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14.2857142857 rounded to the nearest tenth is simply 14.3

This is a fancy way of saying that we want to exponetiate the base 4, to the power of -3.....the result will be the  "anti-log"   [this is always a confusing term, IMHO ]  .......so........

4^-3  = 1/4³  = 1/64  = 0.015625

\(365,537,274,738,959,995\times56,753,456,789,754,323,456,743,345,678\)

                                                                           \(2,924,298,197,911,679,960\)

                                                                         \(25,587,609,231,727,199,650\)

                                                                       \(219,322,364,843,375,997,000\)

                                                                   \(1,827,686,373,694,799,975,000\)

                                                                 \(14,621,490,989,558,399,800,000\)

                                                               \(109,661,182,421,687,998,500,000\)

                                                           \(1,096,611,824,216,879,985,000,000\)

                                                         \(14,621,490,989,558,399,800,000,000\)

                                                       \(255,876,092,317,271,996,500,000,000\)

                                                   \(2,193,223,648,433,759,970,000,000,000\)

                                                 \(18,276,863,736,947,999,750,000,000,000\)

                                               \(146,214,909,895,583,998,000,000,000,000\)

                                           \(1,096,611,824,216,879,985,000,000,000,000\)

                                           \(7,310,745,494,779,199,900,000,000,000,000\)

                                      \(109,661,182,421,687,998,500,000,000,000,000\)

                                  \(1,462,149,098,955,839,980,000,000,000,000,000\)

                                \(18,276,863,736,947,999,750,000,000,000,000,000\)

                              \(255,876,092,317,271,996,500,000,000,000,000,000\)

                          \(3,289,835,472,650,639,955,000,000,000,000,000,000\)

                        \(29,242,981,979,116,799,600,000,000,000,000,000,000\)

                      \(255,876,092,317,271,996,500,000,000,000,000,000,000\)

                  \(2,193,223,648,433,759,970,000,000,000,000,000,000,000\)

                \(18,276,863,736,947,999,750,000,000,000,000,000,000,000\)

              \(146,214,909,895,583,998,000,000,000,000,000,000,000,000\)

          \(1,096,611,824,216,879,985,000,000,000,000,000,000,000,000\) 

        \(18,276,863,736,947,999,750,000,000,000,000,000,000,000,000\)

      \(255,876,092,317,271,996,500,000,000,000,000,000,000,000,000\)

  \(2,193,223,648,433,759,970,000,000,000,000,000,000,000,000,000\)

\(18,276,863,736,947,999,750,000,000,000,000,000,000,000,000,000\)

Add the columns.

\(20,745,503,926,942,120,671,681,790,409,599,247,210,498,151,610\)

The volume of a pyramid is 1/3 of that of its associated prism

The volume of the associated prism  =

b * h  = [(3/2) * sqrt(3)] * s^2 * h     and s = 9 and h = 12   in this case

So we have

 [(3/2) * sqrt(3)] * 9^2 * 12   = about 2525.33 units^3

And 1/3 of this =  about  841.8 units^3  [rounded]

Here's another approach.....

x + 2y + 4z  =   3    (1)

x - y - 2z  = -3        (2)

3x + z = 0     →  z = -3x   (3)

Substitute (3) into (2)

x - y - 2(-3x)  = -3

x - y + 6x  = -3

7x - y  = -3

y = 7x + 3     (4)

Substitute (3) and  (4)  into (1)

x + 2 [7x + 3] + 4(-3x)  = 3

x + 14x + 6 - 12x  = 3

3x = -3       x = -1

Using (4), y = 7(-1) + 3  = -4

Using (3), z = -3(-1)  = 3

So   {x, y, z }   = { -1 , -4,  3 }

1.5% decreasing means that at the end of the decrease, the value of 400,000 will be at 98.5% right?

So take 98.5% in decimal form and multiply it by 400,000

.985*400000 = 394000

394,000

SHHHHHHHHH

Nobody knows ( that final substitution, i typed -2 instead of -4, no biggy)

Ok, you've managed to correct it.

Considering i'm a vampire, I would take the Corn dog.

You've slipped up somewhere Spawn.  Guest#1 has the right results (albeit with a rather long solution method!)

There are an infinite number of ordered pairs for y = -2x + 6

For example:   

(x,   y)

(0,  6)

(1,  4)

(2,  2)

(3,  0)

elimination for first 2

Apply a negative to the second one to eliminate X

x+2y+4z = 3

-x+y+2z = 3

0x+3y+6z = 6

We can take a 3 out of everything

y+2z=2

y = 2-2z

Likewise we can make z = -3x with the last equation

So we have

y= 2-2z

z = -3x

Which means y = 2+6x

Lets substitute for the second equation

x - (2+6x) - 2(-3x) = -3

Solve for x

It boils down to

x-2=-3

So x = -1

Substitute into original equations

3(-1) + z=0

z = 3

Second equation would be easiest for the last substitution

-1 - y - 2(3) = -3

y = -4

x = -1

y = -4

z = 3

This is an absolute value graph that is shifted from the origin to the left by 2 units and up by 5 units.......

The equation for this is:

y = a l x - h l + k        where (h , k)  =  (-2, 5)

So we have

y = a l x - -2 l + 5

y = a l x + 2 l + 5

If the vertex is (-2, 5) and it passes through (3, -10)   we can find "a"  in the formula by finding the slope between these points

a =  [-10 - 5]  / [ 3 - -2]  =  -15/ 5 =  - 3    ....so we have

y =  -3 l x + 2 l + 5

Here is the graph of this along with the point (3, -10) :  https://www.desmos.com/calculator/w4fyscix0k

First find the components in the horizontal and vertical directions.

