Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 15:57:40 GMT -5
Omg halp pls! I'm studying for my statewide algebra contest and I can't figure dis one out. I was never any good at perpandicular lines.
The graph of the line Ax + By = C is perpendicular to the graph y = 0.4x - 3, with A and B relatively prime integers and A > 0. If the lines intersect at the point (10,1) find C. Cannot be determined is a choice, but I'm pretty sure it's wrong. Also if you could briefly explain how to get the answer then I will owe you 3. Thanks ;D
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Post by Jake on Apr 20, 2010 16:38:21 GMT -5
Eek, sorry. You've got some hard maths there! :-\ I just finished revising for my Maths...I coulda used some help too. XD
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Cortney
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Post by Cortney on Apr 20, 2010 16:40:17 GMT -5
If I remember correctly, to find the perpendicular line of any line, you just change the slope to the opposite. I.E, for this problem the new slope would be -0.4x.
However, I'm not too sure where point C comes into this whole thing...I'm not really a math buff lol.
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Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 16:42:20 GMT -5
Actually you would have to flip the number along with adding the negative, so (0.4/1)x would turn into (1/0.4)x. That can be multiplyed by 10 and turn into (10/4)x. But all that does is calculate the slope D:
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Post by Trinton on Apr 20, 2010 17:12:10 GMT -5
Well I'm really stupid, so don't take my word for this, but you have the slope, and you have a point on the line (10,1) so can't you like, draw the line? :S Even if you can, I don't think that actually helps solve the question <.<
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Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 17:19:00 GMT -5
Well the equation isn't in slope intercept form and I think I need more values to be able to graph the line....
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Post by swan on Apr 20, 2010 17:34:37 GMT -5
Cannot be determined is a choice, but I'm pretty sure it's wrong. Are there any other answers? What specific type of algebra would you say this is? That might help refresh my memory.
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Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 17:36:44 GMT -5
Uhhhh I dunno which secific type it is... The other answers are 26, 52, 5, and 17 but I'm not allowed to use calculators. This should all be done on paper or mentally.
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FranticProdigy
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Post by FranticProdigy on Apr 20, 2010 17:44:59 GMT -5
Omg halp pls! I'm studying for my statewide algebra contest and I can't figure dis one out. I was never any good at perpandicular lines. The graph of the line Ax + By = C is perpendicular to the graph y = 0.4x - 3, with A and B relatively prime integers and A > 0. If the lines intersect at the point (10,1) find C. Cannot be determined is a choice, but I'm pretty sure it's wrong. Also if you could briefly explain how to get the answer then I will owe you 3. Thanks ;D You simply have to change the quotient to the variable to be given the desired menuin. Im merely suggesting you lack the ability to solve remedial mathamatical equations.
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Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 17:50:28 GMT -5
I dunno what remedial math equations are.... and I dunno what a menuin is but you sound like you're smart enough to solve it so could you just tell me how to do it? Or at least tell me the answer?
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Post by Trinton on Apr 20, 2010 17:57:41 GMT -5
I'm almost positive he was quoting spongebob.
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Post by Rob on Apr 20, 2010 18:03:54 GMT -5
Okay, I edited this away. I'm not comfortable with my solution. Sorry.
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Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 18:05:12 GMT -5
I'm almost positive he was quoting spongebob. ooooooo sorry I don't watch a lot of spongebob
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Post by nathalie on Apr 20, 2010 18:08:57 GMT -5
If I remember correctly, to find the perpendicular line of any line, you just change the slope to the opposite. I.E, for this problem the new slope would be -0.4x. However, I'm not too sure where point C comes into this whole thing...I'm not really a math buff lol. I think that it's the opposite reciprocal... so like -1/0.4 If i can remember... math was last semester...
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Post by swan on Apr 20, 2010 18:16:30 GMT -5
Solving for y, the slope of the first equation is clearly -(A/B). We know the slope of the second equation is 2/5. So then -(A/B) = When you do this doesn't this make C actually (C/B)? Which would make 26 not C but C/B, which makes C = 52?
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Jub
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Jub says, "Math."
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Post by Jub on Apr 20, 2010 18:27:04 GMT -5
You're right about the C/B thing, that's what I was thinking when I read Real's solution. But how do you get B = 0.5?
