Mathematics Question Thread

[RuiAce]

heeey

log base 2 of x is less than 3

solve

so i know log is defined for x>0 but idk how to do this, pls reply within an hour if u can before my exam aha, thank you

[itssona]

Omg THANK U RUI

[gilliesb18]

what does it mean by a function increasing or decreasing over a domain??
so for ex. i am asked the domain in which the function is (i) increasing and (ii) decreasing, for these questions;
(a) y= |x-2|
(b) f(x)= |x| + 2
(c) f(x)= |2x- 3|
(d) y= 4 |x| -1
(e) f(x)= - |x|

for a) i know that (i) it is x > 2, and for (ii) x < 2
but im really not sure if this is correct and really how to get there with the next few ones.
Can someone help me?

[jakesilove]

what does it mean by a function increasing or decreasing over a domain??
so for ex. i am asked the domain in which the function is (i) increasing and (ii) decreasing, for these questions;
(a) y= |x-2|
(b) f(x)= |x| + 2
(c) f(x)= |2x- 3|
(d) y= 4 |x| -1
(e) f(x)= - |x|

for a) i know that (i) it is x > 2, and for (ii) x < 2
but im really not sure if this is correct and really how to get there with the next few ones.
Can someone help me?

An increasing function is a function with a positive gradient. A decreasing function is a function with a negative gradient.

So, let's look at



This looks like two straight lines, hitting the x-axis at x=2. The line moving off to the right has a positive gradient, and the line moving off to the left has a negative gradient. Thus, the function is increasing for x>2, and decreasing for x<2.

For all of these functions, I would personally just try to sketch them (on paper or in your head). Then, look at where the gradient of the line is positive. That is the domain (ie. x values) for which the function is increasing!

[Dragomistress]

I would like some help with my functions.

How do I graph the attachment?

For an equation of solve graphically, do you have to label the x and y-intercepts?

How do I graph a hyperbola?

[RuiAce]

I would like some help with my functions.

How do I graph the attachment?

For an equation of solve graphically, do you have to label the x and y-intercepts?

How do I graph a hyperbola?

http://www.desmos.com

Please provide an example of a hyperbola you want to sketch.

[Dragomistress]

Let's say the sketch of a hyperbola is
y=3/(x-1) -2

[RuiAce]

Let's say the sketch of a hyperbola is
y=3/(x-1) -2

[Fahim486]

Hey so I'm having trouble with question 11. b) so could someone please explain to me how to do this
Thanks!!

[RuiAce]

Hey so I'm having trouble with question 11. b) so could someone please explain to me how to do this
Thanks!!

Thought: At x=e we may have a horizontal point of inflexion. But I have not verified this.

[cxmplete]

how to do both these questions (sorry it's slanted)

[RuiAce]

how to do both these questions (sorry it's slanted)

Hint for second: \((1+2+3+\dots+100) - (6+12+\dots+96)\).

[BarnesK01]

I need help with the attached question.. Just have absolutely no clue where to start 

[kiwiberry]

I need help with the attached question.. Just have absolutely no clue where to start 

Hey! The flow rate of water is given by \(\frac{dV}{dt}\), so to find the time when the flow rate is 0, set \(\frac{dV}{dt}=0\)
t=0 will be at 8:55 when the pump starts, so the first time after 8:55 when the flow rate is 0 will be when t=35, ie 8:55 pm + 35 minutes = 9:30 pm

To find volume, we need to integrate \(\frac{dV}{dt}\) and sub in the initial conditions given to find c
and finally, volume will be maximum when t=35 as \(\cos (\frac{\pi}{35}\times 35) = \cos \pi=-1\) and so \(V= \frac{700}{\pi} + \frac{700}{\pi} = \frac{1400}{\pi}\) L. Hope that helped

[Kle123]

Hi! Could i get help with this question. Not sure whether me or my peer is right :/