A.Maths Qn
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need help with this, o-lvl standard
Find the value of the constant c for which the line y = 2x + c is a tangent to the curve y = 4x² - 6x + 11. This tangent meets the x-axis at A and the y-axis at B. Calculate the area of the triangle AOB, where O is the origin.
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4x² - 6x + 11 = 2x + c
4x² - 8x + 11 - c = 0
For roots to be real and equal, b² - 4ac = 0
64 - 4(4)(11-c) = 0
16c = 112
c = 7
When y = 2x + 7 meets the x-axis, y=0, i.e.
2x + 7 = 0
x = -3½
⇒ A is (-3½,0).
When y = 2x + 7 meets the y-axis, x=0, i.e.
y = 2(0) + 7 = 7
⇒ B is (0,7).
Area of ∆AOB = ½ | (0,0) (-3½,0) (0,7) (0,0) |
= ½ | -24½ |
= 12¼ units²
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Originally posted by ^tamago^:
4x² - 6x + 11 = 2x + c
4x² - 8x + 11 - c = 0
For roots to be real and equal, b²-4ac=0
64 - 4(4)(11-c) = 0
16c = 112
c = 7
woa i took sometime to understand what you writing...
geez... i gonna fail a mathematics if i am like this >.<"
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differentiate 4x² - 6x + 11
becoming: 8x-6
8x -6 is the gradient.
eqn of tangent: y = 2x +c
8x-6 = 2 ( 2 from the eqn of 2x+C)
x = 1
y = 4-6+11
9 = y
9 = 2(1) +c
c = 7
When y = 2x + 7 meets the x-axis, y=0, i.e.
2x + 7 = 0
x = -3½
⇒ A is (-3½,0).
When y = 2x + 7 meets the y-axis, x=0, i.e.
y = 2(0) + 7 = 7
⇒ B is (0,7).
Area of ∆AOB = ½ | (0,0) (-3½,0) (0,7) (0,0) |
= ½ | -24½ |
= 12¼ units²edit: i realised that this qn can be solved with differentiation too. My mistake was when I immediately sub in the points after knowing x was 1.
however if i found the constant c, then the answer would be correct.
sorry about that wishboy.
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Originally posted by popikachu:
woa i took sometime to understand what you writing...
geez... i gonna fail a mathematics if i am like this >.<"
its easy leh
its just equating 2 of the equations to find the coordinates of the point where the 2 lines intersect.
very basic...
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Originally posted by popikachu:
woa i took sometime to understand what you writing...
geez... i gonna fail a mathematics if i am like this >.<"
practise more.... add maths is really about writing lines and lines of code liddat. -
Originally posted by ^tamago^:
practise more.... add maths is really about writing lines and lines of code liddat.
tammy, i tot this type of Qn use differentiation? -
no it's under coordinate geometry.
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Originally posted by ^tamago^:
no it’s under coordinate geometry.
see too much of differentiation alr -
Originally posted by kenn3th:
see too much of differentiation alr
fret not. i also thot of it but did a mental diff then i saw the find constant c for whatever tangent, this is a sign of coord geometry.
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thanks to all who replied!btw tammy de answer is the correct one according to the answer keyOriginally posted by kenn3th:
meet x axis at A, means y = 0
y =0
= 2(1)+C
c = -2
i tot when y = 2x + c meets x-axis at A, it doesn't really mean tat x = 1
becos x = 1 only when y = 2x + c meets the curve?
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when y = 2x - 2 meets x-axis, y=0, i.e. 2x - 2 = 0 x = 1
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but the answer for c is 7 not -2 leh, how come?
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cos the solution for a line to meet a curve is a set of point(s).
if u wan the line to be a tangent to the curve, there can only be one solution or one point which they should meet.
so u sub them as per normal, but u need to declare the roots of the solution (n real/distinct roots, 1 root or no real roots), then use the discriminant b² - 4ac to finish the job cos u have a variable c. u can't solve them and get a solution.
if u dun understand why, just do the same trick the next time u see a similar question and u're ok. -
oic
so tat means kenn3th de answer is not correct?
and i wanna ask something, if i got a test on differentiation, and this qn comes out, and i use coord geo to solve, i wont get minus mark right?
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if it comes out during a calculus test, u can do as below. but if u try in 'O' levels or major exams which tests every chapter, u might not get any marks at all, or just an answer mark because they are definitely not testing differentiation.
y=4x² - 6x + 11
⇒ dy/dx = 8x - 6
for the tangent of the curve is // to y = 2x + c,
⇒ 8x - 6 = 2
⇒ x = 1
⇒ y = 4 - 6 + 11 = 9
⇒ the tangent meets the curve at (1,9)
since (1,9) is a point on y = 2x + c,
⇒ 9 = 2 + c
⇒ c = 7 -
my a maths returned to teecher le.
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Originally posted by Hello Kitty:
my a maths returned to teecher le.
we are not interested. -
but i oso nt interested in whether u interested anot.
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Originally posted by wishboy:
oic
so tat means kenn3th de answer is not correct?
and i wanna ask something, if i got a test on differentiation, and this qn comes out, and i use coord geo to solve, i wont get minus mark right?
This qn on your assesment book is differentiation?Yea. My answer is not correct. but i have since edited it to use the differentiation method.
i realised i had made a mistake.
For a major exam, if you use amath's solutions to emath qns, like finding gradient, no marks would be deducted. unless they state that you must use xxx solution.
that was what my amath/emath teacher said.
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ya this qn is under the topic of differentiation
thx for the info
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so strange desune....
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omg why is this so hard..................im suppose to be the best in my math class...........oh well i guess we different country have different math....