random question

[yang_dong]

if the question says that it is decreasing proportionally? what does that mean? I'm not sure proportional to what?
so there is a population infected by a disease and with the aid of the vaccination the disease decrease proportionally? If originally the rate was such that for every one person inflected, he/she infects five people, how many people are required to be vaccinated?

[keltingmeith]

You really haven't given us enough information.

A decreasing proportionality could mean two things - let's say a is proportional to b. It could mean that as a decreases, so does b, in which case there is a DIRECT proportionality between the two. Or, it could mean that as a increases, b decreases, which means that there's an INVERSE proportionality between the two. In both cases, there's something decreasing, but they have two different situations:

if there's a direct proportionality, we have . If there's an inverse proportionality, we have . Are you giving us the exact wording of the question, or just picking bits of it out and hoping you're asking us the right things?

[yang_dong]

that's why im so confused with this question, but then I guess we have to make the assumption that it is a inverse proportionality because when you vaccinate the disease, the more vaccination, the less the disease???

how would I solve the question then???

[yang_dong]

quick question

how did they get that? (please see attachment)

i'm trying to graph the graph y = (1/x^2)/(1+x^2)

thank you

[Nato]

quick question

how did they get that? (please see attachment)

i'm trying to graph the graph y = (1/x^2)/(1+x^2)

thank you

Hey,
you can use long division.
Perhaps to make it more visible, see it as -x^2+1 divided by x^2+1 and you can use long division from there.

[keltingmeith]

Another, quicker method:

[yang_dong]

thank you

i have another quick question

how would i differentiate tan^-1(c/x)?

i know that if it as tan^-1(x/c) i could go 1/(x^2+c^2), but this is the other way around?

[keltingmeith]

tan^-1(c/x)=tan^-1(cx^-1)

Then let u= cx^-1, giving us tan^-1(u) and apply the chain rule.

[IndefatigableLover]

thank you

i have another quick question

how would i differentiate tan^-1(c/x)?

i know that if it as tan^-1(x/c) i could go 1/(x^2+c^2), but this is the other way around?

Alright I'll do my best to explain what I'm doing so bear with me.

You know that the derivative of

However if we switched it around then we would get:







From here we'll derive our equation which you should get as:



Here we use a trig identity to get rid of the sin(y)^2 part (so change it into cosec^2(y) before changing it into 1+cot^2(y))



I think it helps but draw a triangle out and then label the sides accordingly for what tan(y) was originally (I'll upload an image later if you don't get it) but we can see that tan(y)^2 is equal to (c/x)^2



Expand it all out:





Flip it around and that's your final answer!



(Damn takes a long time typing it all up in but beaten by EulerFan101)

[yang_dong]

thank you so much

how would i find the antidiff of x/sqrt(25-x^2)

[Jacyan]

substitute u = 25 - x^2, hence du = -2x dx. Then integrate -0.5/sqrt(u) and sub back in u. You should get -sqrt(25 - x^2) + c

[Conic]

Beaten.