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S_∞  = a₁ / (1-r)

 25 = a1 /(1-1/3)

25 * 3/2 = a1   = 37.5    Not possible (already greater than the sum)       ratio must be   MINUS 1/3

S = a1/(1 - -1/3)

25 * 3/4 = a1 = 75/4         75/4 (-1/3) = -75/12   is the second term   (- 6.25)

We place 50 volts across this wire and measure 300 milliamps of current THROUGH the wire  

                                                                       (Voltage does not go THROUGH a wire....current does)

V = IR          50 = .3 (R)      R = 166 2/3 ohms           (300 mAmps =  . 3 Amps )

Cut wire in half    R₂ becomes 1/2 original   :        1/2 (166 2/3) = 83 1/3 ohms

WIth 800 V applied:

  V    =   IR

800  =   I *   83 1/3     I = 800/(83 1/3 )   = 9.6 amps     which is 9600 mAmps

(7x + a)(x+b)     

Now sub in for a and b the following pairs and compute the value of n     n =   7b +a

a            b                n

12        -1                 5

-1        12                 83

-12       1                  -5       etc

1         -12

2          -6

-6          2

-2          6

6          -2

3         -4

-4         3

-3         4

4         -3

what is 12x3   

The product is 36 of course.  Now here's one for you.  What is 2x4?  Answer:  a wooden board 

x+(x+12)=124

2x + 12 = 124

2x = 112

x = 56

=^._.^=

As follows:

Count them here:

\(\displaystyle 2^\frac{1}{2}=y^{\frac{1}{6}}\\~\\ \displaystyle \left(2^\frac{1}{2}\right)^6=\left(y^{\frac{1}{6}}\right)^6\\~\\ \displaystyle 2^3=y\\~\\ y=8\)

Find the minimum value of   3x^2-12x+16

and 

Find the minimum value of 2y^2+6y+9

and think about what you have  

Call x  the  number of $10   increases

We have that   

R =  (200 + 10x)  ( 40000  - 800x)

R = 8000000 + 400000x  - 160000x - 8000x^2   rearrange as

R = -8000x^2 + 240000x + 8000000

The  x that maximizes the  revenue is

-240000/(2 * - 8000)  = 15

So......the price that  maximizes  the revenue  is   (200 +10*15)  = $350

This is my take:

\((ab)^{-1}=2\mod n\\ \text{What does this even mean, well}\\ \text{the inverse of 7 is 1/7 because } 7*(1/7)=1\\ so\\ (ab)^{-1}*(ab)=1\mod n\\ 2ab=1\mod n\\~\\ (a+b)^{-1}(a^{-1}+b^{-1})\\ =\frac{1}{a+b}*(\frac{b+a}{ab})\\ =\frac{1}{ab}\\ \equiv 2\mod n \)

Coding:

(ab)^{-1}=2\mod n\\
\text{What does this even mean, well}\\
\text{the inverse of 7 is  1/7  because } 7*(1/7)=1\\
so\\
(ab)^{-1}*(ab)=1\mod n\\
2ab=1\mod n\\~\\

(a+b)^{-1}(a^{-1}+b^{-1})\\
=\frac{1}{a+b}*(\frac{b+a}{ab})\\
=\frac{1}{ab}\\
\equiv 2\mod n

Where do all your added numbers come from?

I know what the answer is. I answered first.

But neither of you 2 has said where any of your numbers come from.

Oh I get it.

You both arbitrarily chose angle AEG to be 90 degrees  AND angle EGB=45 degrees.

And you arbitrarily chose AB to equal AD

Only you didn't bother to explain that is what you were doing.

This does make it easier,

You do not need to approximate anything though.

If you let AB=x units and  CF=h units  then 

it is easy to work out that h=sqrt6,   and x=sqrt(8/3)

And then that blue area = 8 units squared.

V(e) =Sqrt[2GM / R]

V(e) =Sqrt[(2 x 6.67 x 10^-11 x 5.8 x 10^24) / (6.6 x 10^6)]

V(e) =10,827 m/s =~10.827 km/s - escape velocity of this planet.

Angle AED's  sum of its intercepted arcs  =    AB  +  BC +  DC

Angle DCB's  sum of its intercepted arcs =  ED + AE  +  AB

So ,  combined,  they intercept  arcs of    2AB  + AE  + ED +  DC  +  BC

2AB   = 360°  

AE + ED + DC  + BC  =  180°

So   their combined measures =  (1/2) ( 360 + 180)  =  (1/2) (540)  = 270°

If I'm not mistaken, the answer is:  A / [XYZ] = 851/999

Similar question:  https://web2.0calc.com/questions/help_54234#r3

Call the roots a, b

The sumof the roots   = a +  b  =  3/2

Square this

a^2 + 2ab + b^2    = 9/4

The product of the  roots =  ab =   27/2  ⇒    2ab  =  27

So 

a^2  + 2ab  +  b^2  =   9/4

a^2  + 27  + b^2 =  9/4

a^2  + b^2   =  9/4  - 27  =    2.25  - 27   = -24.75

A sector with a radius of 10 and a central angle of 45º is to be made into a right circular cone. Find the volume of the cone.

("central angle of 45º "   means that a sector of 45º is cut out and the remaining (larger) sector is used to make a cone.)

Circle radius = 10      (this is also the slant height of a cone)

Cone radius = 10(315/360)     r = 8.75

Cone height     h = sqrt(10² - 8.75²) = 4.841229183

Cone volume      V = pi * r² * h/3        V ≈ 388.15 square units

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

The question calls for the right cone; let's check if it's a right cone.

10² = 8.75² + 4.841229183²

100 = 100    correct!!! 

We can write  l x l  as   sqrt (x^2)

So....this implies that....

sqrt  [ ( (2 -  sqrt (x^2) )^2  ]     =  1          square both sides

( (2 - sqrt (x^2))^2     =   1         simplify

4 - 4sqrt (x^2)  +  x^2    = 1

x^2 +  3  =  4sqrt (x^2)            square both sides again

x^4  + 6x^2   + 9  =  16x^2

x^4  - 10x^2 + 9   =   0       factor

(x^2 - 9) ( x^2 - 1)   =  0

x^2  - 9   =  0            x^2  -1  = 0

x = 3 , -3                   x =  -1, 1           which  are the values  found  by the guest   !!!

Each  successive year, the car is worth 1 - .0675    = .9325  = 93.25 %  of what it was worth the previous year

After 9 years, the value is    22400 (.9325)^9    =  $11942.29

Pentagon ABCDE is inscribed in a circle with a center at O and diameter AB. Find the measure of angle AED + angle DCB in degrees.

∠AED + ∠DCB = 270 degrees

Call the intersection of  XW  and VY, T   

In triangle XTV

Angle VXT = (1/2) arc VW  = 55°

Angle XVT = (1/2) arc XY  =  85°

Then angle  XTV = 180 - 55 - 85  = 40°

And by the interesecting chord  theorem

Angle  XTV =  (1/2) (arc WY + arc VW)  = 40    ⇒  arc WY + arc VW = 80       (1)

And  Anhle XUV  = (1/2) (arc WY  - arc VW)  = 30 ⇒ arc WY  - arc VW = 60    (2)

Add (1)  and (2)

2arc WY =   140

arc WY  = 70°

kx^2  - 17x  + 2k   = 0

If this has  two real distinct roots, the discriminant must  be >   0

So

(-17)^2  - 4(k)(2k)  >  0

289  -  8k^2   >   0

289   >    8k^2

289/8  >   k^2          take the  positive root

sqrt (289/8)  >  k

≈ 6.01  >  k

So....the max integral value for k   =  6