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March 29, 2024, 04:10:02 am

Author Topic: Tips for Macrob  (Read 55007 times)  Share 

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Eric11267

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Re: Tips for Macrob
« Reply #240 on: September 23, 2017, 09:38:43 am »
+2
Hello guys!
How has your day been so far?

I was wondering if anyone knew why the answer to this question was n+1?

What is the maximum number of terms in a polynomial of degree n?

Thank you so much!

For example if you have a polynomial of degree 2, it could be something like x^2+2x+1 which has three terms

Phoenix11

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Re: Tips for Macrob
« Reply #241 on: September 23, 2017, 10:00:24 am »
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Oh ok
Thank you so much!
 :)
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Phoenix11

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Re: Tips for Macrob
« Reply #242 on: September 24, 2017, 09:04:01 am »
0
Hi everyone!
I was just wondering if anyone knew how to solve this question.
(x3-x2+3x+2/x2-1

Thank you.
 :)
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Eric11267

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Re: Tips for Macrob
« Reply #243 on: September 24, 2017, 09:14:55 am »
+1
Hi everyone!
I was just wondering if anyone knew how to solve this question.
(x3-x2+3x+2/x2-1

Thank you.
 :)
You can only solve that using a graphics calculator unless you missed out on a bracket in your question

Phoenix11

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Re: Tips for Macrob
« Reply #244 on: September 24, 2017, 09:33:19 am »
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Sorry about the misrepresentation.
I meant (x^3-x^2+3x+2)÷(x^2-1).
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Eric11267

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Re: Tips for Macrob
« Reply #245 on: September 24, 2017, 09:39:04 am »
+3
Sorry about the misrepresentation.
I meant (x^3-x^2+3x+2)÷(x^2-1).

By doing long division you would get x-1+(4x+1)/(x^2-1)
But if you wanted to solve when the equation was equal to zero, its still not possible without a graphics calculator because the numerator is a cubic that can't be grouped.

Phoenix11

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Re: Tips for Macrob
« Reply #246 on: September 24, 2017, 09:43:21 am »
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Okay.
How did you get that answer though?
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Eric11267

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Re: Tips for Macrob
« Reply #247 on: September 24, 2017, 10:03:16 am »
+1
Its like long division but without the numbers.
Check out these websites for a better explanation
http://www.purplemath.com/modules/polydiv2.htm
https://www.mathsisfun.com/algebra/polynomials-division-long.html

Shadowxo

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Re: Tips for Macrob
« Reply #248 on: September 24, 2017, 11:59:44 am »
+5
Sorry about the misrepresentation.
I meant (x^3-x^2+3x+2)÷(x^2-1).

I'm assuming the question asks you to simplify that equation
There are a couple ways to do it, and it'll depend on what you've been taught. One way is long division, like Eric did. Another way is to just group terms / introduce terms.


If you haven't learnt this, don't worry about it. It's just another way to do it. How they expect you to do it will depend on what you've been taught :)
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Phoenix11

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Re: Tips for Macrob
« Reply #249 on: September 27, 2017, 10:02:48 am »
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Thank you Shadowxo and Eric11267 for your responses!

Quick question.
Does anyone know acts of selfishness of the nurse or Mercutio(except when he challenges Tybalt to fight) in Romeo and Juliet?
Thank you so much.
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Jessica1231

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Re: Tips for Macrob
« Reply #250 on: September 29, 2017, 06:45:39 pm »
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Guys how do you solve the following questions.

Find the equation of the circle with centre (2,-3) which touches the x axis.

Fidn the equation of the circle which touch the x axis, have radius 5 and pass through the point(0,8)



Thanks guys ;)

Eric11267

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Re: Tips for Macrob
« Reply #251 on: September 29, 2017, 07:01:37 pm »
+3
Guys how do you solve the following questions.

Find the equation of the circle with centre (2,-3) which touches the x axis.

Fidn the equation of the circle which touch the x axis, have radius 5 and pass through the point(0,8)



Thanks guys ;)
For the first question, you know the coordinates of the centre you just need to determine the radius. Since the centre is three unit below the x axis, for it to only touch the x axis, the radius would be 3.
So your equation would be (x-2)2+(y+3)2=32

The second question is a bit harder though.
Since you know it has a radius of 5 and touches the x axis, you know the centre is either 5 units above the x axis or 5 units below the x axis. But since it passes through the point (0,8) you can deduce that it is above the x axis.
So you know the centre of the circle has a y coordinate of 5 and a radius of 5 and passes through the point (0,8). Because it is a circle, the distance from the centre to any point on the circle will be the radius. So you know the distance from the centre to the point (0,8) will be 5.

Let a be the x coordinate of the centre, giving you the two points (a,5) and (0,8). Using the distance formula this gives you:

This gives two circles which have centres of (-4,5) and (4,5), giving you two equations;
(x-4)2+(y-5)2=52 or
(x+4)2+(y-5)2=52

Hope this helps :)

Jessica1231

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Re: Tips for Macrob
« Reply #252 on: September 29, 2017, 07:10:02 pm »
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For the first question, you know the coordinates of the centre you just need to determine the radius. Since the centre is three unit below the x axis, for it to only touch the x axis, the radius would be 3.
So your equation would be (x-2)2+(y+3)2=32

The second question is a bit harder though.
Since you know it has a radius of 5 and touches the x axis, you know the centre is either 5 units above the x axis or 5 units below the x axis. But since it passes through the point (0,8) you can deduce that it is above the x axis.
So you know the centre of the circle has a y coordinate of 5 and a radius of 5 and passes through the point (0,8). Because it is a circle, the distance from the centre to any point on the circle will be the radius. So you know the distance from the centre to the point (0,8) will be 5.

Let a be the x coordinate of the centre, giving you the two points (a,5) and (0,8). Using the distance formula this gives you:

This gives two circles which have centres of (-4,5) and (4,5), giving you two equations;
(x-4)2+(y-5)2=52 or
(x+4)2+(y-5)2=52

Hope this helps :)
Thaaaaank you soooo much! Can you also help me with this one?
Find the equation of a circle which passes through the points A(0,2), B(2,0) and C(-4,0)

Shadowxo

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Re: Tips for Macrob
« Reply #253 on: September 29, 2017, 07:17:17 pm »
+3

Great answer by Eric :)
Another way to do it, is by using the formula for the circle again. As you know the centre is (a,5) and the radius is 5, you can write the equation of the circle as
(x-a)2+(y-5)2=25
Subbing in (0,8) you get
a2+9=25
a2=16
Which results in the same answer as Eric got


Thaaaaank you soooo much! Can you also help me with this one?
Find the equation of a circle which passes through the points A(0,2), B(2,0) and C(-4,0)

You have two useful points (2,0) and (-4,0). From this you can deduce that the centre has an x value between these two points (as they have the same y value). So h=(2-4)/2 = -1
From this the equation of the circle is
(x+1)2+(y-k)2=r2
Sub it a couple of these points to get the values of k and r
« Last Edit: September 29, 2017, 07:26:44 pm by Shadowxo »
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Phoenix11

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Re: Tips for Macrob
« Reply #254 on: January 08, 2018, 10:59:10 am »
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Hello guys!
I was wondering if anyone knew how to solve this question?
Find the values of p for which the equation px2+2(p+2)x+p+7=0 has no real solution.
Thank you so much guys!
Phoenix11-
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