Pre Calc help? Just a few questions

[jlynh]

I'm doing math by correspondance and my teacher and my resources aren't very helpful so I was looking for a few explanations on questions that I know should be very easy...

My first question is can someone please explain in laymen's terms how to solve for |x| / | x +2| < 2

I know you have to start by realizing that you will have 4 different cases of answers, and you will have to do | x | and | x +2 | separately.

I am unsure of whether I have to bring | x +2 | to the numerator? Also, for | x | would my answers just be -2 and 2? I am confused and sorry. I am not looking for answers, just even one example for | x +2 | <2 would help me a lot.

My second question is a word problem.

A baloon is being inflated. If it's radius is increasing at a speed of 2cm/s, determine it's surface area as a function off t. Begin with a(x)=4"pi"x^2.

The only question I have is what formula to use after a(x)=4"pi"x^2

Thank you

 

[burakaltr]

I'm doing math by correspondance and my teacher and my resources aren't very helpful so I was looking for a few explanations on questions that I know should be very easy...

My first question is can someone please explain in laymen's terms how to solve for |x| / | x +2| < 2

I know you have to start by realizing that you will have 4 different cases of answers, and you will have to do | x | and | x +2 | separately.

I am unsure of whether I have to bring | x +2 | to the numerator? Also, for | x | would my answers just be -2 and 2? I am confused and sorry. I am not looking for answers, just even one example for | x +2 | <2 would help me a lot.

My second question is a word problem.

A baloon is being inflated. If it's radius is increasing at a speed of 2cm/s, determine it's surface area as a function off t. Begin with a(x)=4"pi"x^2.

The only question I have is what formula to use after a(x)=4"pi"x^2

Thank you

abs(x)/abs(x+2)= ABS[x/(x+2)]

SA=4*Pi*r**2
dr/dt=2
r=2t

SA=4*Pi*4*(t**2)=

16*Pi*(t**2)

 

[jlynh]

Hi and thank you for replying,

However can you please explain what you did with the 2nd question?
Sorry, I still don't understand.


Thank you

 

[burakaltr]

Hi and thank you for replying,

However can you please explain what you did with the 2nd question?
Sorry, I still don't understand.


Thank you

Sure

The speed of inflation is 2 units per sec , which translates to dr/dt = 2 units.

I assume that the balloon is being inflated from zero initial radius. So instead of saying r=2*t+constant, I say dr=2dt and integrate to get r as a function of t.

Surface_Area=4*PI*(r**2), yes ?

so plug in r=2t