VCE Methods Question Thread!

[Splash-Tackle-Flail]

Does it matter what form you write a logarithm in? Eg would log10(121) and 2log10(11) both be ok?

[cosine]

Does it matter what form you write a logarithm in? Eg would log10(121) and 2log10(11) both be ok?

Both perfectly fine!

[cameotodd]

Can someone help me with this question, it's question one from the 3/4 Essentials book exercise 5H.

In the initial period of its life a particular species of tree grows in the manner described by
the rule d = d0 10^mt where d is the diameter of the tree in centimetres, t years after the
beginning of this period. The diameter after 1 year is 52 cm and after 3 years, 80 cm.
Calculate the values of the constants d0 and m.

Thanks

[Apink!]

Hi guys
How can I solve this question?
Find the equation to the normal of f(x) = x^2 which is parallel to the line y= 4x+2

I keep getting the wrong answer.
Thank you so much! (:

[faso]

Hi guys
How can I solve this question?
Find the equation to the normal of f(x) = x^2 which is parallel to the line y= 4x+2

I keep getting the wrong answer.
Thank you so much! (:

My answer was y=4x+33/64
is that the right answer ?

[kinslayer]

Hi guys
How can I solve this question?
Find the equation to the normal of f(x) = x^2 which is parallel to the line y= 4x+2

I keep getting the wrong answer.
Thank you so much! (:

The normal to a curve at any point has gradient equal to -1/m, where m is the gradient of the tangent at that point.

If the normal is parallel to y = 4x + 2, its gradient is 4.

The gradient of the tangent to f(x) = x^2 is equal to f'(x) = 2x.

Setting 2x = -1/4 we get x = -1/8, and f(-1/8) = 1/64. So our normal intersects the graph at (-1/8, 1/64).

So if our normal is y = 4x + c, we have 1/64 = -1/2 + c and therefore c = 33/64. The equation of the normal is y = 4x + 33/64.

[kinslayer]

Can someone help me with this question, it's question one from the 3/4 Essentials book exercise 5H.

In the initial period of its life a particular species of tree grows in the manner described by
the rule d = d0 10^mt where d is the diameter of the tree in centimetres, t years after the
beginning of this period. The diameter after 1 year is 52 cm and after 3 years, 80 cm.
Calculate the values of the constants d0 and m.

Thanks

.





So you have two equations:





Solve simultaneously with CAS to get m = 0.0935, d_0 = 41.9 correct to 3 significant figures. Exact solution:

http://www.wolframalpha.com/input/?i=solve+simultaneously+52+%3D+x*10%5Ey%2C+80+%3D+x*1000%5Ey

[Apink!]

Thank you faso and kinslayer!
Apparently, the answer is y= 4x + (9/16)
But I think you guys are right (cause you always are )
Thank you so much for helping me! (:

[cameotodd]

Thanks kinslayer

[qwerty101]

help on this pls

[keltingmeith]

help on this pls

q(2m)=a(2m)^2+3(2m)-4=-2 (by the remainder theorem)
So, now we play around with what we've got:

a4m^2+3*2m-4+2=0
4a*m^2+6*m-2=0

Now we have a quadratic in m. So, for there to be one solution, we want the discriminant to equal 0, so:

(6)^2-4(4a)(-2)=0
36+32a=0
a=-36/32=-9/8

[cosine]

Solve sin(5pix)= sqrt(3)cos(5pix) over [0, 1] I can't seem to find the last solution of 13/15, however I can get the others. Any help please ?

[Floatzel98]

Solve sin(5pix)= sqrt(3)cos(5pix) over [0, 1] I can't seem to find the last solution of 13/15, however I can get the others. Any help please ?

Well you have done the first steps so i'll skip to solving for the domain




All divided by 5pi



My guess is that you forgot to go around to 4 pi to get the last solution. You must have stopped only 2 revolutions in. make sure you find out what domain you need to solve for properly before you look for all the solutions

[lzxnl]

Solve sin(5pix)= sqrt(3)cos(5pix) over [0, 1] I can't seem to find the last solution of 13/15, however I can get the others. Any help please ?

You have tan 5pix = sqrt 3 for 0<=x<=1
What I like to do here is make a note that 0<=5pix<=5pi using the above restriction. This way I know what values of x I need. I never miss solutions this way.

[Cosec]

Does anyone know if linear approximation is required/examinable?