VCE Methods Question Thread!

[Ahmad_A_1999]

Let x1 be the x-coordinate of the left side of the rectangle, and let x2 be the x-coordinate of the right side of the rectangle.

We want to find the length of the rectangle = x2 - x1

We know that the base of the triangle is 6 units (8-2 from the diagram). We also assume that the rectangle is in the centre of the triangle, meaning that there is x1 units between the corner of the triangle and the corner of the rectangle. Since it is in the middle, there is x1 units on both sides = 2x1 units altogether.

Therefore, our length = 6 - 2x1 (does this part make sense? This is the trickiest part of the question )

Since our length is in terms of x1, we sub x1 into our linear equation (from part a) to find the corresponding y-value for x1.

Y = 3x1 - 4

We then need to further subtract 2 units, as the rectangle is 2 units above the x-axis, to find the width.

Width = (3x1 - 4) - 2 = 3x1 - 6

Area = length x width
         = (6 - 2x1)(3x1 - 6)

Find the derivate of the area (in terms of x1). Make derivative = 0 to find maximum x1 values. Sub into area equation to find maximum area.

Hope this helps! Let me know if anything doesn't make sense

Hey! Thanks for the response! 

I don't get it 

I'm confused about finding the length of the rectangle, I'm okay with the other parts though, 

[amigos]

Hey peoples - can I please get some help with this question:

When a polynomial P(x) is divided by x-1 and x+2 the remainders are 3 and -9 respectively. Find the remainder when it is divided by (x-1)(x+2).

Thanks! 

Edit: Also, can I simplify the following any further?

[MisterNeo]

Edit: Also, can I simplify the following any further?

To answer your second question, it can be further simplified.

[RuiAce]

Hey peoples - can I please get some help with this question:

When a polynomial P(x) is divided by x-1 and x+2 the remainders are 3 and -9 respectively. Find the remainder when it is divided by (x-1)(x+2).

Thanks! 

Edit: Also, can I simplify the following any further?

[humblepie]

Could someone please explain how to find the range of y=e^x2 without using CAS?

Thanks

[MisterNeo]

Could someone please explain how to find the range of y=e^x2 without using CAS?

Thanks

The range of a function is "all possible y-values".
This function has multiple levels of powers so you need to work top-down.
The exponential is to the power of x². This means that the exponential is to the power of values greater or equal to 0 because you can't get a negative from squaring.


Basically, you have to work top-down the powers to find values of y that can't exist.

[TheCommando]

The range of a function is "all possible y-values".
This function has multiple levels of powers so you need to work top-down.
The exponential is to the power of x². This means that the exponential is to the power of values greater or equal to 0 because you can't get a negative from squaring.


Basically, you have to work top-down the powers to find values of y that can't exist.

Why is it 1
Why cant it bbe 0

[Sine]

Why is it 1
Why cant it bbe 0

[TFAnime123]

Can someone help out with this question?

The solution to the equation 4^2x-1 =36 can be written in the form a + log e (b)/log e (4), where a and b are positive integers. Find a and b.

[Jaswinder]

\[4^2^x^-^1=36\]

\[\log_{e}36/\log_{e}4=2x-1\]

\[\frac{1}{2}(\log_{e}36/\log_{e}4 +1) =x\]

\[(\log_{e}6/\log_{e}4 +0.5) =x\]

[humblepie]

Would really appreciate some help with this question:

Solve for x: -n/xⁿ⁺¹ > -(n+1)/xⁿ⁺²

The answer is 0<x< (n+1)/n (I don't understand why x has to be greater than 0)

Thanks in advance!

[scout]

Would really appreciate some help with this question:

Solve for x: -n/xⁿ⁺¹ > -(n+1)/xⁿ⁺²

The answer is 0<x< (n+1)/n (I don't understand why x has to be greater than 0)

Thanks in advance!

Hmm I agree... why can't x also be LESS than zero (just not equal to zero)? 

[Syndicate]

Would really appreciate some help with this question:

Solve for x: -n/xⁿ⁺¹ > -(n+1)/xⁿ⁺²

The answer is 0<x< (n+1)/n (I don't understand why x has to be greater than 0)

Thanks in advance!

Think about it graphically by letting n be equal to any integer (except -1, 0 or -2 of course).

(use desmos if you want)

[scout]

Think about it graphically by letting n be equal to any integer (except -1, 0 or -2 of course).

(use desmos if you want)

I suppose it can't be shown algebraically (without trial and error) ?

[Lavar Big BBB Balls]

Hi

For this http://imgur.com/a/Bl2Ew

I don't understand how 9dii and iii can have a different answer? ii is dependent and iii is independent but what they're both saying is "given the sum of the 2 numbers is at least "x", what is the probability of A occurring?".

If we know C or D occurs then wouldn't this affect the probability of A occurring? this makes me believe that they are both dependent.

note: I know that for iii Pr(A|D) = Pr(A) which means it's independent but it doesn't seem very intuitive otherwise.

Thanks