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FranticProdigy
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Post by FranticProdigy on Apr 20, 2010 18:44:35 GMT -5
I'm almost positive he was quoting spongebob. LOL!
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Nakor
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Post by Nakor on Apr 20, 2010 18:59:18 GMT -5
y = 0.4x - 3
The slope is y=0.4x, and is offset by the -3 (this means the line is moved three notches lower on y without actually changing the direction of its slope).
The perpendicular slope to y=0.4x is x=-0.4y (swap the variables, and make it negative). x=-0.4y can be simplified to y=x/(-0.4) and then to y=-5x/2 and then (if you please) to y=-2.5x
Alternatively, you could have taken the y=0.4x and made the fraction y=2x/5 (or y=(2/5)*x), then flipped it and added the negative to get y=-5x/2. Do not divide C by 2 (or even include it yet).
Anyway, you then need the offset for the new equation -- it won't (necessarily) be -3 like in the other one. Let's stick the C back into the new equation. That makes it:
y = -2.5x + C
We know that this is true for (10,1) -- that is when x=10 and y=1. So substitute and simplify:
1=-2.5*10 + C 1=-25+C C=26
Therefore the final equation is:
y=-2.5x+26 (If C had been negative, it would have been y=-2.5x-26.)
Now the question was phrased as Ax + By = C, so we need to make a slight rearrangement:
2.5x + 1y = 26
And there you have C=26.
//Edit:
Removing stuff edited out by a prior edit.
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TheIslander
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Post by TheIslander on Apr 20, 2010 19:18:08 GMT -5
C=52, you are all close.... since C/2 = 26. You are all complicating it WAY to much, and all missing one fundamental (final) step which is not Geometry. Here it is step by step: What we know: 1. There exists a line (y= 0.4x - 3) 2. The examiner wants the C (y intercept) of the PERPENDICULAR to the line mentioned above at the point (10,1).
3. The equation of the perpendicular is "Ax + By = C" as the examiner stated.
Let us work out geometry first, 1 and 2 are useful... 3 is NOT since he just gave you an algebraic representation of a line (not geometrical since there arent any values and you cannot imagine it) Rules to remember: 1. The GENERAL equation of a line is (y = mx + c) where m is the slope/gradient and c is the Y-INTERCEPT (where it cuts the y axis aka x=0). 2. M1 * M2 = -1 // Where M1 and M2 are two gradients of PERPENDICULAR lines. 3. To compose a line which is a tangent (parallel) or a normal (perpendicular) you must ALWAYS use this equation: y - y1 = m(x - x1)
The above 3 rules are FUNDAMENTAL to co-ordinate geometry and showing you know them is showing the examiner you mean business. So lets get cracking:
Step 1: You know that y = 0.4x - 3 that means 0.4 * M2 = -1 implying that M2 = -2.5 [this means the gradient of the perpendicular line you want is -2.5 USING RULE 2 AS STATED ABOVE]
Step 2: Since they cut at (10,1) and the gradient is -2.5 you substitute into the equation in RULE 3 where x1 and y1 are the points of intersection y - 1 = m= -2.5(x - 10) ... some steps to bring it in the form mentioned in rule 1... y = -2.5x + 26
Step 3: Steps 1 and 2 are geometry, step 3 however is algebra and logic. In the beginning I told you you dont need to know Item 3.. ofcourse you DO now. but now you know that: The general equation of a line : y = mx + c The eq of the perpendic line is : y = -2.5x + 26 The eq of the line he wants is : y = (-A + C)/B Find what is common between -2.5 and 26? 1/2. This implies: The general equation of a line : y = mx + c The eq of the perpendic line is : y = (-5x + 52)/2 The eq of the line he wants is : y = (-A + C)/B
Therefore A =5, B = 2, C = 52. [SOLVED]
Quite a bitchy question. In maths you learn different topics, the skill is in CONNECTING the topics. Some people will work the geometry bit (till step 2) because they fail to reason that there is something more to it STEP 3. this makes you connect topics and proves you are an A student.
I may be wrong because I am still sitting for my A-level, but I am quite confident that I am right. If you want I will give this question to my tutor and he will work it out for me. (to check answers) but if you can check it with someone/something else that it would be better because my tutor doesnt like me that much. hehe
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TheIslander
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Post by TheIslander on Apr 20, 2010 19:32:28 GMT -5
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