VCE Methods Question Thread!

[Planck's constant]

Love your work, Ancora_Imparo.
You will be an AN Study Guide author before too long

[Smiley_]

don't know why im stuck on this one

1 A firm manufacturing jackets finds that it is capable of producing 100 jackets per day, but it
can only sell all of these if the charge to wholesalers is no more than $50 per jacket. On the
other hand, at the current price of $75 per jacket, only 50 can be sold per day.
Assume that the graph of price, $P, against number sold per day N is a straight line.
a Sketch the graph of P against N.
b Find the equation of the straight line.
c Use the equation to find:
i the price at which 88 jackets per day could be sold
ii the number of jackets that should be manufactured to sell at $60 each.

[Phy124]

don't know why im stuck on this one

1 A firm manufacturing jackets finds that it is capable of producing 100 jackets per day, but it
can only sell all of these if the charge to wholesalers is no more than $50 per jacket. On the
other hand, at the current price of $75 per jacket, only 50 can be sold per day.
Assume that the graph of price, $P, against number sold per day N is a straight line.
a Sketch the graph of P against N.
b Find the equation of the straight line.
c Use the equation to find:
i the price at which 88 jackets per day could be sold
ii the number of jackets that should be manufactured to sell at $60 each.

You know that 100 jackets (N₁) can be sold per day at a price ($P₁) of $50 a jacket and that 50 jackets (N₂) can be sold at a price ($P₂) of  $75 per jacket, so these are two points on your graph.

- For "a" draw a line which goes through these two points on the set of axis described in the question

- For "b" use the formula for deriving the equation of a straight line (y-y₁=m(x-x₁), where; m = (y₂-y₁)/(x₂-x₁))

- For "ci" sub in 88 for N and solve for $P

- For "cii" Sub in 60 for $P and solve for N

[Markkiieee]

What is the largest possible domain for the function: f(x) = sqroot(9x-x^2)

[507]

You cannot square root a negative, so in order for f(x) to be defined:
-x^2+9x>=0
-x(x-9)>=0
So the domain is 0<=x<=9 (graphing -x^2+9x>=0 may help in visualising this.)

[Markkiieee]

You cannot square root a negative, so in order for f(x) to be defined:
-x^2+9x>=0
-x(x-9)>=0
So the domain is 0<=x<=9 (graphing -x^2+9x>=0 may help in visualising this.)

thans, what does the 9x do to the grap?

[Daenerys Targaryen]

makes another x intercept

[abcdqdxD]

State the transformations to get from y=10e^x to y=10e^(2x-1)+1

Is it dilation by factor of 1/2 parallel x, translate 1 unit in positive y direction, 1/2 units in positive x direction?

[Daenerys Targaryen]

State the transformations to get from y=10e^x to y=10e^(2x-1)+1

Is it dilation by factor of 1/2 parallel x, translate 1 unit in positive y direction, 1/2 units in positive x direction?

yes

[Markkiieee]

What are the formulas for dilation?

[Ancora_Imparo]

Maybe this can help: THE FOOLPROOF GUIDE TO TRANSFORMATIONS

[Smiley_]

A chemical manufacturer has an order for 500 litres of a 25% acid solution (i.e. 25% by
volume is acid). Solutions of 30% and 18% are available in stock.
a How much acid is required to produce 500 litres of 25% acid solution?

[Will T]

When will the gradient function be undefined? The answers say when x = 1/3, but I don't quite get why it will be undefined at that point.
Also, what does 'sign' mean in reference to the CAS syntax you get if you type that on a CAS?

[Daenerys Targaryen]

at x=1/3 is the cusp of the absolute value graph. at the cusp of any graph the gradient is undefined

[Conic]

When will the gradient function be undefined? The answers say when x = 1/3, but I don't quite get why it will be undefined at that point.
Also, what does 'sign' mean in reference to the CAS syntax you get if you type that on a CAS?

"Sign" refers to the sign or signum function, which is related to derivatives of modulus functions.
http://en.wikipedia.org/wiki/Signum_function