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The functions f and g are given by f(x)=√x and g(x)=6x. Let R be the region bounded by the xaxis and the graphs of f and g, as shown in the figure in the link below. Please show your work.
 one year ago
 one year ago
The functions f and g are given by f(x)=√x and g(x)=6x. Let R be the region bounded by the xaxis and the graphs of f and g, as shown in the figure in the link below. Please show your work.
 one year ago
 one year ago

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Bladerunner1122Best ResponseYou've already chosen the best response.1
The functions f and g are given by f(x)=√x and g(x)=6x. Let R be the region bounded by the xaxis and the graphs of f and g, as shown in the figure in the link below. Please show your work. http://goo.gl/jXIZD 1. Find the area of R. 2. The region R is the base of a solid. For each y, where 0<=y<=2, the cross section of the solid taken perpendicular to the yaxis is a rectangle whose base lies in R and whose height is 2y. Write, but do not evaluate, an integral expression that gives the volume of the solid. 3. There is a point P on the graph of f at which the line tangent to the graph of f is perpendicular to the graph of g. Find the coordinates of point P.
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
I calculated 22/3 for 1. Is that right? What do I do for 2 and 3?
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
@hartnn @experimentX
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
wow .. could you summarize ... I am hard time reading through all.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
hmm for area of region you can do \[ \int_0^4 f(x) dx + \int_4^6 g(x) dx\]
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Right. I believe I've already gotten the answer for the area. Which is exactly what you gave. Which ends up being 16/3 + 2 = 22/3. I'm not sure what to do for 2 and 3.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
could you draw figure of 2 ??
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
dw:1362066203257:dw Is that what it's supposed to look like? It says the height is 2y and the base is R (which I don't understand).
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
No ... draw 3d coordinates. with xy at flat.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1362066629575:dw
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
What does that do for us?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1362067183705:dw Q 2 says that your volume is like this
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Isn't it supposed to be a rectangle?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
No ... just like wedge.
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
How is the "wedge" represented with the functions that I have?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1362067339866:dw
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
So is the integral √x dx on the interval of [0,2]? I'm not quite sure what I should be seeing.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
... let's ignore Region 2 for a whle.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
dw:1362067567201:dw
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
You make nice drawings. ;) But I'm still not sure how to evaluate them.
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
for volume ... use this integraldw:1362067702501:dw do same for other region.
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
So are you saying that it ends up being the integral from [0,4] of 2f(x)^2 + the integral from [4,6] of 2 g(x)^2 dx?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yes ... how do you find volume .. .simplify it , you will ge tthat expression \[ \iiint dV\]
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Now what should I do about part 3?
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Part 3 is looking for a point on f where it's perpendicular to g(x). I assume that the point must be somewhere between x=01. How do I find it?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
the part 3 is not difficult .. just find the slope using f'(x) and equate it with m1*m2 = 1 ... my being slope of g(x)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
woops!! what's up with my typing!! f'(x)*m2 = 1 and m2 is slope of g(x)
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
f'(x) = 1/2√x so 1/2√x * 1 = 1?
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yea ... use that value to find .. x and use x to find y.
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
In order for that equation to work, I would need to find a way for 1/2√x = 1 so then 1 * 1 =1 right? Well, what if 1/2√x doesn't reach one at any given moment?
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
never mind. lol. X = 1/4th I think.
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
So now that I have x how would I get y? Plug it into the equation of f?
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Hurray!! THanks!! I wish I had more medals to give you. ;)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
it's okay!! you are welcome :)
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Found y as 1/2
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
yep ... that's correct!!
 one year ago

Bladerunner1122Best ResponseYou've already chosen the best response.1
Yay my life is now complete!! xD
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
haha ... I'll give more complete answer for 2 \[ \int_0^4 \int_0^{f(x)} \int_0^{2y} dz dy dz + \int_0^4 \int_0^{g(x)} \int_0^{2y} dz dy dz\] First case, put y=f(x) ... second case, put y=g(x)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
Woops!! \[ \int_0^4 \int_0^{f(x)} \int_0^{2y} dz dy dz + \int_4^6 \int_0^{g(x)} \int_0^{2y} dz dy dz \] and simplifty it.
 one year ago
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