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@@ What is Happening?  [Wrap4]   Sun 22/11/15   Sydney, Australia Time 10:38 pm   ♪ ♫

Hi,

Our great answers today were provided by CPhill, Will85237 the Riddler and guests. Thanks you  

Interest Posts:

If you ask or answer an interesting question, you can private message the address to me (with copy and paste) and I will include it.  Of course only members are able to do this.  I quite likely will not see it if you do not show me.  

1) How do members score points and edit posts?      Thanks for asking Riddler  

http://web2.0calc.com/questions/points_1#r6

2)  Riddler invites you to post fun-facts.  Thanks Riddler  

Can you add to the fun facts. ??

Another very nice answer Chris :)

You are becoming an expert at using GeoGebra    -:))

these geometry questions that Mellie is presenting are really fun. :)

Nice answer Chris   

This is so cool! Thanks Will85237 for answering the question it really helped me!

The length of a rectangle is 3 cm more than the width. If the width is increased by 2 cm and the length is decreased by 1 cm, the figure becomes a square with an area of what number is meant to be here? sq. cms. What is the original perimeter of the rectangle?

1.) A 10 x 18 meter garden plot has a uniform path around it.Walking around the path, a boy found that it was 80 meters. How wide is the walk?

Draw the garden plot. put the lengths on the sides

Draw the path.

4 sections of the path (the outer edge of the path)  have the same lengths as the garden, only the corners are different.

Each corner will have an added length of x units by x units. Look at your diagram and see if you can understand what i am referring to.

Maybe you can take it from there?  Let me know how you get on :)

2.) The length of a picture is 4/3 times its width. It is placed in a picture frame of uniform width of 2 cms, what are the dimensions of the picture?

I do not understand this question ://

In an isosceles triangle, the length of one of the two equal sides is 3 less than 4 times the third side. If the perimeter of the triangle is the same as the perimeter of a 144 sq. cms. square, what are the lengths of the sides of the triangle?

This is very similar to the one i just did:/

Th only real difference is that you need to also find the perimeter of a sqare of area 144 cm^2 

How would you do that?

What is the formula for the area of a square?

When you do the triangle, draw a little pic, it will help you think more clearly.

Let me know how you get on :)

Hi Mashiro, welcome to the forum, it is nice to meet you. :)

In an isosceles triangle, the length of one of the two equal sides is 3 less than twice the third side. If the perimeter of the triangle is 19 cms, what is the length of each side?

Let the different side be x units long

The equal sides are both      2x-3   units long

The perimeter is 19

so

19=  x+  2x+3   +   2x+3

Can you finish it?

Are you answering your own questions?   LOL       

Hi :)

Why does A=p(1+(r/n))^nt give me the correct answer when compounding interest annually, weekly, etc, but A=p(r)^nt only works annually?

The first formula is what I remember from previous years, and the second is what my book gives me to solve.

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I don't think that the second forumuar is correct, not for compound interest anyway.

Sometimes you see A=p(1+r)^n 

If you take this as meaning r= annual interest rate as a decimal and n is the number of years invested then it is only good for annual investments.  It is often used this way when students are first introduced to compound interest.

----------------------------

Your other formula is just a general purpose formula that can be used for any compounding periods.

If you really understand what you are doing then you may just like to use this formula   A=p(1+r)^n 

BUT r must be the rate for the compounding period (not the yearly one) and n must be the number of compounding periods (not tne number of years)   

The number of compounding periods is always going to be the number of years times the number of times interest is added each year which is called  nt in your original formula 

AND

the interest rate is always going to be the number of years divided by the number of times interest is added each year. which is called n/t   in your original formula.

That is how I think of it. 

However,

if you are really comfortable with your original formula      p(1+(r/n))^nt       you should probably just keep using it. :)   

Does that make sense?

l=7, w=5

Hi  Mellie,

Can you say hello to me please and let m know how you are getting on.  

Also can you let me know if you understand please.

Have you already studied this stuff and the trigonometry from the last question too.

It seems very hard for you. (Hard for almost everyone.)  ://   

Let AB=6, BC=8, and AC=10. What is the area of the circumcircle of triangle ABC minus the area of the incircle triangle ABC?

I will draw the triangle on the number plane.  The vertices will be B(0,0)  C(0,8) and A(6,0)

I know it is a right angled triangle because 6,8,10 is a pythagorean triad.

I am going to find the equation of the circumcircle first.  That is the big one around the outside of the triangle.

