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Hi, asinus! As a matter of fact, there are two solutions; here they are:    ( see diagram )

1)    In both cases, the red line is tangent to all 3 circles.

2)    Both circles, C and D are the tangents to circles A and B.

3)    The red line intersects line AB.

R = 6.75            r = 3.375   

-b /2a  = 2         where b = 'a'    and   a = 2

- a /4 = 2

a = -8

2x^2 -8x+b    = -5   when x = 2

8 - 16 + b = -5

b = 3

Please... DO NOT post questions more than once !!!!!!!!!!!!!!!!

https://web2.0calc.com/questions/still-need-help_1

1 meter = 39.37 inches = 1.0936132 yard

 $ 29.95 / m^2    *   1 meter /1.0936132 yd  * 1 meter / 1.0936132 yd  = $ 25.04/yd²

^{Now you can see which costs less...}

31 people have to shake hands with 30 other people 

31 * 30 = 930     BUT each handshake involves TWO people , so divide that number by 2    = 465 handshakes  ( as gs found below)

If x = 2017 and y = 1/2017, then find

 \(\large \left(\frac{\frac{x}{y}+2}{\frac{x}{y}+1}+\frac{x}{y}\right)\div \left(\frac{x}{y}+2-\frac{\frac{x}{y}}{\frac{x}{y}+1}\right) \)

Hello Guest!

\(\large \left(\frac{\frac{x}{y}+2}{\frac{x}{y}+1}+\frac{x}{y}\right)\div \left(\frac{x}{y}+2-\frac{\frac{x}{y}}{\frac{x}{y}+1}\right) \)

=\(\large \left(\frac{2017^2+2}{2017^2+1}+2017^2\right)\div \left(2017^2+2-\frac{2017^2}{2017^2+1}\right)\large \color{blue}=1 \)

  !

Three balls would require    a box that is square on the ends    w   and h = 4.4 cm

    the length of the box would be    3 * 4.4

so volume would be     4.4   x 4.4   x  3 * 4.4   cm³

now calculate the actual volume of the THREE balls     sphere volume = 4/3 pi r³         remember there are THREE and the RADIUS is 1/2 diameter...

   subtract the volume of the three spheres from the red equation....

In the original post, there was this equation:  

   x² + 2xh + h² + y² + 2yh + h²  =  x² + h² + 2ab + y² + h²

Subtract x², h², y², and h² from both sides and you are left with:  2xh + 2yn  =  2ab

40m = ___________yds = __________ft

Hello Guest!

\(40m\times\frac{yd}{0.9144m}=43.7445\ yds\times\frac{3fts}{yd}=131.2336fts\times\frac{12inch}{feet}=1574.8031\ inch\)

   !

I asked for how CPhill got that expression...

Can anybody else help?

The formula for number of handshakes is n(n-1)/2 where n is the number of people. Plug 31 for n into the equation.

n(n-1)/2

=31(31-1)/2

=31(30)/2

= 465 handshakes

Let a be the tens digit and b the ones digit. Then the two digit number is 10a+b. We then know that 10a+b+a+b=50. Simplifying, we get 11a+2b=50. Using guess and check, a must be 4 and b 3. Therefore the two digit number is 43.

if we plug in 1 into this we can find the sum of all the coefficents which is 3^16 and if we plug in -1 into the equation we have the same thing except that the odd terms are negitive becasue -1 to the power of any odd term would make it negitve and even makes it even, and plugging in -1 we get 2^16 now add these values together we get what we want multiplied by 2 so then we divide it all by to giving us the answer: (3^16+2^16)/2 you can do that complicated part on your own .

Your age now =A
Father's age now =F
F - 10 =8*(A - 10)
A / (F - 10) =7 / 16, solve for A, F
A = 14 years - your age now
F = 42 years - Your father's age now.

Grandpa =32 + 21 + 10 =63 years - his age now.

14 + 42 + 63 =119 years - your combined ages !.

The approximate conversion from miles to kilometers is 1.609. Multiply 150 by 1.609 to get 241.35, which rounds to the nearest whole number 241. Therefore the speedometer reads 241 km/h.

Since there are 1000 m in a km, there are 1000 x 26  =  26 000 m in 26 km

Since there are 60 sec in a min, there are 60 x 15  =  900 sec in 15 min

Since there are 60 x 60 = 3600 sec in an hour, there are 3600 x 3  =  10 800 sec in 3 hr.

There will be  900 sec + 10 800 sec  =  11 700 sec in 3 hr 15 min.

average speed  =  26 000 m  /  11 700 sec  =  2.22  meters per second

x + ay + 1  =  0   --->   ay  =  -x - 1   --->   y  =  (-1/a)·x - (-1/a)   --->   slope  =  -1/a

2x - by + 1  =  0   --->   -by  =   -2x - 1   --->   y  =  (2/b)·x + (1/b)   --->   slope  =  2/b

Since the above two lines are perpendicular, their slopes are negative reciprocals

   --->   -1/a  =  -b/2   --->   a  =  2/b   

x - (b - 3)·y - 1  =  0   --->   -(b - 3)·y  =  -x + 1   --->   (b - 3)·y  =  x - 1   --->   y  =  ( 1/(b - 3) )·x - 1/(b - 3)

   --->   slope  =  1/(b - 3)

Since this line is parallel to the first line, they have equal slopes:  -1/a  =  1/(b - 3)   --->   3 - b  =  a

Combining   a  =  2/b   with   3 - b  =  a   --->    3 - b  =  2/b   --->   3b - b²  =  2   --->   b² - 3b + 2  =  0

   --->   (b - 2)(b - 1)  =  0   --->   either   b = 2   or   b = 1

If  b = 2   --->   a  =  2/b   --->   a  =  2/2  =  1

If  b = 1   --->   a  =  2/b   --->   a  =  2/1  =  2

Let your mother's age now = M
Let your age now =A
M - 7 =7*(A - 7),
(M+8) =2*(A+8). solve for A, M
A = 10 years - your age now
M = 28 years - your mother's age now.

tan(40^o)  =  CD / AD     --->     tan(40^o)  =  CD / 10     --->     CD  =  10 · tan(40^o)

tan(30^o)  =  BD / AD     --->     tan(30^o)  =  BD / 10     --->     BD  =  10 · tan(30^o)

Use a calculator to find the lengths of CD and BD and then add those two lengths together.

Convert 4,590,000cm to kilometers
4,590,000/100 cm/1000 meters=45.9 kilometers
So now, the scale on the map is =1 cm =45.9 km
Convert inches to cm:
1 inch =2.54 cm
2 3/8 inches * 2.54 cm =6.0325 cm - the distance between Calgary and Edmonton on the map.
Every 1 cm on the map =45.9 km on the ground.
So:6.0325 cm on the map * 45.9 km on the ground =276.89175 =~277 km - the ground distance between Calgary and Edmonton.

1 mile  =  5280 feet

A quarter mile has  5280 feet / 4  =  1320 feet

1 foot has 12 inches.

1320 feet  =  1320 feet x 12 inches per foot  =  15840 inches

1 meter  =  39.37 inches

400 meters  =  400 meterx x 39.37 inches per meter  =  15748 inches

You can finish it from here ...

See the solutions here:

https://web2.0calc.com/questions/please-help-question-not-answered [Max's Answer]

 https://web2.0calc.com/members/alan/?answerpage=751 [Alan's Answer]

Thanks for the help!!

Sorry but I don't understand how you got identity 3. The first two i reconize but the third one looks new to me, can you explain it or derive it please?

Oh but thanks for answering my question