.:zora:.

A small funnel in the shape of a cone is being emptied of fluid at the rate of 12 cubic centimeters per second ( the tip of the cone is downward). The height of the cone is 8 cm and the radius of the top is 4 cm. How fast is the fluid level dropping when the level stands 2 cm above the vertex of the cone?

If you could help me do this step-by-step I'd really appreciate it!

Thanks in advance!

I'm having trouble with this question.

Steps would be awesome, and thanks in advance!

I have the answer, but I have no idea how the 1/4 got into the answer.

1/4 cos(1-2x^2)+C

I'm having trouble finding the dy/dx of y=(tan(3x))^(ln x). Step-by-step would be awesome because I'm studying for finals and I need to know the process.

Thanks so much in advance!

I'm reviewing for my calculus course by going through old assignments, and I've come across one involving a Norman window. "If the perimeter of the window is 10ft, express the area A of the window as a function of the width x of the window."

I got my area no problem, A=xh+0.5pi(0.5x)^2, but I also need to know the perimeter, which is

P=2h+x+0.5pi(x)=10ft

But why is it not P=2h+x+pi(x)=10ft? The perimeter (circumference) of a circle is 2pi(r), but we need only half, so I would've divided 2pi(r) by 2 and get pi(r) (which is wrong).

I'm feeling pretty dumb right now, so I'd REALLY appreciate if someone could walk me through it like a 5 year old. Thanks!

My work so far:

f(x)=x-ln7x

f'(x)=1-(1/x)

I got one critical number...

x=1

and I have no idea how to get the other one.

Also, I'm in a course that doesn't allow calculators, but I feel like I would need to use a calculator to find the actual numbers (I can't think in terms of ln or log), is there a trick to just estimate the number accurately so I don't need to punch in 1-ln7(1) into a calculator?

I've gotten as far as sin^2(t/2)=1/8 and after that I'm lost!

Thanks in advance!

I'm having trouble understanding how the left limit is -7 and the right is 7. When you deal with absolute values and piecewise defined functions, aren't you supposed to just put "-" in front of the abs value? (e.g. -(5-x) ) and for the right, leave it positive (e.g. (5-x) )? How would I cancel out the (5-x) and (x-5) when they aren't equal unless you multiply by -1?

My work:

lim x->5- [(x-5)(x+2)]/[-(5-x)]

=-[(x-5)(x+2)]/[-(5-x)] cancel out denominator and (x-5)

=-(x+2)

=-7

lim x->5+ [(x-5)(x+2)]/[(5-x)]

How am I supposed to cancel this?

Thanks in advance!

I'm about to move away for my first year of university! My parents have kindly bought a condo-townhouse hybrid (odd, but quite ingenious!) for me to reside. Due to the close proximity between units, and because there is a communal entrance/exit (it is a rectangular building with one main entrance where numbers are punched in to get through an electric door, like condominiums, but each unit, once inside, is truly a 3 level house), I believe I'll be seeing and -possibly- bothering my neighbours over the summer because of some renovation work that needs to be done, and moving all my things in, etc. I feel like I should put little gifts by their doors the day I move in, as a sort of hello. I have thought about cookies (which I LOVE baking!) but I've considered dietary restraints that my new neighbours may have. Perhaps a potted plant (not all cause allergies to flare up, do they?)? I don't want to gift something that is too extravagant (I don't want to think that I'm about to put them into a trap!) nor do I want to gift something that is forgettable, or could be taken as an insult. I don't expect to become the best of friends with all or any of my neighbours, but at least feel comfortable in exchanging pleasantries if we bump into each other. From what I can tell from the entrance buzzer list (every tenant's name is listed) there is quite a mix of ethnic diversity. I believe there are 9 or so presents I need to get. -Perhaps a fancier one for my neighbour next door, as he/she/they will have to bear my bathroom being redone?-

What do you suggest I leave as a "Hello!" to my new neighbours? (I appreciate your answer!)

I'm about to move away for my first year of university! My parents have kindly bought a condo-townhouse hybrid (odd, but quite ingenious!) for me to reside. Due to the close proximity between units, and because there is a communal entrance/exit (it is a rectangular building with one main entrance where numbers are punched in to get through an electric door, like condominiums, but each unit, once inside, is truly a 3 level house), I believe I'll be seeing and -possibly- bothering my neighbours over the summer because of some renovation work that needs to be done, and moving all my things in, etc. I feel like I should put little gifts by their doors the day I move in, as a sort of hello. I have thought about cookies (which I LOVE baking!) but I've considered dietary restraints that my new neighbours may have. Perhaps a potted plant (not all cause allergies to flare up, do they?)? I don't want to gift something that is too extravagant (I don't want to think that I'm about to put them into a trap!) nor do I want to gift something that is forgettable, or could be taken as an insult. I don't expect to become the best of friends with all or any of my neighbours, but at least feel comfortable in exchanging pleasantries if we bump into each other. From what I can tell from the entrance buzzer list (every tenant's name is listed) there is quite a mix of ethnic diversity. I believe there are 9 or so presents I need to get. -Perhaps a fancier one for my neighbour next door, as he/she/they will have to bear my bathroom being redone?-

What do you suggest I leave as a "Hello!" to my new neighbours? (I appreciate your answer!)

http://bcove.me/y770mn20

What is the song in the background? It bugs me because I don't know! Thank you for helping!

My home network has 4 passwords, and I typed the same password I use on my laptop that I'm using right now, onto my iPhone, and my iPhone connects to the network, however, whenever I need to use the internet, or any app that needs the internet, it doesn't work and tells me I have no internet connection!

How can I fix this? Thanks!

My iPhone detects my house's wifi (all bars are "shown" in the symbol) and it says it's connected in the settings, however, I have no internet.

How can I fix this? I turned off my data, and I only want to use wifi.

My mother pays for my phone bills and my cousin just gave me his iPhone. I want to use wifi and wifi only (Rogers is expensive!). So is there anyway I can make sure I'm only using wifi?

I'm not too good with these things!

Sanjay drove 570 km from Regina to Winnipeg in 6.5 h. He drove part of the way at 100 km/h and the rest ay 60 km/h. How far did he drive at each speed?

I'm really bad at these questions! An explanation is greatly appreciated, and thank you!

formula to find distance between two points:

d=√[(x2-x1)^2+(y2-y1)^2]

The line segment CD joining C (-2,5) and D (d,1) has length of 5. Find d.

How would go about finding the answer? Could you please explain? Thank you! I really appreciate it!

The line segment CD joining C(-2,5) and D(d,10) has length 5. Find d.

How would I show my work? Thanks for explaining, I greatly appreciate it!

A (-1, 3√3-1), B (-4, -1), C (2, -1)

I know they're all 6. Except the 3√3-1 throws me off, so I only get 6 with BC.

Help! Can someone please explain? I would appreciate it very much!

Sara left Kootenay National Park at 8:00 am and drove toward Vancouver at 85 km/h. Allana left the park an hour later and drove along the same route at 100 km/h. At what time did Allana overtake Sara?

How would I go about solving this problem? An explanation is greatly appreciated! Thank you!