Mathematics Question Thread

[RuiAce]

Hi there, can I please have help expressing |a+b| without any absolute values, by using the properties of absolute values

[Shadowxo]

Hi there, can I please have help expressing |a+b| without any absolute values, by using the properties of absolute values

Two ways of doing  this:
|a+b| = \(\sqrt{(a+b)^2}\)

Or as Rui said, creating a hybrid function

[RuiAce]

Two ways of doing  this:
|a+b| = \(\sqrt{(a+b)^2}\)

Or as Rui said, creating a hybrid function

Yep. That being said though, AFAIK in the 2U course they're more relaxed about \( \sqrt{x^2}=|x|\). Some people are taught it, but others aren't and I've never seen it necessary in a 2U exam.

They need to know the piece-wise definition though.

[QC]

|a+b| = the distance of a+b to the origin which is sqrt((a+b)²)). Can also be writen as a piecemeal function as it is equal to a+b OR -a-b

[RuiAce]

|a+b| = the distance of a+b to the origin which is sqrt((a+b)²)). Can also be writen as a piecemeal function as it is equal to a+b OR -a-b

a+b is just a number.

"The distance of a+b to the origin" - where is a+b on the Cartesian plane? Unless by origin you were intending to refer to 0 on the number line.

[QC]

a+b is just a number.

"The distance of a+b to the origin" - where is a+b on the Cartesian plane? Unless by origin you were intending to refer to 0 on the number line.

Yeah, I always refer to 0 as the origin in both the Cartesian plane and number line, apologies for confusion

[joyg]

Hey, can someone please help me with the following to questions:

Differentiate- e^3x/x² and e^{2x + 1}/2x + 5

[RuiAce]

Hey, can someone please help me with the following to questions:

Differentiate- e^3x/x² and e^{2x + 1}/2x + 5

Hard to tell what's going on with the second one, because of the absence of the brackets.
Could be \( \frac{e^{2x+1}}{2x+5}\) or \( \frac{e^{2x+1}}{2x}+5\), to which the absence of brackets assumes the latter.
____________________________

[laurenf58]

Could someone please tell me how do I find the co-ordinates of the points A and B where the tangent (y=-4x+25) cuts the x and y axes respectively?

Thanks!

[legorgo18]

Could someone please tell me how do I find the co-ordinates of the points A and B where the tangent (y=-4x+25) cuts the x and y axes respectively?

Thanks!

Hi, i havent done these for a long time but i think you just sub x and y=0

Sorry if im wrong

[kiwiberry]

Could someone please tell me how do I find the co-ordinates of the points A and B where the tangent (y=-4x+25) cuts the x and y axes respectively?

Thanks!

[RuiAce]

Hi, i havent done these for a long time but i think you just sub x and y=0

Sorry if im wrong

Other way around so that it's respective to the question maybe, but the method is definitely correct (as kiwiberry demonstrated).

Keep going with the LaTeX. Advice here is to use \left( \right) if you have to put a bracket around a fraction.

(Which, Jake should probably do as well)

[katnisschung]

need help on this past hsc question on integration
(unfortunately i can't upload a pic..)

the diagram shows the cross-section of a creek with the depths
of the creek shown in metres at 4 metre intervals
the creek is 12 metres in width

i) use the trapezoidal rule to find an approximate value for the area of the cross section
=12 m^2
(im pretty sure its right... don't have answers but everyone got this)
ii) water flows through this section of the creek at a speed of 0.5 ms^-1
calculate the approx volume of water that flows past this section in one hour

need help... how do i find the volume??\
thanks!

[RuiAce]

need help on this past hsc question on integration
(unfortunately i can't upload a pic..)

the diagram shows the cross-section of a creek with the depths
of the creek shown in metres at 4 metre intervals
the creek is 12 metres in width

i) use the trapezoidal rule to find an approximate value for the area of the cross section
=12 m^2
(im pretty sure its right... don't have answers but everyone got this)
ii) water flows through this section of the creek at a speed of 0.5 ms^-1
calculate the approx volume of water that flows past this section in one hour

need help... how do i find the volume??\
thanks!

[anotherworld2b]

Could i have some help with this question please? I am a bit confused about how i differentiated it wrong