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March 19, 2024, 05:31:16 pm

Author Topic: Tips for Macrob  (Read 54949 times)  Share 

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Phoenix11

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Re: Tips for Macrob
« Reply #180 on: October 18, 2016, 04:33:19 pm »
0
Wow!
You are so good at writing!
I was only lucky to get 15 in JAC!

It's okay. Thanks for trying though.
 :)
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Phoenix11

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Re: Tips for Macrob
« Reply #181 on: August 19, 2017, 10:57:28 am »
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Hello everyone!
How are you?
Long time, no see!
I was just wondering if anyone knew how to solve these questions?

a) Use the discriminant to show that the line y=2x+1 does not intersect the parabola y=x^2+3.
b) Determine for which values of k the line y=2x+k does intersect the parabola y=x^2+3.

Thank you so much, you guys!
 :) :) :)
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GalacticProcess

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Re: Tips for Macrob
« Reply #182 on: August 19, 2017, 11:59:34 am »
+3
Hello everyone!
How are you?
Long time, no see!
I was just wondering if anyone knew how to solve these questions?

a) Use the discriminant to show that the line y=2x+1 does not intersect the parabola y=x^2+3.
b) Determine for which values of k the line y=2x+k does intersect the parabola y=x^2+3.

Thank you so much, you guys!
 :) :) :)
Hey!
I'm not very good at explaining so can someone else please explain the steps in more detail? Thanks.
Spoiler
For an intersection, we need to have both equations equal to each other.
Using the quadratic equation, we know that
Therefore,
Now we can use the discriminant formula:


Since D<0, we know that the lines do not intersect.
Spoiler
Again we equal both equations to each other and rearrange:

Using the discriminant formula:


For there to be one solution For there to be 2 solutions
Therefore, for any solutions

For there to be any intersections, k≥0.
I've put them into spoilers so that it doesn't consume too much space. If anyone finds any mistakes, please let me know. :)
« Last Edit: August 20, 2017, 12:16:50 pm by GalacticProcess »

emonerd

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Re: Tips for Macrob
« Reply #183 on: August 19, 2017, 12:04:22 pm »
+2
Hello everyone!
How are you?
Long time, no see!
I was just wondering if anyone knew how to solve these questions?

a) Use the discriminant to show that the line y=2x+1 does not intersect the parabola y=x^2+3.
b) Determine for which values of k the line y=2x+k does intersect the parabola y=x^2+3.

Thank you so much, you guys!
 :) :) :)
hey ! So it's been a while since i did this desciminant stuff but I'm pretty sure for part a) you equate the two equations and then combine both equations so that the right hand side of the equations equals to 0. Them you use the values for 'a', 'b' and 'c' and substitute them into the discriminant which is b^2-4ac and if the answer is > 0 there should be 2 points of intersection, if the answer = 0 than there is only one point, it should be tangent. If the answer is < 0 (which is the answer you should get in this question) there are no points of intersection. Correct me if I'm wrong guys, I'm a bit rusty on this haha


EDIT: Ah galactic, you beat me to it xD ohwell, you explained it alot better hahaha
« Last Edit: August 19, 2017, 12:09:09 pm by emonerd »
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Phoenix11

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Re: Tips for Macrob
« Reply #184 on: August 19, 2017, 12:13:55 pm »
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Thank you so much for your replies GalacticProcesses and emonerd!
I really appreciate it!
Everything makes much more sense now!


(P.S, Galactic Processes, I think it's supposed to be b=-2 instead of -1 (probably a typing mistake) as you said to let you know... The steps really helped however!

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GalacticProcess

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Re: Tips for Macrob
« Reply #185 on: August 19, 2017, 12:46:37 pm »
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Thank you so much for your replies GalacticProcesses and emonerd!
I really appreciate it!
Everything makes much more sense now!


(P.S, Galactic Processes, I think it's supposed to be b=-2 instead of -1 (probably a typing mistake) as you said to let you know... The steps really helped however!
Glad that it was helpful. Yeah the -1 was a typo. Edited. :)

Phoenix11

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Re: Tips for Macrob
« Reply #186 on: August 20, 2017, 11:40:07 am »
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Hello everyone!
I was just wondering if anyone knew how to solve this question?
I am having trouble with it.

The line y=mx is a tangent to the parabola y=x^2-2x+4 (i.e. the line touches the parabola at just one point).
a) Find the possible values of m.
 :) :)
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Shadowxo

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Re: Tips for Macrob
« Reply #187 on: August 20, 2017, 12:16:03 pm »
+3
Hello everyone!
I was just wondering if anyone knew how to solve this question?
I am having trouble with it.

The line y=mx is a tangent to the parabola y=x^2-2x+4 (i.e. the line touches the parabola at just one point).
a) Find the possible values of m.
 :) :)
So the line y1=mx intersects the line y2=x2-2x+4 when y1=y2

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Phoenix11

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Re: Tips for Macrob
« Reply #188 on: August 20, 2017, 01:25:44 pm »
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Hi!
Thank you for responding!
Now if the value of m is changed so that the line now intersects the parabola in two places, what is the set of possible values of m?
I got the answers 2 and -6 but I don't know how to put the correct signs in front.
I am a bit confused.
Thank you so much!
 :) :)
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VanillaRice

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Re: Tips for Macrob
« Reply #189 on: August 20, 2017, 01:40:35 pm »
+3
Hi!
Thank you for responding!
Now if the value of m is changed so that the line now intersects the parabola in two places, what is the set of possible values of m?
I got the answers 2 and -6 but I don't know how to put the correct signs in front.
I am a bit confused.
Thank you so much!
 :) :)
Since there are two solutions, you will have


The left side gives you a parabolic equation. Since you know the intercepts, do a quick sketch of the curve y=(m+2)2 - 16 and find the values of m for which the graph is greater than zero i.e. above the m-axis.
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Phoenix11

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Re: Tips for Macrob
« Reply #190 on: August 20, 2017, 06:02:30 pm »
0
Hello.
Thank you for responding.
But how would the answers be m>2 and m<-6?
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VanillaRice

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Re: Tips for Macrob
« Reply #191 on: August 20, 2017, 06:25:34 pm »
+4
Hello.
Thank you for responding.
But how would the answers be m>2 and m<-6?

Have a sketch of the graph ∆ = (m+2)2 - 16 and label the intercepts
(Note ∆ is basically the same as y, and m is the same as x - we're just using different letters/variables to fit the question)
You can see that when m > 2 OR m < -6, the value of ∆ (discriminant) is positive i.e. this is when the discriminant is greater is zero.

Hope that clarifies things  :)
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Phoenix11

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Re: Tips for Macrob
« Reply #192 on: August 20, 2017, 06:41:26 pm »
+1
Yes, I understand now!
Thank you!
 :) :)
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jz27

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Re: Tips for Macrob
« Reply #193 on: August 21, 2017, 07:50:14 am »
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Phoenix11

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Re: Tips for Macrob
« Reply #194 on: August 21, 2017, 05:53:40 pm »
+1
 :) :) :)
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