Horizontal:  Fx = 9 - 14*cos(65°)    or  Fx = 3.083   

Vertical:   Fy = 14*sin(65°)  or Fy = 12.688

The resultant has magnitude sqrt(Fx² + Fy²)  = 13.058

It has an angle to the horizontal axis of  tan^-1(Fy/Fx)  =  76.34°  

.

Solve the following system:
{x+2 y+4 z = 3 |     (equation 1)
x-y-2 z = -3 |     (equation 2)
3 x+z = 0 |     (equation 3)
Swap equation 1 with equation 3:
{3 x+0 y+z = 0 |     (equation 1)
x-y-2 z = -3 |     (equation 2)
x+2 y+4 z = 3 |     (equation 3)
Subtract 1/3 × (equation 1) from equation 2:
{3 x+0 y+z = 0 |     (equation 1)
0 x-y-(7 z)/3 = -3 |     (equation 2)
x+2 y+4 z = 3 |     (equation 3)
Multiply equation 2 by -3:
{3 x+0 y+z = 0 |     (equation 1)
0 x+3 y+7 z = 9 |     (equation 2)
x+2 y+4 z = 3 |     (equation 3)
Subtract 1/3 × (equation 1) from equation 3:
{3 x+0 y+z = 0 |     (equation 1)
0 x+3 y+7 z = 9 |     (equation 2)
0 x+2 y+(11 z)/3 = 3 |     (equation 3)
Multiply equation 3 by 3:
{3 x+0 y+z = 0 |     (equation 1)
0 x+3 y+7 z = 9 |     (equation 2)
0 x+6 y+11 z = 9 |     (equation 3)
Swap equation 2 with equation 3:
{3 x+0 y+z = 0 |     (equation 1)
0 x+6 y+11 z = 9 |     (equation 2)
0 x+3 y+7 z = 9 |     (equation 3)
Subtract 1/2 × (equation 2) from equation 3:
{3 x+0 y+z = 0 |     (equation 1)
0 x+6 y+11 z = 9 |     (equation 2)
0 x+0 y+(3 z)/2 = 9/2 |     (equation 3)
Multiply equation 3 by 2/3:
{3 x+0 y+z = 0 |     (equation 1)
0 x+6 y+11 z = 9 |     (equation 2)
0 x+0 y+z = 3 |     (equation 3)
Subtract 11 × (equation 3) from equation 2:
{3 x+0 y+z = 0 |     (equation 1)
0 x+6 y+0 z = -24 |     (equation 2)
0 x+0 y+z = 3 |     (equation 3)
Divide equation 2 by 6:
{3 x+0 y+z = 0 |     (equation 1)
0 x+y+0 z = -4 |     (equation 2)
0 x+0 y+z = 3 |     (equation 3)
Subtract equation 3 from equation 1:
{3 x+0 y+0 z = -3 |     (equation 1)
0 x+y+0 z = -4 |     (equation 2)
0 x+0 y+z = 3 |     (equation 3)
Divide equation 1 by 3:
{x+0 y+0 z = -1 |     (equation 1)
0 x+y+0 z = -4 |     (equation 2)
0 x+0 y+z = 3 |     (equation 3)
Collect results:
Answer: |  x = -1     y = -4      z = 3

Solve for x over the real numbers:
2^(7 x+5) = 8^(3-x)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(2) (7 x+5) = 3 log(2) (3-x)

Expand out terms of the left hand side:
7 log(2) x+5 log(2) = 3 log(2) (3-x)

Expand out terms of the right hand side:
7 log(2) x+5 log(2) = 9 log(2)-3 log(2) x

Subtract 5 log(2)-3 x log(2) from both sides:
10 log(2) x = 4 log(2)

Divide both sides by 10 log(2):
Answer: |x = 2/5

Well, pi*diameter is the circumference of a circle, so pi*radius would be the arc length of a semicircle.

Line them up like this :

8  5  10  16  8  0

6  3   6   12  6  0

4  1   2    8   4  0

The final pattern......inferring the answers by noticing the pattern in each column should be  :

2  -1  -2   4   2   0

Not sure what you want here:

6/2+8x(3+8)^2=?

6/2 + 8*11^2=

3 + 8*121 =

3 + 968 =971. This is a prime number. There is not much you can do with it.

2^(3x-1)*4^(2x+3)=8^(3-x)

We can write 4ⁿ as (2²)ⁿ → 2²ⁿ  and 8ⁿ as (2³)ⁿ → 2³ⁿ

so 2^(3x-1)*4^(2x+3)=8^(3-x)  becomes   2^(3x-1)*2^(4x+6) = 2^(9-3x)

Since 2^a*2^b = 2^a+b we can further write  2^(3x-1+4x+6) = 2^(9-3x)  or  2^{(7x + 5)} = 2^{(9 - 3x)}

From this it is clear that 7x + 5 = 9 - 3x   so  10x = 4  or x = 4/10 → 0.4

No prob....it was an honest mistake......BTW I'm  not always correct.....LOL!!!!

2^(3x-1)*4^(2x+3)=8^(3-x)

2^(3x-1)*4^(2x+3)=2^(7x + 5) As you can see, the left hand side does not equal the right hand side.

We need to find the perimeter of two half circles, one with a radius of 15/ 2  = 7.5 m, and the other with a radius of [7.5 - 1.25] = 6.25 m

This is given by :

pi [ 7.5 + 6.25]  = about 43.2 meters

The rest is easy......the total length of the 11 segments =  11*1.25 = 13.75m

So....the total length  of the wrought iron = 43.2 + 13.75 = about 56.95 m

674238787584579758479837240937856938746593874658290320397582658293892079074903247283956662037610651824560946001083974823604784675738657832456100010746587301567746573941183470.3477000688888888888888888888...

CPhill: You are absolutely right as always! Sorry about that. I took the volume intead of surface area. Was too hasty in reading the question!.