VCE Methods Question Thread!

[brightsky]

have a look at the explanation provided by itute (their solutions can be found on their website).

[zvezda]

I cant seem to cind an explanation. I found solutions but no explanation

[BubbleWrapMan]

This post has a few explanations:

Re: VCAA 2011 Exam 2 Question 4f

[allusionx]

Help plox

Find the equation of the tangent to the curve y = 3x^2 at the point where x = a. If this tangent meets the y-axis at P, find in terms of a the y-coordinate of P.

[BubbleWrapMan]

Hint: The tangent has a gradient of 6a and passes through the point (a, 3a^2). You're looking for the y-intercept of the tangent.

[Jeggz]

Help plox

Find the equation of the tangent to the curve y = 3x^2 at the point where x = a. If this tangent meets the y-axis at P, find in terms of a the y-coordinate of P.

So by asking us to find the tangent to the curve, the question is simply asking us to find the gradient of the curve at the point . To find the gradient, we first need differentiate y.

hence at the point the tangent will have a gradient of . We know that the point this tangent passes through is and so we can find the equation of the tangent in the form .


EDIT: Beaten but posting anyways 

[allusionx]

Hint: The tangent has a gradient of 6a and passes through the point (a, 3a^2). You're looking for the y-intercept of the tangent.

So by asking us to find the tangent to the curve, the question is simply asking us to find the gradient of the curve at the point . To find the gradient, we first need differentiate y.

hence at the point the tangent will have a gradient of . We know that the point this tangent passes through is and so we can find the equation of the tangent in the form .


EDIT: Beaten but posting anyways 

TY men 

[Markkiieee]

TY men 

One's a boy, one's a girl

[zvezda]

This post has a few explanations:

Re: VCAA 2011 Exam 2 Question 4f

Cheers

[fleet street]

Hi, I've been working on this problem and can't seem to get a good way of doing it.


Let
a. Find
b. Write in terms of y

The first part can be solved:

However, I don't know how you'd get the second part. The book says the answer is

Thanks!

[b^3]

Expanded the fraction out using this little trick or use long division.


EDIT: 2600^th post.

[Alwin]

Let

The first part can be solved:

However, I don't know how you'd get the second part. The book says the answer is

All that's required is a bit of algebraic manipulation



since (1-x)^2 same as (x-1)^2

take out the power

plus and minus x

split into two fractions

simplifying, since y=x/(1-x)

Hence, as required
EDIT: -sigh- yet again beaten by b^3 congrats on your 2600^th post!! this is my 88^th haha.. I won't be catching up any time soon =]

[Sanguinne]

On any day the cost pert item for a machine producing n items is given by dC/dn=40-2e^0.01n where n E [0,200] and C is the cost in dollars.
a) use the rate to find the cost of producing the 100th item.
b) Express C as a function of n.
c) What is the total cost of producing the first 100 items?
d) Find the average cost of production for:
     i) the first 100 items
     ii) the second 100 items

i am able to part a but my problem is with part b. i understand that you have to integrate the dc/dn but my quesiton is how do solve the constant, c that comes from the integration.

[BubbleWrapMan]

It costs $0 to make 0 items

[Homer]