Mathematics Question Thread

[kiiaaa]

Thank you! that really clears it up


I also had another question- may be a sort of stupid one but:

for what type of questions do we change our calculator into radians mode and which types of questions should it be in degrees?
I've confused myself a lot and would like some clarification please so during the exam in don't waste a minute or two contemplating which mode it should be in hahaha =P =P =P =P

Thank you

[Natasha.97]

Thank you! that really clears it up


I also had another question- may be a sort of stupid one but:

for what type of questions do we change our calculator into radians mode and which types of questions should it be in degrees?
I've confused myself a lot and would like some clarification please so during the exam in don't waste a minute or two contemplating which mode it should be in hahaha =P =P =P =P

Thank you

Hi!
- Radians usually always involve pi, e.g. find tan theta = 1 over sqroot of 2 from 0<x<2pi
- Degrees is the exact opposite, e.g. find tan theta = sqroot 3 from 0<x<360 degrees
Hope this helps!

[Shadowxo]

Thank you! that really clears it up


I also had another question- may be a sort of stupid one but:

for what type of questions do we change our calculator into radians mode and which types of questions should it be in degrees?
I've confused myself a lot and would like some clarification please so during the exam in don't waste a minute or two contemplating which mode it should be in hahaha =P =P =P =P

Thank you

Just adding, almost everything is in radians (eg differentiation, integration, etc) while degrees is often used for angles in trig, such as "find this angle in degrees". Usually the default is radians unless they ask for it in degrees or give you a value in degrees.
You should also be able to tell when something is in degrees and radians - radians will be a smaller number often including Pi (typically 0-2pi ie 0-6.28), while degrees will be much larger, eg 30-360°
Also converting degrees to radians just requires *pi/180 while radians to degrees is *180/pi

[RuiAce]

Thank you! that really clears it up


I also had another question- may be a sort of stupid one but:

for what type of questions do we change our calculator into radians mode and which types of questions should it be in degrees?
I've confused myself a lot and would like some clarification please so during the exam in don't waste a minute or two contemplating which mode it should be in hahaha =P =P =P =P

Thank you

Essentially, the above are the main guidelines you should need. However, the following are the only two necessary and sufficient checks:

1. If an angle is involved IN the question, look out for the circle. Because if I told you to compute \(\sin 45\), without that \(^\circ\) degree symbol there, I mean radians.
2. If an angle is NOT involved in the question, ordinarily you should always be assuming radians for the exact reason Shadow said at the start.

[kiiaaa]

Hi!
- Radians usually always involve pi, e.g. find tan theta = 1 over sqroot of 2 from 0<x<2pi
- Degrees is the exact opposite, e.g. find tan theta = sqroot 3 from 0<x<360 degrees
Hope this helps!

Just adding, almost everything is in radians (eg differentiation, integration, etc) while degrees is often used for angles in trig, such as "find this angle in degrees". Usually the default is radians unless they ask for it in degrees or give you a value in degrees.
You should also be able to tell when something is in degrees and radians - radians will be a smaller number often including Pi (typically 0-2pi ie 0-6.28), while degrees will be much larger, eg 30-360°
Also converting degrees to radians just requires *pi/180 while radians to degrees is *180/pi

Essentially, the above are the main guidelines you should need. However, the following are the only two necessary and sufficient checks:

1. If an angle is involved IN the question, look out for the circle. Because if I told you to compute \(\sin 45\), without that \(^\circ\) degree symbol there, I mean radians.
2. If an angle is NOT involved in the question, ordinarily you should always be assuming radians for the exact reason Shadow said at the start.

THANK YOU SO MUCH GUYS FOR YOUR HELP!

also, i had a few more questions and was wondering if you could help me please.

- how do you integrate for chain rule type questions? like for like you know how for chain rule for differentiation you bring down the power of the brackets then times by what's in the bracket. how do you integrate a chain rule type question? ( have attached an example) [ INTEGRATE: (5+3x)²

- also if they ask to integrate something which has the denominator of 'x' how do you integrate it as if i convert it to be 'x^-1' and integrate it will be '-1^0' which is basically 1 which is why I'm confused how to tackle such questions and was wondering if you could sort of teach me how to solve these questions please? ( i also attached an example of what I meant in case my blabber didn't make sense) [INTEGRATE: ( x² +3x)/x]

Thank you soo much and i hope all of that makes sense? i really appreciate your help 

EDIT:  so the picture that has the example is too big of a file to upload so ill try my best to do write the question to show what i mean. i hope it makes sense. if not please let me know

[pikachu975]

THANK YOU SO MUCH GUYS FOR YOUR HELP!

also, i had a few more questions and was wondering if you could help me please.