Let the centre be Q(h,k) and the radius=R

QA=QB=QC=R

The equation of the circumcircle is  

\((x-h)^2+(y-k)^2=R^2\\ \)

\(QA^2=(6-h)^2+(0-k)^2\\ QA^2=36+h^2-12h+k^2\\ R^2=h^2+k^2-12h+36\qquad (1)\\\)

\(QC^2=(0-h)^2+(8-k)^2\\ QC^2=h^2+k^2-16k+64 \qquad (2)\\\)

\(QB^2=(0-h)^2+(0-k)^2\\ R^2=h^2+k^2\qquad(3)\)

\(\mbox{Sub (3)  into (1)}\\ h^2+k^2=h^2+k^2-12h+36\\ 0=-12h+36\\ 12h=36\\ h=3\\ \mbox{Sub (3)  into (2)}\\ h^2+k^2=h^2+k^2-16k+64\\ 0=-16k+64\\ 16k=64\\ k=4\\ \mbox{The centre of the circumcircle is (3,4)}\\ R^2=3^2+4^2=25\\ R=5\\ Area = \pi*25 \)

Now lets look at the incircle

Let the centre be Z

The distance from Z to the x axis = distance of Z to the y axis = p

So the centre of the incircle must be Z(p,p) and p must also be the radius of the incircle.

Now I need the equation of line joining A(6,0) and C(0,8)

The gradient = -8/6 = -4/3   and the y intercept is  8

So the equation of the line is

y=(-4/3)x+8

3y=-4x+24

4x+3y-24=0

Now I need the perpendicular distance from    (p,p)   to the line    4x+3y-24=0

and I know that this distance is equal to p

I will use the perpendicular distance formula.

\(p=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2}}\\ p=\frac{|4p+3p-24|}{\sqrt{4^2+3^2}}\\ p=\frac{|7p-24|}{5}\\ 5p=|7p-24|\\ 5p=7p-24 \qquad or \qquad 5p=24-7p\\ -2p=-24 \qquad or \qquad 12p=24\\ p=12 \qquad or \qquad p=2\\ \mbox{But p must be less than 6 so p=2}\\ \mbox{So the centre of the incircle is (2,2) and the radius is 2}\\ \mbox{The area of the incircle is }\pi*4\; units\; squared\)

So the area between the circumcircle and the incircle is

\(Area=25\pi-4\pi\\ Area=21\pi\;\;units \;\;squared\)

Here is the pic.   

I did not know that!

Did you know that the neck of a giraffe has exactly the same number of cervical vertebrae (neck bones) as a numan neck has.

That is SEVEN.

BUT

In a giraffe each one is TEN INCHES long.

How about that !!

Because you making some mistake somewhere! If you give us the numbers you are trying to calculate, then will show you where your mistake is.

Here's 6

1.   angle  XUW  = angle 1  = 90                                      given

2.   angle XUY   = 180                                                      XUY  is a straight angle = 180 

3.  angle XUY =  angle YUW + angle XUW                      angle addition theorem

4.  angle XUY - angle XUW  = angle YUW                      subtract angle XUW from both sides of 3

5.  180  -  90     = angle YUW                                           substituting 1 and 2 into 3

6.  180  =   angle YUW + 90                                              add 90 to both sides of 4

7.  180  =  angle 2  +  90                                                    angle YUW =  angle 2

Sorry, I meant to say the "average".  Given that, try and see if you can get the answers that Melody got. But, you must give the methods used. Good luck.

Guest #1  .... you never said the deposits could not be greater than 100000/5 !   In fact , the answer requires it !   D'oh!

"x" is someone who took you for all you were worth.....and the Kidz.....

Here's 5

1.     angle 1  = angle 3                                                                               given

2.   angle JOK  = angle LOM                                                                      given

3.  angle JOK + angle KOL  = angle KOL +  angle LOM                        add angle KOL to  each side of 2

4.  angle JOL       =   angle  KOM                                                          angle addition theorem

Here's 4

1.   angle 1 + angle 2  = 90                                                     given,  defintion of complementary

2.   angle 3 + angle 2  = 90                                                    given,  definition of  complementary

3.   angle 1 + angle 2  = angle 3 + angle 2                             equating 1, 2 with substitution

4.   angle 1 = angle 3                                                              subtract angle 2 from both sides of 3

Here's the way I'd do 3......

1.   angle  XUY  = 180                                                 XUY  is a straight- angle

2.   angle XUW + angle YUW  =                                 angle addtiton theorem

      angle XUY

3.   90  +  angle YUW  = 180                                      substitution, angle XUW = angle 1  = 90

4.   angle YUW = 180 - 90                                           subtract 90 from both sides of 3

5.  angle YUW  =  90  = angle 2                                   simplification  of 4    

If Jack is not sharing his chips then the FOUR get ZERO and Jack gets SIX !!!   Way to play Jack!

....but....I don't know Jack !

~jc

If Jack is not sharing his chips then the FOUR get ZERO and Jack gets SIX !!!   Way to play Jack!

....but....I don't know Jack !

= 3     Sometimes  more if you are using fertility drugs.

Could be cancer or an abcess...or just a cavity.... you should ask your dentist.