Jun 10 07:30 AM PDT  08:30 AM PDT Learn about the similarities and differences, pros and cons, between these two exams Jun 10 08:00 PM PDT  09:00 PM PDT Learn how to evaluate your profile, skills, and experiences to determine if, when, and where you should apply to graduate school. Jun 11 08:00 PM EDT  09:00 PM EDT Real GRE® prep. Really free. Twice monthly, join a Manhattan Prep instructor for a free onehour GRE prep session. Next sessions are June 11 or June 28th Jun 12 10:00 PM PDT  11:00 PM PDT Magoosh is excited to offer you a free GRE practice test with video answers and explanations. If you’re thinking about taking the GRE or want to see how effective your GRE test prep has been, pinpoint your strengths and weaknesses with this quiz! Jun 14 10:00 PM PDT  11:00 PM PDT Check out Greenlight Test Preps Free Content. Free Video Modules  "GRE Question of the Day" emails  Flashcards and more.
Author 
Message 
TAGS:


Senior Manager
Joined: 20 May 2014
Posts: 283
Followers: 23
Kudos [?]:
60
[2]
, given: 220

The figure shows the graph of the equation y =k–x^2, where k [#permalink]
29 Oct 2017, 01:27
2
This post received KUDOS
Question Stats:
60% (04:05) correct
39% (02:43) wrong based on 23 sessions
Attachment:
Coordinate Geometry  area NE question.png [ 10.06 KiB  Viewed 9539 times ]
The figure shows the graph of the equation \(y = k – x^2\), where k is a constant. If the area of triangle ABC is \(\frac{1}{8}\), what is the value of k? Give your answer to the nearest 0.01




Director
Joined: 03 Sep 2017
Posts: 518
Followers: 2
Kudos [?]:
417
[3]
, given: 66

Re: The figure shows the graph of the equation y =k–x^2, where k [#permalink]
31 Oct 2017, 00:55
3
This post received KUDOS
In order to find the coordinates of the vertices of the triangle, let's exploit the equation of the parabola.
To find the coordinates of points B and C, let's evaluate the parabola at y = 0, i.e. \(0 = x^2+k\) which leads to \(x=\pm\sqrt{k}\).
Then, vertices A has the same coordinates of the vertex of the parabola, i.e. evaluating at x = 0, we get \(y=k\).
Then, we can impose an equation for the area of the triangle as follows \(\frac{BC*OC}{2} = \frac{2\sqrt{k}*k}{2} =\frac{1}{8}\). Solving for k, we get \(k\sqrt{k}=\sqrt{k^3}=\frac{1}{8}\), i.e. k = 1/4 = 0.25.



Intern
Joined: 27 Aug 2018
Posts: 36
Followers: 0
Kudos [?]:
21
[1]
, given: 7

Re: GRE Math Challenge #2 (170 level question) [#permalink]
20 Sep 2018, 04:29
1
This post received KUDOS
Tough question. The first part of the solution:Let the origin be O. The area of the triangle ABC is 1/8. The area of the triangle ABC = the area of the triangle AOB*2 The area of the triangle AOB = (distance between Origin and B * distance between Origin and A)/2 The area of the triangle ABC = ((distance between Origin and B * distance between Origin and A)/2)*2 => The area of the triangle ABC = distance between Origin and B * distance between Origin and A = 1/8 The second part of the solution:Point A is the point when x=0 If x=0, then y=k0 => y=k So, we now know that the distance between the origin and the point A is k. Points B and C are points when y=0 0=kx^2 => x^2 = k => x = + sqrt(k) So, we now know that the distance between the origin and the point B is sqrt(k)The third part of the solution:k*sqrt(k) = 1/8 k^3 = 1/64 k = 1/sqrt(8) k = 0.35 Kudos if you liked this solution



Founder
Joined: 18 Apr 2015
Posts: 11328
Followers: 241
Kudos [?]:
2838
[0], given: 10731

The figure shows the graph of the equation y = k – x^2, [#permalink]
11 Dec 2018, 14:11
Attachment:
#GREpracticequestion The figure shows the graph of the equation.jpg [ 11.01 KiB  Viewed 6175 times ]
The figure shows the graph of the equation \(y = k – x^2\), where k is a constant. If the area of triangle ABC is \(\frac{1}{8}\), what is the value of k? Give your answer to the nearest 0.01
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.