- how do you integrate for chain rule type questions? like for like you know how for chain rule for differentiation you bring down the power of the brackets then times by what's in the bracket. how do you integrate a chain rule type question? ( have attached an example) [ INTEGRATE: (5+3x)²

- also if they ask to integrate something which has the denominator of 'x' how do you integrate it as if i convert it to be 'x^-1' and integrate it will be '-1^0' which is basically 1 which is why I'm confused how to tackle such questions and was wondering if you could sort of teach me how to solve these questions please? ( i also attached an example of what I meant in case my blabber didn't make sense) [INTEGRATE: ( x² +3x)/x]

Thank you soo much and i hope all of that makes sense? i really appreciate your help 

EDIT:  so the picture that has the example is too big of a file to upload so ill try my best to do write the question to show what i mean. i hope it makes sense. if not please let me know

For the first example since the terms in the bracket are linear then you just do reverse of chain rule: add one to the power, and DIVIDE by the derivative of the brackets.

For the second example you split up the fraction into x + 3 by dividing through by x. Sometimes when x is on the bottom you use logs, or you split up the fraction.

[kiiaaa]

For the first example since the terms in the bracket are linear then you just do reverse of chain rule: add one to the power, and DIVIDE by the derivative of the brackets.

For the second example you split up the fraction into x + 3 by dividing through by x. Sometimes when x is on the bottom you use logs, or you split up the fraction.

Absolute legend! thank you sooo much

[anotherworld2b]

Can I have help with part d please?

[Shadowxo]

Can I have help with part d please?

If you're doing it by hand you may want to expand the brackets

[RuiAce]

If you're doing it by hand you may want to expand the brackets

That symbol is just \geq or \ge

[katnisschung]

How and why can I use the discriminant for this q.

If one particle starts at the pt x=0 and travels with a velocity of v=2t^3 -7t+5
And a second particle starts at Tue point x=7 and travels with a velocity of v=8+2t^3. Will these particles collide?
Integrated to find x=1/2 t^4 -7/2t^2 +5t
And x=8t+2/4t^4+7
Equated these and answers suggest using discriminant?? Pls explain

[Opengangs]

How and why can I use the discriminant for this q.

If one particle starts at the pt x=0 and travels with a velocity of v=2t^3 -7t+5
And a second particle starts at Tue point x=7 and travels with a velocity of v=8+2t^3. Will these particles collide?
Integrated to find x=1/2 t^4 -7/2t^2 +5t
And x=8t+2/4t^4+7
Equated these and answers suggest using discriminant?? Pls explain

Let's forget about particle movement for the time being, and recall what the discriminant stands for.
If we're trying to find the number of roots of a polynomial (such as a quadratic), we use the discriminant, because that will indicate how many real roots the function is going to yield.

For instance: x² + 3x + 2 = 0 is going to yield two roots, since the discriminant, 9 - 8, is > 0.
In this way, we can also find whether or not two lines will intersect.

To further illustrate this, let's assume two quadratics: y = x² - 2 and y = -2x² + 3
To find whether or not they will intersect (or collide), we need to find the points of intersection (by equating).
x² - 2 = -2x² + 3

Move everything to one side to form a third polynomial. This quadratic is the equation of the quadratic when the two previous quadratic functions are subtracted from each other (so, we simply find its root to find the intersection point).
3x² - 5 = 0

To determine the no. of roots within this new quadratic, we need to find the x-values for this statement to be true (using the quadratic formula). If the discriminant is less than zero, then the two original functions will not meet, because there are no real x-values to yield the new quadratic to be true.

We can relate this concept back to our question with velocity and displacement.
The first particle moves with a velocity of: v = 2t³ - 7t + 5
So, integrating this, we get: x₁ = (t⁴)/2 - (7/2)t² + 5t + C
Substituting in x = 0, when t = 0, C = 0.
x₁ = (t⁴)/2 - (7/2)t² + 5

The second particle moves with a velocity of: v = 8 + 2t³
So, integrating this, we get: x₂ = 8t + (t⁴/2) + C
Substituting in x = 7, when t = 0, C = 7
x₂ = 8t + (t⁴/2) + 7

Equating: (t⁴)/2 - (7/2)t² + 5 = 8t + (t⁴/2) + 7
From here, we move every term to one side:
(7/2)t² + 8t + 2 = 0
7t² + 16t + 4 = 0

From here, we get a simple quadratic. To determine the number of roots that this quadratic has, we take the discriminant.
This new quadratic is simply the first particle subtracted with the second particle, and is just as relevant to finding the point of intersection.
Thus, to determine whether or not the two particles collide, we use the discriminant.

[RuiAce]

How and why can I use the discriminant for this q.

If one particle starts at the pt x=0 and travels with a velocity of v=2t^3 -7t+5
And a second particle starts at Tue point x=7 and travels with a velocity of v=8+2t^3. Will these particles collide?
Integrated to find x=1/2 t^4 -7/2t^2 +5t
And x=8t+2/4t^4+7
Equated these and answers suggest using discriminant?? Pls explain

Which is related to the fact that \(\Delta \ge 0\) implies solutions exist. Whereas \(\Delta < 0\) implies that they do not.
____________________________

[katnisschung]

Legend ruiace!! Thanks yep I see how the discriminant is a shortcut to see if there are any possible solutions rather than actually finding them

[anotherworld2b]

I was wondering how to do this question.
So far I gave this for part a
E(X) = 3(12) = 36