, replace \(x_0, x_1, \dots, x_4\) with \(0, \frac\pi4, \dots, \pi\) as specified.

[anotherworld2b]

I see
I was wondering for this question what [O;5] is. Does that mean the upper limit is five and the lower limit 0?

What you wrote out so far is correct. Now, replace \(x_0, x_1, \dots, x_4\) with \(0, \frac\pi4, \dots, \pi\) as specified.

[jakesilove]

I see
I was wondering for this question what [O;5] is. Does that mean the upper limit is five and the lower limit 0?

Yep, it does!

[Jenny_trn]

Hi, currently stuck on this question!
1. Why isn't the y=3 included in the volume function thing . like V= pie integral [3 - log2x] (as shown in the question?)
2. also when you re-arrange y= log2x, in terms of x, when you square it, what are the steps to reach the final answer --> e^yln4 as shown?

[RuiAce]

Hi, currently stuck on this question!
1. Why isn't the y=3 included in the volume function thing . like V= pie integral [3 - log2x] (as shown in the question?)
2. also when you re-arrange y= log2x, in terms of x, when you square it, what are the steps to reach the final answer --> e^yln4 as shown?

1 - Is unnecessary, as your rotation means that you're integrating with respect to \(y\) and not \(x\). Also note that the \(y=3\) actually appears as the upper boundary of your integral: \(V=\pi\int_0^{\boxed{\textbf{3}}}...\). Of course, if we rotated about the x-axis then we'd have \( V=\pi \int_1^{\log_2 3}(3-\log_2 x)^2\,dx \)

[Jenny_trn]

Hi!
stuck on part ii) of this question
answer to part i) was (square root n + 1) - ( square root n)

I'm not sure how part i is used to find out the value of the sum from part i)
Thanks in advance!

[RuiAce]

Hi!
stuck on part ii) of this question
answer to part i) was (square root n + 1) - ( square root n)

I'm not sure how part i is used to find out the value of the sum from part i)
Thanks in advance!

[anotherworld2b]

Hi I attempted to do a question using the trapezoidal rule. I was wondering if someone could check my working please.
I also had a question about whether or not my answer 18.9 (using trapezoidal rule) would be considered off? I used my class pad and the answer was 19.63?

[jamonwindeyer]

Hi I attempted to do a question using the trapezoidal rule. I was wondering if someone could check my working please.
I also had a question about whether or not my answer 18.9 (using trapezoidal rule) would be considered off? I used my class pad and the answer was 19.63?

Looks good to me assuming there is no calculator error! Your answer is within 5% of the actual, that's a good estimate!

[anotherworld2b]

oh okay
I thought the answer had to be exact :3
I was wondering why do you need 'n' to be even to use Simpson's rule? Why can't n be odd like in the trapezoidal rule?

Looks good to me assuming there is no calculator error! Your answer is within 5% of the actual, that's a good estimate!