A drinking fountain projects water at an initial angle of 50 degrees above the horizontal, and the water reaches a maximum height of .150 m above the point of exit

a. Calculate the speed at which the water leaves the fountain.

b. The radius of the fountain's exit hole is 4.00 x 10^-3 m. Calculate the volume rate of flow of the water.

c. The fountain is fed by a pipe that at once point has a radius of 7.00 x 10^-3 m and is 3.00 below the fountain's opening. The density of water is 1.0 x 10^3 kg/m^3. Calculate the gauge pressure of the feeder pipe at this point.


The fuck is the volume flow rate? How do we find the velocity it exits the pipe at? How is it possible to find the pressure only knowing the radius the depth? This doesn't make any sense.

Volume flow rate is the rate of flow of a volume of a liquid as a function of time (I believe).

For finding the initial velocity, you know the angle and the maximum height. Use kinematics to find the y component of velocity needed to get it to that height against the acceleration due to gravity. From there, you can use trig to determine the initial velocity.

I didn't really look to hard at the rest.

Are you sure it's .150 meters?

Yes. It is.

If anyone wants to object, feel free to do so.. I did this kind of stuff a while ago, so I'm not 100%.

You're right, except it would be sin(50). Now just the last part...

Oh crap. Woops.

:/

So, I have
a. v = 2.24 m/s
b. Volume flow rate = 1.13 x 10-4 m^3/s

How do I go about finding part c?

Quick question: When looking at a histogram and you have to identify what kind of data it is, what do these terms mean?

• Clustered Data
• Bimodal Data
• Spread Data

This may help for the Bimodal part.


I'll try and find the others. Surprisingly, I've never covered these in the topics of Histograms...

Thanks. They're probably slightly made up terms. It's really basic stuff we're doing but the teacher never said what it actually meant.

Well I would guess that,

Bimodal: 2 peaks. (From website)
Clustered: All close scores in both x and y axis.
Scattered: Scores over a long period on the x axis.

Polynomials Question:

7. Draw sketch graphs of y=2sinx and y=x and show that the equation x - 2sinx = 0 has a root near x=2. Find this root correct to two decimal places.


Working out:


f(x) = x - 2sinx
f'(x) = 1 - 2cosx

Therefore x₂ = 2 - [(2-2sin(2))÷ (1-2cos(2))]

Which = 3.93... Which doesn't sound right. The answer should be around 1.9

But when I try the same thing in Radians instead of Degrees mode, I get 2 - 0.099 which = 1.90.

I just want to know why I must use Radians to get the right answer, and not Degrees?

sin, cos and tan are functions that repeat every 2pi. When you put it in "degree mode", you basically stretch them out to repeat every 360 degrees. It's telling the calculator, "Okay, whatever I put in there, divide by 180/pi before actually calculating it."

It's kind of like if you had a function "d = mpg(x)" that would tell you how many miles d you could go on x gallons of gas - if you give the gas as milliliters, the answer isn't going to be nearly right.

Aah, thank you for that. :)

Protip: Be sure to switch your calculator's mode when going from a class that uses Radians to a class that uses Degrees. Almost failed a Calc test that way.

>_<

You almost learnt it the hard way..

Relevant picture.

Is .999 repeating equal to 1?

Yes. Here's a simple algebraic proof that doesn't take into account unreal numbers and the like, but it should be a place to start.

1/9 = .1111111...

9*(1/9) = 9* .11111111...

1 = .9999999999...

You can read more here.

Hi, I have a bunch of calculus problems that I don't fully understand. Would someone mind helping me get these answers? I have to draw them up in paint as I am uncertain as to how to make a differentiation sign in html. calculus problem 2.png

[Mod-Edit: Please use the link option in the image uploader for large, screen-stretching images]

Basically, the d/dx and the integral undo each other. So really, what you're doing is replacing the t with x^3 (the 2 part of the integral goes away because it is a constant).

So basically, from there, it's just a bit of chain rule stuff that turns it into 3x²sin(x⁶).

Doesn't the bottom value on the integral sign mean that doesn't work though?

No. It still works. The the integrand you get is something along these lines:

New function of x - some constant that happens when you plug 2 into the indefinite integral.

Then, you derive that and the constant disappears. From there, basically, it just undoes the integral (more or less) but the chain rule has to be used when you derive it.

thanks.

If a is a multiple root of the polynomial equation P(x)=0, prove that P'(a)=0.

I know it's simple, I just can't remember how to do it.