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 2 years 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.
 2 years 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.

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Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1The 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.

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1I calculated 22/3 for 1. Is that right? What do I do for 2 and 3?

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1@hartnn @experimentX

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1wow .. could you summarize ... I am hard time reading through all.

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

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1Right. 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.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1could you draw figure of 2 ??

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1dw: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).

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1No ... draw 3d coordinates. with xy at flat.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362066629575:dw

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1What does that do for us?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362067183705:dw Q 2 says that your volume is like this

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1Isn't it supposed to be a rectangle?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1No ... just like wedge.

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1How is the "wedge" represented with the functions that I have?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362067339866:dw

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1So is the integral √x dx on the interval of [0,2]? I'm not quite sure what I should be seeing.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1... let's ignore Region 2 for a whle.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362067567201:dw

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1You make nice drawings. ;) But I'm still not sure how to evaluate them.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1for volume ... use this integraldw:1362067702501:dw do same for other region.

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1So 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?

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

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1Now what should I do about part 3?

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1Part 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?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1the 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)

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

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1f'(x) = 1/2√x so 1/2√x * 1 = 1?

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yea ... use that value to find .. x and use x to find y.

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1In 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?

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1never mind. lol. X = 1/4th I think.

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1So now that I have x how would I get y? Plug it into the equation of f?

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1Hurray!! THanks!! I wish I had more medals to give you. ;)

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1it's okay!! you are welcome :)

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1yep ... that's correct!!

Bladerunner1122
 2 years ago
Best ResponseYou've already chosen the best response.1Yay my life is now complete!! xD

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.1haha ... 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)

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