VP
Joined: 20 Apr 2016
Posts: 1278
WE: Engineering (Energy and Utilities)
Followers: 19
Kudos [?]:
1216
[1]
, given: 241

Re: The figure shows the graph of the equation y = k – x^2, [#permalink]
16 Dec 2018, 04:48
1
This post received KUDOS
Carcass wrote: Attachment: #GREpracticequestion The figure shows the graph of the equation.jpg The figure shows the graph of the equation \(y = k – x^2\), where k is a constant. If the area of triangle ABC is \(\frac{1}{8}\), what is the value of k? Give your answer to the nearest 0.01 Explanation::Given \(y = k  x^2\) Now considering the y  axis and x = 0 Therefore, \(y = k  0\) or \(y = k\) So the point A coordinate =\(k,0\) Similarly, for point c, \(y =0\) then,\(y = k x^2\) or\(0 = k  x^2\) or\(x = \sqrt{k}\) therefore point c , coordinate will be = \( \sqrt{k},0\) and point B, will be \(\sqrt{k},0\) Now the area of \(\triangle ABC = \frac{1}{8}\) or \(\frac{1}{2} * 2\sqrt{k}* k = \frac{1}{8}( base = \sqrt{k} + \sqrt{k}) = 2\sqrt{k}\) and height = point A and the distance = k) or \(k = \frac{1}{4} = 0.25\)
_________________
If you found this post useful, please let me know by pressing the Kudos Button
Rules for Posting
Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months GRE Prep Club tests



Director
Joined: 09 Nov 2018
Posts: 506
Followers: 0
Kudos [?]:
54
[0], given: 1

Re: The figure shows the graph of the equation y = k – x^2, [#permalink]
06 Jan 2019, 18:46
pranab01 wrote: height = point A and the distance = k) How? Please explain.



Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10
Kudos [?]:
162
[0], given: 4

Re: The figure shows the graph of the equation y = k – x^2, [#permalink]
06 Jan 2019, 19:34
AE wrote: pranab01 wrote: height = point A and the distance = k) How? Please explain. Both xaxis and yaxis are perpendicular to each other, so the line from origin to A is the altitude of the triangle... And we know that when x=0, y=k, so coordinates of point A are (0,k).. Thus the height of the triangle is k
_________________
Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html



Director
Joined: 09 Nov 2018
Posts: 506
Followers: 0
Kudos [?]:
54
[0], given: 1

Re: The figure shows the graph of the equation y =k–x^2, where k [#permalink]
07 Jan 2019, 05:54
IlCreatore wrote: Then, we can impose an equation for the area of the triangle as follows \(\frac{BC*OC}{2} = \frac{2\sqrt{k}*k}{2} =\frac{1}{8}\). Solving for k, we get \(k\sqrt{k}=\sqrt{k^3}=\frac{1}{8}\), i.e. k = 1/4 = 0.25.
Is it OC or AC?



Director
Joined: 09 Nov 2018
Posts: 506
Followers: 0
Kudos [?]:
54
[0], given: 1

Re: The figure shows the graph of the equation y = k – x^2, [#permalink]
07 Jan 2019, 06:00
chetan2u wrote: AE wrote: pranab01 wrote: height = point A and the distance = k) How? Please explain. Both xaxis and yaxis are perpendicular to each other, so the line from origin to A is the altitude of the triangle... And we know that when x=0, y=k, so coordinates of point A are (0,k).. Thus the height of the triangle is k Now I got It. My confusion was how the Point A is (0,k). Now it is clear. In equation if x=0, what is y, and here, y is k.



Director
Joined: 22 Jun 2019
Posts: 522
Followers: 4
Kudos [?]:
99
[0], given: 161

Re: The figure shows the graph of the equation y =k–x^2, where k [#permalink]
04 Nov 2019, 21:22



Founder
Joined: 18 Apr 2015
Posts: 11328
Followers: 241
Kudos [?]:
2838
[0], given: 10731

Re: The figure shows the graph of the equation y =k–x^2, where k [#permalink]
14 Dec 2019, 09:20
Merged similar topics. Up for further discussion
_________________
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.




Re: The figure shows the graph of the equation y =k–x^2, where k
[#permalink]
14 Dec 2019, 09:20





