in the xy-plane, line l passes through the origin, and is perpendicular to the line 4x+y = k
where k is the constant
If the two lines intersect at the point (t, t+1),
what is the value of t?
a) -4/3
b) -5/4
c) 3/4
d) 5/4
e) 4/3
please help
2006-09-03 21:01:09 · 9 answers · asked by blazin rabbit 2 in Science & Mathematics ➔ Mathematics
it is perpendicular to 4x+y = k, so the line is like this: 4y-x=k'. it passes through the origin, so k'=0.
the line is 4y-x=0
so we have: 4(t+1) -t=0
4t-t = -4
3t= -4
t= -4/3
2006-09-03 21:23:18 · answer #1 · answered by M M 1 · 0⤊ 0⤋
we have 4x+y=K the other passes by the origine ==> y=ax.
they r perpendiculaire means 4 * a = -1 ==> a= -1/4.
for that we have y= -1/4*x ===> y= -x/4
(t;t+1) is an intersecion point it is included in the line whose equation is y= -x/4 ===> t+1= -t/4 ===>> 5t= -4 =>>
t= -5/4 pretty sure about it.
2006-09-04 06:27:48 · answer #2 · answered by maz o 1 · 0⤊ 0⤋
if 4x+y=k,
then y= - 4x+k.
solve for k by substituting y=t+1, x=t,
you'll get k= 5t+1.
then, if L is perpendicular to the line 4x+y=k,
it must have a gradient that is 1/4 as the gradient of normal (a line perpendicular to another line, in this case L) is calculated by -1/(gradient of line)
therefore you can get the general equation y= x/4 + C
BUT since you know that the line L passes through the origin, it doesn't have any y-intercepts! so C=0!
write an equation of C using the equation, and you'll get C= y - x/4.
substitue the values of x and y in to the equation and equate it to zero, and i believe you'll get t= -4/3 if i'm not wrong (a). :)
do email me if you see any careless mistakes :D
2006-09-04 04:28:15 · answer #3 · answered by musicalif3 2 · 0⤊ 0⤋
4x + y = k
y = -4x + k
Thus, the slope of the second line is -4 and the slope of the perpendicular line l is 1/4 (negative reciprocal).
The other line is given by
y - (t + 1) = 1/4 (x - t)
4y - 4t - 4 = x - t
4y = x + 3t + 4
Thus, the equation for line l is
4y = x + 3t + 4
and it passes through the origin so
4(0) = 0 + 3t + 4
0 = 3t + 4
3t = -4
t = -4/3
^_^
^_^
2006-09-04 06:47:28 · answer #4 · answered by kevin! 5 · 0⤊ 0⤋
-4/3
2006-09-04 04:02:48 · answer #5 · answered by morningstar 3 · 0⤊ 0⤋
ok here's what i can give u (i've only taken algebra 1)...the slope of the other line is going to be 1/4 because the line give has a slope of -4. that's all i know to help...i'm sorry if it's not much
2006-09-04 04:09:57 · answer #6 · answered by LiSa iS a PRiNceSS =) 2 · 0⤊ 0⤋
the answer is -4/3
2006-09-04 06:47:48 · answer #7 · answered by sam 2 · 0⤊ 0⤋
this is too easy man.
i can give you a clue only....do the problem as if no variables were given to you....im trusting you can do the problem if "t" was not used.
2006-09-04 04:06:12 · answer #8 · answered by viajero_intergalactico 6 · 0⤊ 0⤋
hey dude.. whr did u pick this question frm? is this an IIT question or sumthin???
2006-09-04 04:06:46 · answer #9 · answered by arjunr_bond007 2 · 0⤊ 0⤋