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With dimensional analysis:

Total hours needed   =   5 p x 6 hr/d x 16 d = 480 p - hr

480 p-hr /(8p 4h)/d   = 15 days

small circle area = pi r^2   is equal to Large circle area (pi L^2)   minus small circle area(pi r^2)

pi r^2  =  pi L^2 - pi r^2

2 pi r² = pi L²

2 r² = L²

2 = L² / r²

sqrt2 = L / r

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Hi there...

If you know that "(a+b)=84".

And you know that "((a/2)-(b/3))" equals a difference of "12".

You could then say that "(a/2)=((b/3)+12)".
Which equals "24" on both sides.
That in turn means that​ if "(a/2)" equals "24" then "a" must equal "48".

And if "(a+b)=84", that means that "b=(84-48)" equals "36".
 

Just to do a quick check...

"((a/2)-(b/3))" = "((48/2)-(36/3))"
That should equal "12", if not check your math.

Because if "((a/2)-((b/3)+12))" is correct, that in turn means that "((48/2)-((36/3)+12))" should equal "0".

I hope that helped a bit?


Kind regards
BizzyX


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Yeppers....

Right triangle    hypotenuse = l    (length of ladder)      base leg = l-20    height leg = l-10

Pythgorean theorem

(l-20)² + (l-10)² = l²       Expand, simplify to

l²-60l+500 = 0      Quadratic formula yields    l = 50 ft   or 10 (throw out)

The Height leg =  l-10 = 50 - 10 = 40 ft

   = 1  +  5  +  15  +  35     = 56

x+ 3y = -5      find slope, m when in the form   y = mx+b

3y = - x -5

y = -1/3 x  - 5/3        slope = -1/3    as is the parallel slope

y = -1/3 x + b

2  = -1/3 (-7) + b

2 = 7/3 + b

-1/3 = b

y = -1/3x  - 1/3          re-arrange to   'Ay + Bx = 3'   form

y + 1/3x  = -1/3

-3y -x = 1                  

-9y-3x=3         B-A   then equals  -3 - - 9   = +6

Solve for x:
x^2 = (x - 20)^2 + (x - 10)^2

Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
x^2 = 2 x^2 - 60 x + 500

Move everything to the left hand side.
Subtract 2 x^2 - 60 x + 500 from both sides:
-x^2 + 60 x - 500 = 0

Factor the left hand side.
The left hand side factors into a product with three terms:
-(x - 50) (x - 10) = 0

Multiply both sides by a constant to simplify the equation.
Multiply both sides by -1:
(x - 50) (x - 10) = 0

Find the roots of each term in the product separately.
Split into two equations:
x - 50 = 0 or x - 10 = 0

Look at the first equation: Solve for x.
Add 50 to both sides:
x = 50 or x - 10 = 0

Look at the second equation: Solve for x.
Add 10 to both sides:

x = 50        or             x = 10{Discard}

x  = 50 feet - length of the ladder.

50 - 10 = 40 feet - The height of the side of the building to the top of the ladder.

50 - 20 =30 feet - The distance from the foot of the ladder to the wall.

excuse me why does this just happen to be a question in the aops homework? In high school math contest? Problems 3 and 4?

50 mach * 50 min /50 book   = 50 mach-min/ book

50 mach-min / book   / 20 mach       *  20 book    =   50 min

1.    If you draw a Venn diagram, you will see 244 in only  band     161 in only orchestra      73 in both   122 neither

       out of 600                               244 /600  + 161 /600  = 405/600    =   27 /40

so the range is [4, inf) ?

That's funny, because it's an anonymous guest who is saying it. 

_.

KC.  I don't believe anybody doesn't know what the Super Bowl is, even people outside the US.

If you take these terms as your geometric progression:       2, 6, 18                       [a = 2, r = 3]

and you take these terms as your arithmetic progression:  -2, 2, 6, 10, 14, 18      [a = -2, d = 4]

then the 2nd, 3rd, and 6th terms of the arithmetic progression are the three consecutive terms of the geometric progression.

What's the Super Bowl?(Seriously, what is it?)

What is the units digit of the sum of the squares of the first 2007 odd, positive integers?

1^2=1

3^2=9

5^2=25

7^2=49

9^2=81

1+9+5+9+1 ..... 25

last digit of the sum of the squares of numbers lesss than 10 = 5

2000/10=200

200*5=1000

so

1+9+25 = 35

Thge last digit will be 5

I put the answer into Wolfram|Alpha and it says the answer is 2.

If

f(x) =x^9+1      is divided by   x-1   then the remainder will be f(1)

Sorry, I have had an error pointed out to me.

f(1)= 1^9+1 = 2

therefore the remainder will be TWO.

Just like you though.

Get the quotient using long division.  

Guest is right about the fractional part.

If you beleive everything that people, especially anonymous guests, tell you on the internet then you are as stupid as they are.

Are you the guest that has been putting garbage one liners all over the forum?

I can give you a hint: try expressing one of the lengths as a variable and try to find the other two lengths in term of your variable. Then what can you do?

Just evaluate them one by one and should get:

 =56

1- I count 1891 numbers which have at least 1 two.