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Zekarias
Group Title
I AM CERTAIN THAT NO ONE WILL ANSWER THIS QUESTION...
Suppose that l be a line through the points (0,3)and (5,2) and tangent to the graph of the function \[F(x)=\frac{ x^2p }{ 3x+1 }\] where ‘p’ is real number. What is the equation of a line parallel to l and tangent to the graph of F.
A) 4x+4y+7 = 0 B) 9x+9y+37 = 0 C) x+y3 = 0 D) 4x+6y37 = 0
 one year ago
 one year ago
Zekarias Group Title
I AM CERTAIN THAT NO ONE WILL ANSWER THIS QUESTION... Suppose that l be a line through the points (0,3)and (5,2) and tangent to the graph of the function \[F(x)=\frac{ x^2p }{ 3x+1 }\] where ‘p’ is real number. What is the equation of a line parallel to l and tangent to the graph of F. A) 4x+4y+7 = 0 B) 9x+9y+37 = 0 C) x+y3 = 0 D) 4x+6y37 = 0
 one year ago
 one year ago

This Question is Closed

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
I will post the answer exactly after one hour.
 one year ago

mathslover Group TitleBest ResponseYou've already chosen the best response.2
Hint: Never challenge OpenStudy
 one year ago

sriramkumar Group TitleBest ResponseYou've already chosen the best response.0
m= 23/50 = 1 the equation will be y3= 1(x0) x+y3 =0
 one year ago

TheViper Group TitleBest ResponseYou've already chosen the best response.2
Right @mathslover :)
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
so its not D
 one year ago

sriramkumar Group TitleBest ResponseYou've already chosen the best response.0
@hartnn that means???
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
that means answer can be a,b or c
 one year ago

sriramkumar Group TitleBest ResponseYou've already chosen the best response.0
yep.... but the answer hasn't yet finished... @hartnn
 one year ago

KKJ Group TitleBest ResponseYou've already chosen the best response.0
I will the slope of the line through the two points
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
p=7 B)9x+9y+37=0
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
solve y=3x=F(x)=.... u get two roots of x, equate them because the line is tangent and can have only one intersection point. from this i got p=7. now answer can only be either A or B so solving both of them with F(x), gave only B) option with one intersection point, A) doesn't even intersect.
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
PLZ DONT POST THE SOLUTION
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
I am here to post the answer.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
whats wrong with my answer? and method ??
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
w/c is your ans?
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
correct but the approach not.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
didn't u get p=7, the same way as i got ?
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
you use the options to answer the question, isn't it?
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
Time is up @sauravshakya
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
OK.......
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
Here is the answer
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
First of all what you have to do is finding l so as to get p \[l:\frac{ y3 }{ x0 }=\frac{ 23 }{ 50 }\] \[l:y=x+3\]thus \[F(x)=\frac{ x^2p }{ 3x+1} =x+3=y\]simplifying the above expression \[4x^{2}8xp3=0\]Now since l is tangent to F(x), the quadratic equation above has only one solution. That means \[b^{2}4ac=0\] \[(8)^{2}4(4)(p3)=0\]thus \[(8)^{2}4(4)(p3)=0\]\[p=7\]Now we get F(x) to be \[F(x)=\frac{ x^2+7 }{ 3x+1 }\]Therefore lets solve F’(x)=1 so as to get the coordinate of the unknown line. \[F'(x)=\frac{ 2x(3x+1)3(x^{2}+7) }{ (3x+1)^2 }=1\] \[3x^{2}+2x21=9x^{2}6x1\] \[12x^{2}+8x20=0\]thus \[x=1 or x=\frac{ 5 }{ 3 }\]and \[F(1)=2 and F(\frac{ 5 }{ 3 })=\frac{ 22 }{ 9 }\]Thus we got this two points (1,2) and (5/3,22/9). The two possible lines therefore are \[\frac{ y2 }{ x1 }=1{\rightarrow}y=x+3\]w/c is the given line l. And \[\frac{ y(\frac{ 22 }{9 }) }{ x(\frac{ 5 }{ 3 })}=1{\rightarrow}9y+9x+37=0\]w/c is the answer.
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
why f'(x) = 1 ?
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
b/c the slope at that point is 1
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
Because the line l and the required line are parallel
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
So, both of their slope is 1
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
it wasn't that difficult.
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
yes but need smart approach
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
YEP....... Actually I did a algebra mistake, as usual
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
lol! checking options(when given) is the smartest approach!! :P
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
agreed with @hartnn
 one year ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.1
that saves time in exam
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
For exam only
 one year ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
atleast i got the answer...
 one year ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.2
ok thanks for your help....... closing
 one year ago
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