Mathematics Question Thread

[mary123987]

Hey guys,
Not so much of me needing help with a specific question, but tomorrow's my 2U exam (topics covering quadratic function, locus and geometric application). Any last minute tips or anything I should do before my exam?

Thanks!

Hey firstly all the best for tomorrow !  i think at this point just chill familiarise yourself with the formula sheet and any formulas that mightnt be on it . Next thing is at this point you should really be focussing your weakness if you think hey i am actually great at quadratic function then skip over to the other topics and vice versa.
If your mind is wondering and you feel like oh i dont feel ready even though you are do some harder questions , if your up for it past HSC questions.
But overall honstly just chill now the most important thing before a maths exam is SLEEP!
All the best , your gonna smash it

[nhlj143]

If you have any time to spare please help our dying brain.  If you can please help us with all but If not just the ones circled in red please. if you thank you so so so so bery much

[RuiAce]

If you have any time to spare please help our dying brain.  If you can please help us with all but If not just the ones circled in red please. if you thank you so so so so bery much

There is no limit to the amount of questions you can ask but when you have multiple questions please consider spreading them out in the future. It can be very off-putting seeing a whole pile of questions all at once, as opposed to having them appear one at a time.

Q5 of the first paper is quite unsuitable to the 2U course, as the algebraic approach requires far too much handwork. The geometric approach would be to write down the answer by inspection.
i) The perpendicular bisector of the interval joining the points A and B (which is a line)
ii) The line basically halfway between them



Due to how similar they are, and the fact similar questions should've been covered in class, please provide any thought process for the leftovers.
________________________________________________________________





Note: The question was clearly wrong to have dropped \(AM^2\), because we don't know that \(AM = 1\).

[nhlj143]

Thank you, and sorry If it looked so confronting. We panicked because there is a test today

[jamonwindeyer]

Thank you, and sorry If it looked so confronting. We panicked because there is a test today

Good luck with the test!! Fingers crossed you smash it

[Never.Give.Up]

hi,
i was just wondering whether anyone could help me with how to use desmos...
we have to graph the following equation:

y= -1/3125 (x-250)^2 +50

What other points do I have to find/how do I find other points to make this graph work??

Thanks so much for your help 

[Opengangs]

hi,
i was just wondering whether anyone could help me with how to use desmos...
we have to graph the following equation:

y= -1/3125 (x-250)^2 +50

What other points do I have to find/how do I find other points to make this graph work??

Thanks so much for your help 

Find the x and y intercepts.
x-intercept occurs when y = 0 (that is, -1/3125 (x - 250)^2 + 50 = 0
-x^2 + 500x - 62500 + 156250 = 0
x^2 - 500x - 93750 = 0
Use the quadratic formula to find where the x intercepts are.

y-intercept occurs when x = 0
y = -1/3125 (-250)^2+50 = 30

Find stationary points.
Take the first derivative.
dy/dx = -2/3125 * (x - 250) = (500 - 2x)/3125
Let dy/dx = 0. 500 - 2x = 0
2x = 500
x = 250

Since it's a concave down parabola, we know at (250, 50), the parabola will be a maximum value. Thus, the range becomes: y <= 50
From these points, we can graph the parabola.

You can see this graph in action here.

[itssona]

heey
2. the sum of two numbers is 6. find the numbers if the sum of their cubes is a minimum

apparently the approach is to differentiate, for maxima/minima problems? how do I do this?
thank youu

[RuiAce]

Just do the same old thing from here; differentiate, set derivative = 0 and test that it's a minimum. You'll find that \(x=3\) which consequently also implies \(y=3\).

[itssona]

only got one equation for this but dunno how to get the other :/

A rectangular block, the length whose base is twice the width, has a total surface area of 300cm^2. Find the dimensions of the block if it is of maximum value

[RuiAce]

only got one equation for this but dunno how to get the other :/

A rectangular block, the length whose base is twice the width, has a total surface area of 300cm^2. Find the dimensions of the block if it is of maximum value

Did you mean maximum value meant to say volume, oops

(Hints though: \(b = 2l\) and \(lb+bh+lh=300\))

[itssona]

Did you mean maximum value?

(Hints though: \(b = 2l\) and \(lb+bh+lh=300\)) (Edited)

ah forgot about using b=2l thanks ruii

[Dragomistress]

Hello hello!

[Shadowxo]

Hello hello!

Hey
So we want to find the minimum cost for the trip, ie find Total Cost in terms of V (average speed) then find where d(Total Cost)/dV =0
c is the cost in cents per hour, so TC (Total Cost) = c*t (cost per hour multiplied by the number of hours)
We know distance travelled = velocity * time, so
1000=V*t
t=1000/V
Substitute that in and we get

From there you should be able to find where the derivative = 0 (you should find V = 86.6 rounded to 87)

[itssona]

wondering why the answer to this isn't (9/14 x 9/14)
the answer is 17/42

the question is:
students studying at least one of the languages, french and Japanese, attend a meeting. Of the 28 students present, 18 study french and 22 study Japanese.
(i)whats the probability that two randomly chosen students both study french?
(ii) what is the probability that a randomly chosen student studies both languages?

thank you