VCE Methods Question Thread!

[Bluegirl]

You'd have to work it out. Your calculator can do that for you. If you try and solve the equations by hand but get to 0=0 or something, that means you have infinitely many solutions. If you get 1=0, that means there are no solutions.

Brightsky, I'm not sure R^4 makes sense to VCE students

Is this normally an extended response question/do people usually work it out on a calculator? Kinda stuck working it out by hand

[Only Cheating Yourself]

Guys, how do you solve a quadratic equation using the quadratic formula to get the exact answer?  I can't seem to do it, i can only get in the surd form but i can't get as a integral number?

[Nato]

Guys, how do you solve a quadratic equation using the quadratic formula to get the exact answer?  I can't seem to do it, i can only get in the surd form but i can't get as a integral number?

using the quadratic formula, or just solving a quadratic equation, you are not always going to get numbers that are integers.

for example is you have you can get a pretty good feeling you're not going to get an answer that is an integer. For this i'd recommend using the quadratic formula

so we have as our formula. and after subbing in a,b,c we get:

which further simplifies to

well, when we look at the solutions of this equation which are , clearly they are not integers.

BUT, this is leaving them in exact form. So if you were given a similar question, and get a number under the square root which you can't make an integer from to get an 'exact answer', don't worry. Because this is an exact answer, you can't simplify it anymore.

i can only get in the surd form but i can't get as a integral number

the surd form is correct, and is still an exact answer, unless it was some like which can clearly be simplified.

[Only Cheating Yourself]

using the quadratic formula, or just solving a quadratic equation, you are not always going to get numbers that are integers.

for example is you have you can get a pretty good feeling you're not going to get an answer that is an integer. For this i'd recommend using the quadratic formula

so we have as our formula. and after subbing in a,b,c we get:

which further simplifies to

well, when we look at the solutions of this equation which are , clearly they are not integers.

BUT, this is leaving them in exact form. So if you were given a similar question, and get a number under the square root which you can't make an integer from to get an 'exact answer', don't worry. Because this is an exact answer, you can't simplify it anymore.

the surd form is correct, and is still an exact answer, unless it was some like which can clearly be simplified.

Thanks, this how i left my answers,
but for e.g solve
x^2+9x+20=0
when i sub it into the formula its a surd but the book has whole numbers?

[Russ]

If you don't need to use the quadratic formula then don't use it? Just solve that with inspection

[Only Cheating Yourself]

If you don't need to use the quadratic formula then don't use it? Just solve that with inspection

The question has already been factorized by inspection.

[Russ]

Inspection is just a generic term that refers to solving it without applying a formula/complex rule etc. (I think, I haven't done math for a while). In this case, you can work out the two possible values for x via basic application of the null factor law.

I could be wrong, but that equation can be turned into (x+4)(x+5) = 0 and then solved from there?

[Eluminum]

Hi, can you guys help me out on this, I'm kinda stuck
(Extended response question: calculator allowed)
1. The rate of flow of water R ml/min into a vessel is described by the quartic equation
R= kt^3 (20-t, 0 < t <20, where t minutes is the time elapsed from the beginning of the flow. The graph is shown below. (upright graph, TP of (15,20). Y int (0,0)

a) Find k

( the answer is k= 4/3375 btw)

[Conic]

Hi, can you guys help me out on this, I'm kinda stuck
(Extended response question: calculator allowed)
1. The rate of flow of water R ml/min into a vessel is described by the quartic equation
R= kt^3 (20-t, 0 < t <20, where t minutes is the time elapsed from the beginning of the flow. The graph is shown below. (upright graph, TP of (15,20). Y int (0,0)

a) Find k

( the answer is k= 4/3375 btw)

The point (15,20) tells us that when t=15, R=20.

(subbed in R=20 and t=15)



(divided both sides by 5)

Please help me with this question.

Spoiler

So I've done part a) and I found to be . I'm kinda confused on part b) , I don't remember how to find the suitable domain.

Looking at the diagram, x must be larger than 12, and y must be larger than 20 (if they weren't, the shape wouldn't be right). So you end up with x>12 and y>20. In part a, you should have found that y=80-x while finding the formula for the area. Substitute this into the second inequality and you get 80-x>20, or 60>x. Since x is greater than 12 and less than 60 you get the domain 60>x>12.

[Only Cheating Yourself]

Inspection is just a generic term that refers to solving it without applying a formula/complex rule etc. (I think, I haven't done math for a while). In this case, you can work out the two possible values for x via basic application of the null factor law.

I could be wrong, but that equation can be turned into (x+4)(x+5) = 0 and then solved from there?

ye you're right thanks

[Only Cheating Yourself]

guys, what does the +- sign mean before the square root?  Also how do i write the +- sign on a ti spire cad calculator?

[Nato]

How could i go about sketching this efficiently and effectively. Using addition of ordinates

f: R\{0}->R, f(x) = (1/x) + (1/x^2)

[Orb]

guys, what does the +- sign mean before the square root?  Also how do i write the +- sign on a ti spire cad calculator?

It means there are two solutions, let's say you have a +- root 49, then it would either result in a + root 49 or a - root 49, so the result you would generally get from solving a quadratic.

You don't generally need to input that onto your CAS, but if you do, you write it as two separate solutions/equations, in the above example you would just put in a+ root 49 AND a - root 49.

Hope that helps!

[lzxnl]

How could i go about sketching this efficiently and effectively. Using addition of ordinates

f: R\{0}->R, f(x) = (1/x) + (1/x^2)

Stuff addition of ordinates.

When x approaches +-infinity, f approaches zero.
We can rewrite this function as (x+1)/x^2. As x approaches zero from either direction, the function approaches positive infinity. We also have an intercept at x=-1.

Differentiating the original equation gives f'(x)=-1/x^2 - 2/x^3
Setting this equal to zero gives 1/x^2+2/x^3=0 => x=-2
Now when x>0, the graph just decreases uniformly to zero. That you can see because f'(x)<0 for x<0. Draw this bit like y=1/x with the horizontal asymptote.

The graph changes direction at x=-2. f(-2) = -1/4, and given that the graph later on approaches infinity when x approaches zero, it must be a local minimum. So, local minimum at x=-2.

If you can make sense of what I just typed, you'll be able to sketch the graph.

[T-Infinite]

Someone please refresh my memory on how to do these types of questions,

"An aircraft, used for fire spotting, flies from its base to locate a fire at an unknown distance, x km away. It travels straight to the fire and back, average 240km/h for the outward trip and 320km/h for the return trip. If the plane was away for 35 minutes, find the distance, x km."

Please provide steps I just blanked out while trying to interpret these types of questions.