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Find two convinient points on the line to calculate the equation of the line as

  1/2x  - 1/2       the shaded area is GREATER than this line AND does NOT include the line itself

y > 1/2x - 1/2

You have about 50 candidates for your 2 numbers. Just reverse the digits of any of these 50 numbers.

 501  511  521  531  541  551  561  571  581  591  602  612  622  632  642  652  662  672  682  692  703  713  723  733  743  753  763  773  783  793  804  814  824  834  844  854  864  874  884  894  905  915  925  935  945  955  965  975  985  995  Total = 50

complete the square on 'x'     (take 1/2 of 'x' coefficient ....square it and fill in the blank

x^2 +22x + 121    = (x+11)²

Need diameter of cable   (or radius)

From 1st equation  y = 20 - 2x     sub this into 2nd eqaution

x^2 + x (20-2x) =47

-x^2 +20x - 47 = 0              quadratic equation shows x =   10 +-sqrt 53

sub into one of the equations (the first is easiest ) to find y = -2sqrt53    when x = 10 + sqrt 53

                                                                                   and y = 2 sqrt53    when x = 10 - sqrt53

tysm

figured it out nvm

         x(10 - x)  =  40

         10x - x²  =  40

       -x² + 10x  =  40

-x² + 10x - 40  =  0

 x² - 10x + 40  =  0

Quadratic formula with   a = 1   b = -10   c = 40

x  =  [ -(-10) + sqrt( (-10)² - 4(1)(40) ] ( 2(1) ]

   =  [ 10 + sqrt( 100 - 160 ) ] / 2

   =  [ 10 + sqrt( -60 ) ] / 2

   =  [ 10 + 2sqrt(-15) ] / 2

   =  5 + sqrt(15)·i

Other answer:  5 - sqrt(15)·i

Use the distance formula:  d  =  sqrt( (x₂ - x₁)² +(y₂ - y₁)² )

--->   10sqrt(2)  =  sqrt( ( 4 - x )² + ( 7 - 21 )² )

Square both sides:

--->   200  =  (4 - x)² + (-14)²

--->   200  =  (4 - x)² + 196

--->       4  =  (4 - x)² 

Find the square root of both sides:

--->     4 - x  =  2          or          4 - x  =  -2

                x  =  2                             x  =  6

Etc. ...

E P I C :D

Let  A₁·A₂·A₃· ...  =  X

Square both sides:

     ( A₁·A₂·A₃· ... )²  =  X²

      (A₁)²·[ (A₂)²·(A₃)²·(A₄)²· ... ]  =  X² 

But:  (A₁) = 3     (A₂)² = A₁     (A₃)² = A₂     (A₄)² = A₃  

So:  (A₁)²·[ (A₂)²·(A₃)²·(A₄)²· ... ]  =  3·[ A₁·A₂·A₃· ... ]  =  X²  

and:  A₁·A₂·A₃· ...  =  X   --->         =  3·[ X ]  =  X²     --->   3  =  X

So, the product is 3.

Solve for x:
x + 1/x = 1

Bring x + 1/x together using the common denominator x:
(x^2 + 1)/x = 1

Multiply both sides by x:
x^2 + 1 = x

Subtract x from both sides:
x^2 - x + 1 = 0

Subtract 1 from both sides:
x^2 - x = -1

Add 1/4 to both sides:
x^2 - x + 1/4 = -3/4

Write the left hand side as a square:
(x - 1/2)^2 = -3/4

Take the square root of both sides:
x - 1/2 = (i sqrt(3))/2 or x - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:
x = 1/2 + (i sqrt(3))/2 or x - 1/2 = -(i sqrt(3))/2

Add 1/2 to both sides:

x = 1/2 + (i sqrt(3))/2   or   x = 1/2 - (i sqrt(3))/2
 [1/2 + (i sqrt(3))/2]^1000 + 1/ [1/2 + (i sqrt(3))/2]^1000 = - 1  

You have 5 distinct combinations. 
(1,2,2,3),  (1,2,3,3),  (1,3,3,3),  (2,2,3,3),  (2,3,3,3)
Each combination has the following number of permutations: [4!/2! + 4!/2! + 4!/3! + 4!/2!2! + 4!/3!]=12 + 12 + 4 + 6 + 4 = 38 permutations.

got it

Need the image ! 

Find the maximum value of the function f(x) = -3x^2 + 9x + 7.

Hello Guest!

The extremes of a function are at the zeros of the 1st derivative of the function.

\(f(x) = -3x^2 + 9x + 7\\ \frac{df(x)}{dx}=-6x+9=0\\ x_{max}=1,5\)

\(y = -3x^2 + 9x + 7\\ y=-3\cdot 1.5^2+9\cdot 1.5+7\)

\(y_{max}=13.75\)

\(P_{max}(1.5,\ 13.75)\)

  !

Looking for the hypotenuse (wire) of a right triangle with legs   210   and 100 m

210² + 100²  =  wire²

wire length = 232.59       then they want you to add 1 meter to this  and round = ...........

This is a dome shaped parabola due to the   negative leading coefficient

the 'x' value of the vertex will be found by   - b/2a     where b = 9   and a =-3

use this value of 'x' in the equation to find the 'y' value of the vertex which will be the function's maximum value.....

 Hi! Please stop! We already told you on ur last post! PLEASE! YOU ARE WASTING OUR TIM! AND EVEN URS TOO!

AZ580 =For A you have 26 letters  x Z also 26 letters x 9 choices for first number x 10 choices for the 2nd x 10 choices for the 3rd  = 26  x  26  x  9  x  10  x  10 =608,400 plates possible.

Midpoint = (-4,6)

Slope = (4 - 8)/(-3 - 5) = 1/2

Perpendicular bisector: y - 6 = -2(x + 4) = -2x - 8

==> y = -2x - 2

m + b = -4

Guest #2: You started OK, but I think you went astray towards the end. The geometric mean is 1/99th root of the products of all the terms of the sequence (when multiplied together). So, based on that, this is what I got as the "geometric mean" of the 99 terms of this sequence:

productfor(n, 0, 98, (717897987691852588770249/140737488355328)*(2/3)^n=(6.901497877 E+106)^(1/99)=12  - which is the geometric mean of the 99 terms of this sequence.

Yes, please stop because it is wasting others time! Please ask questions that can be answered at please, please don't do what the Guest just did! 

s=1;a=1;listfor(i, 1, 25,s=(2#(3)) * 2#s

OUTPUT =(1.732050808, 2.279507057, 2.615056629, 2.800923042, 2.898753029, 2.948942029, 2.974361459, 2.987153223, 2.99356972, 2.996783135, 2.998391136, 2.99919546, 2.999597703, 2.999798845, 2.999899421, 2.99994971, 2.999974855, 2.999987427, 2.999993714, 2.999996857, 2.999998428, 2.999999214, 2.999999607, 2.999999804, 2.999999902) =It converges to 3

A formula for the area of a parallelogram is:  Area  =  a · b · sin(C)

For it to apply in this situation, we need the size of angle B:  angle(B)  =  180^o - angle(A)  =  135^o.

Area  =  10 · 14 · sin(135^o)  =  ...