All Answers 356371 Answers

An isosceles triangle with equal sides of 5 inches and a base of 6 inches is inscribed in a circle. What is the distance between the center of the circle and the base?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

BC = 5      MC = 3         BN = 2.5

BM = sqrt(5² - 3²)

BM / BC = BN / BO        BO = 3 ¹/₈

OM = BM - BO = ⁷/₈

Midpoint :   Add the  x values and divide  by 2.....Add the y values  and  divide by 2....so we have

[  ( 8 + 2)  / 2   ,  ( 15 + 3)   / 2  ]  =

[   10  / 2 ,   18 / 2  ]

(  5 , 9  )

Sum of midpoint coordinates  =  14

Maybe CPhill figured the host team was preset.  I think that this is a reasonable assumption.

Obviously if it is not pre-set you would need to multiply the answer by 4.

Just as GA says.

Derek actually had given CPhill a point Ginger .....   CPhill didn't give himself one...

10xy  + 14x  +  15y  =  183         add  21  to both sides

14x  + 10xy  +  15y  + 21   =  183 +  21        factor  the  left  side, simplify the right

(2x  + 3) ( 7 + 5y)   =   204

If   x  =  7    and  y  =   1      we  have  that

(17)  (12)  =  204

So

x  +  y    =   7   +  1    =    8

f ( x ) = 7 csc ( x / 2 ) - 2

CPhill’s solution is incomplete; it does not include the number of ways to select the host team.

GA

Your hyperbolic gratitude is interesting; especially since you didn’t bother to give CPhill a point.

GA

Derek actually had given CPhill a point Ginger .....   CPhill didn't give himself one...

OOPS ... The hyperbolic gratitude is still interesting, though.   

NP, catmg....I'm  just glad  you found  the original problem....!!!!

The  series   is

1   5    17   53    161    485     1457    4373   

Just   two terms

80% = .8

.8 * 30 = 24

=^._.^=

Oh oops, I didn't realize it was a different problem. 

But the same solutions still apply. :))

Distance formula is so smart. 

=^._.^=

This isn't EXACTLY  the  same  problem, but  you  can use  the  answer that catmg  referenced   to  find  the  distance  between  the center of  the  circle  and the  base  as

sqrt  ( 3.125^2  - 3^2)  = 

0.875  units

I just thought of a nice different solution, so I'll post it here. :))

I'm going to refrence Melody's graph since I'm not sure how to make my own yet. 

Note than if you split this triangle in half, you get a 3, 4, 5 traingle. 

Let's call the radius r. 

The point (3, 4) a. 

The point (0, 0) b. 

The point (6, 0) c. 

The point (3, 0) d. 

And the center C. 

Since aC = r, Cd = 4 - r. 

bC = r too. 

ad = 3. 

By pythagreon

(4-r)^2 + 3^2 = r^2

r^2 - 8r + 16 + 9 = r^2

8r = 25

r = 25/8

=^._.^=

THX, catmg.....I didn't even remember  this one   !!!!

If  the halfway point  fan  travels   90 in  in 2 min.....then  it  must travel  45  in  in one minute

So  we  can  find  the  radius  of  this "smaller "  circle  that  the  halfway  point travels through as

45  =  80 * 2pi  *  r

45   =  160 pi  * r

45 / ( 160 pi)  =  r    =  9/ (32 pi)  in  

And  a point  at  the  outer  edge  must  travel   on  a  circle  with  a radius of  twice  as much  =  9 / (  16 pi)  in

So.....the  total  distqance  that this point  travels in  30 min =

(No. of  revs in 30 min) * ( 2 pi )  * (r)  =

30 ( 80)  ( 2pi)  ( 9 / (16 pi) )   =   2400  * 18  * (9/16)   =    2700  in

Melody, CPhill, and Tigsy already did an amazing job answering this problem. :))

https://web2.0calc.com/questions/math_51432

=^._.^=

y  =  ab^x        (0 , 6)   is on  the  graph

So

6  =  a b^0

6 =  a (1)

6  = a

And ( 1,9)  is  on  the  graph....so.....

9 =  6 * b^1

9  = 6 b

b  = 9/6  =  3/2

The  function  is

g(x)  =  6 * (3/2)^x

Number  of   unique  sequences   =    number  of  words of  length  n  composed of  letters  A, B or  C 

                                 n !

__________________________________________________

(occurences of A) ! * (occurences of B) ! * (occurences of C) !

  Riyan has 6 erasers 

and Darius has 6 * 8 = 48 erasers

Hence solved Darius has 48 erasers.

Solution

Let Riyan has x erasers, then Darius has 8x

According to question,

 8x = x + 42

8x - x = 42

 7x = 42

   x = 6

: Riyan has 6 erasers 

and Darius has 6 * 8 = 48 erasers

Hence solved Darius has 48 erasers.

cos  (C  + A)  =  cosCcos A  -  sinC sinA

cos A  =    0

sin C =   1

cos B   =  sin A

So

cos ( C  +  A)  =  0  -  (1)(3/5)  =    -3/5   =  - .6

d = 9j

d-12 = j + 12   sub in the red equation

9j -12 = j + 12

8j = 24

j = 3                  so j had 3 to start with...then gets 12 and has  15 ....they BOTH now have 15   for a sum total of 30 shells

The  total  perimeter   of  the  shaded  region   is  just  the  sum  of the  perimeters  of both  circles  =

2pi [ 3  +  6  ]   =

18  pi    inches

Sorry....I  should  have  written  the  exponent  as  ( 1 * 2)   rather  than (2 * 1)

Same  answer however

Yeppers......!   I didn't actually work through to a solution....   must be a wording error in the Question somewhere....

   I have seen several erroneous problems lateley    ~EP