Mathematics Question Thread

[S200]

isn't the distance \(\sqrt {(p^2,q^2))}\)?

[RuiAce]

isn't the distance \(\sqrt {(p^2,q^2))}\)?

What you mean by the square root of a point?

This seems like a really simple mc question but I keep getting the wrong answer: What is the distance from the point (p,q) to the line px+qy=0, could anyone help me out? (:

[Calley123]

Please help! Loan repayments under series and sequence. How do I take the 3 months of no interest into consideration?

[S200]

What you mean by the square root of a point?

Sorry, I was a little gone when I posted that. I meant \(\sqrt{p^2+q^2}\) (from distance between two points, (0,0) and (p,q))...

Please help! Loan repayments under series and sequence. How do I take the 3 months of no interest into consideration?

Could you attach the question instead of (or as well as) the answer?

[jamonwindeyer]

Please help! Loan repayments under series and sequence. How do I take the 3 months of no interest into consideration?

At a guess (as S200 says, the question might be helpful!) but I think all you would do is just take the monthly repayments off without adding any interest for the first three months of your derivation! So:



Or something similar

[kauac]

Hi, would love some working out for this question (sample answer seems to skip a few steps).

HSC 2013 13 d) iii:

After 20 years the family borrows an extra amount, so that the family
then owes a total of $370 000. The monthly repayment remains $2998,
and the interest rate remains the same.
How long will it take to repay the $370 000?

Thanks!

[lexi24216]

Hi, I am having trouble with this question........
If y = a^x  find dy/dx when x=1:
Solution says:

When x=1;
In step 2, I don’t understand why lna was placed in front of a^x
Thanks

[fun_jirachi]

Hi, would love some working out for this question (sample answer seems to skip a few steps).

HSC 2013 13 d) iii:

After 20 years the family borrows an extra amount, so that the family
then owes a total of $370 000. The monthly repayment remains $2998,
and the interest rate remains the same.
How long will it take to repay the $370 000?

Thanks!

Yessssss this thread is alive again!!!!

Ok so, essentially you're looking at 370000 being your new starting amount ie. P, and you're already given M as 2998 and r as 1.005. Since you want to know how long it takes to repay the whole thing, you set up the equation to be equal to zero, and your only variable left to find is n, the number of years, and that's what you want.



Just manipulate the equation, moving the 2998 by whatever to the right side, and go from there to get to:

And from there you manipulate again to get:

Use your log laws, and you should get the 192.46. Round it up, as they won't have finished in 192 months, and you have your answer.

Hope this helps!

EDIT: just saw the new question, gonna edit the solution in so i don't double post
The thing is, when you differentiate an exponential, the derivative is only the same as the original function if the base of the exponential is e. In this case, it isn't and its an arbritary constant a.
So basically you convert it to base e like so:

Using log laws, so you get to:

and then differentiating the expontential like usual, bring down the constant in the power, in this case lna, then keeping the top, which is
, as established and you get your derivative of
and yeah just sub in 1 at the end to get your answer

[kauac]

For motion questions in app. of calculus:

Is there a set method to solving questions like 'find the distance the particle travels in x seconds' ?

[S200]

Does area under the graph work?

For the graph f(x)=displacement of x

[kauac]

Does area under the graph work?

For the graph f(x)=displacement of x

Sometimes it seems to work, other times, it doesn't?

[S200]

If \(f(x)\)=displacement, \(f^{\prime}(x)\)=velocity. You could get the final velocity add all of the velocities before?
Gotta be a shorter way though.

Sometimes it seems to work, other times, it doesn't?

When doesn't it work?

[RuiAce]

If \(f(x)\)=displacement, \(f^{\prime}(x)\)=velocity. You could get the final velocity add all of the velocities before?
Gotta be a shorter way though.
When doesn't it work?

When the displacement is negative.

He asked for the distance, so we need to consider the unsigned area. This means that if we want to use your approach, we must treat any areas below the t-axis as positive as well, which can be done by putting absolute value brackets around them.

For motion questions in app. of calculus:

Is there a set method to solving questions like 'find the distance the particle travels in x seconds' ?

Essentially, you do need to watch out for the particle turns around. (Of course, if it does turn around, then we expect that \(v = 0\) there.)

Once you figure out where the particle turns around, divide your region into those intervals and consider the distance travelled between those intervals separately. For example, if a particle follows the equation \( x = 2(t-1)(t-3)\), then consider the distance travelled between 0 and 1, separate to the distance travelled between 1 and 3, separate to any distance travelled after 3.

Having said that, that is a very crude example. A proper question would be appreciated if you require more detail.

[kauac]

Once you figure out where the particle turns around, divide your region into those intervals and consider the distance travelled between those intervals separately. For example, if a particle follows the equation \( x = 2(t-1)(t-3)\), then consider the distance travelled between 0 and 1, separate to the distance travelled between 1 and 3, separate to any distance travelled after 3.

So work out the separate distances according to where the particle turns around, and then add them all up?

[S200]

Well, if question asks for displacement, add them.

If it wants distance from origin, you would probably have to minus one from the other.