A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 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
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.

This Question is Closed

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

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

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

Bladerunner1122
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1No ... draw 3d coordinates. with xy at flat.

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

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

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

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

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

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

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

Bladerunner1122
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1... let's ignore Region 2 for a whle.

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

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

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

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

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

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

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

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

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

Bladerunner1122
 one year ago
Best ResponseYou've already chosen the best response.1Found y as 1/2

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

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

experimentX
 one year 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
 one year 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.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.