VCE Methods Question Thread!

[Monkeymafia]

How many ways can a board of 3 be chosen from 2 males and 4 females?

a) without any restrictions
b) with at least one male in the board?

mod edit: removed duplicate post (probably posted by mistake)   

[deStudent]

http://m.imgur.com/a/S2aL8

For this question, why can't you make x+5 a square, then solve for x? The answer has e^3 -5 only.

Since x+5 is being squared, you can have the minus value as well right?

Thanks

[Gogo14]

http://m.imgur.com/a/S2aL8

For this question, why can't you make x+5 a square, then solve for x? The answer has e^3 -5 only.

Since x+5 is being squared, you can have the minus value as well right?

Thanks

you can square it, but you have to reject the negative answer as you cannot log a negative number

[deStudent]

you can square it, but you have to reject the negative answer as you cannot log a negative number

Thanks. So the restriction on x is solely determined by the original form of the equation?

[Shadowxo]

Thanks. So the restriction on x is solely determined by the original form of the equation?

Yes, it must match the initial conditon / be valid in the initial equation

[deStudent]

Thx^^

http://m.imgur.com/ZedmrDR

Is the answer is +- 3 or just +3? I got +- since your fourth rooting 81? Book says +3

Thanks

[Sine]

Thx^^

http://m.imgur.com/ZedmrDR

Is the answer is +- 3 or just +3? I got +- since your fourth rooting 81? Book says +3

Thanks

Yes the maths works out for the fourth root of 81 to be -3 or 3. However the base of a log must be positve x>0. Thus only 3 is the solution.

[deStudent]

For solving exponential inequalities like these http://m.imgur.com/FFCziDM
I did them all by using a rough imaginary sketch and finding the first value of x that satisfies the inequality.

Would this method be better than the other method of taking the log base 10 of each side? I find it harder to determine the direction of the inequality using that method, but it seems like it flips sign when you're dividing by a log that's argument is less than 0 which is because the graph is flipped over the y-axis right?

These questions seem pretty simple so I'm just double-checking incase my preferred method runs in to problems in more complex questions.

Ty

[Sine]

For solving exponential inequalities like these http://m.imgur.com/FFCziDM
I did them all by using a rough imaginary sketch and finding the first value of x that satisfies the inequality.

Would this method be better than the other method of taking the log base 10 of each side? I find it harder to determine the direction of the inequality using that method, but it seems like it flips sign when you're dividing by a log that's argument is less than 0 which is because the graph is flipped over the y-axis right?

These questions seem pretty simple so I'm just double-checking incase my preferred method runs in to problems in more complex questions.

Ty

IMO

whenever you have an inequality that is NOT linear you need to consider the inequality as equal (and solve finding the points of intersection) then do a sketch to determine(usually easily read off from the graph by using the points of intersection) what domain satisfies the inequality.

[gameboy99]

Can someone help me with these polynomial questions http://i.imgur.com/kns8f05.png
Thanks 

[Syndicate]

Can someone help me with these polynomial questions http://i.imgur.com/kns8f05.png
Thanks 

17)




18)
If a quadratic has no real solutions, this means that the determinant is less than 0.

[illuminatisky]

if P(x) = x^3 - 6x^2 + nx + 2 and P(2) = 3P(-1), obtain the value of n. Found this one so confusing because of the 3P

[Syndicate]

if P(x) = x^3 - 6x^2 + nx + 2 and P(2) = 3P(-1), obtain the value of n. Found this one so confusing because of the 3P

P(2) = 8 - 24 + 2n+2  = 2n- 14
3P(-1) = 3 x P(-1) = -3 - 18 - 3n + 6 = -3n -15

P(2) = 3P(-1)
-3n - 15 = 2n - 14
5n = -1
n = -1/5

[illuminatisky]

P(2) = 8 - 24 + 2n+2  = 2n- 14
3P(-1) = 3 x P(-1) = -3 - 18 - 3n + 6 = -3n -15

P(2) = 3P(-1)
-3n - 15 = 2n - 14
5n = -1
n = -1/5

Cheers!

[Gogo14]

Why finding the derivative of trig functions, why must the angle be in radians?why not degrees?