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Hi Solveit  

I think it is supposed to be "uniform prism"

It still does not have any truely mathematical meaning I don't think but I would take it to mean a right prism.

One where the front is at right angles to each side.  One that looks 'uniform'.

Last year's tuition=$44,000

This year's tuition=$44,000 X 104%=$45,760.

1000! / [500!*500!] / 2^1000=0.025225 X 100=2.5225%

It was 100%

It went up by 4%

So now it is 104%

Take the integral:
integral sin^4(x) dx
Use the reduction formula,  integral sin^m(x) dx = -(cos(x) sin^(m-1)(x))/m + (m-1)/m integral sin^(-2+m)(x) dx, where m = 4:
  =  -1/4 sin^3(x) cos(x)+3/4 integral sin^2(x) dx
Write sin^2(x) as 1/2-1/2 cos(2 x):
  =  -1/4 sin^3(x) cos(x)+3/4 integral (1/2-1/2 cos(2 x)) dx
Integrate the sum term by term and factor out constants:
  =  -1/4 sin^3(x) cos(x)-3/8 integral cos(2 x) dx+3/8 integral 1 dx
For the integrand cos(2 x), substitute u = 2 x and  du = 2  dx:
  =  -1/4 sin^3(x) cos(x)-3/16 integral cos(u) du+3/8 integral 1 dx
The integral of cos(u) is sin(u):
  =  -(3 sin(u))/16-1/4 sin^3(x) cos(x)+3/8 integral 1 dx
The integral of 1 is x:
  =  -(3 sin(u))/16+(3 x)/8-1/4 sin^3(x) cos(x)+constant
Substitute back for u = 2 x:
  =  (3 x)/8-1/4 sin^3(x) cos(x)-3/8 sin(x) cos(x)+constant
Which is equal to:
Answer: | =  1/32 (12 x-8 sin(2 x)+sin(4 x))+constant

Simplify the following:
5/6^(80 (5/6-1)/10-1)

80 (5/6-1)/10 = (80 (5/6-1))/10:
5/6^((80 (5/6-1))/10-1)

Put 5/6-1 over the common denominator 6. 5/6-1  =  5/6-(6)/6:
5/6^((80 5/6-(6)/6)/10-1)

5/6-(6)/6  =  (5-6)/6:
5/6^((80 (5-6)/6)/10-1)

5-6 = -1:
5/6^((80×-1/6)/10-1)

80×(-1)/6 = (80 (-1))/6:
5/6^((-80)/6/10-1)

((80 (-1))/6)/10 = (80 (-1))/(6×10):
5/6^((-80)/(6×10)-1)

6×10  =  60:
5/6^((-80)/60-1)

The gcd of -80 and 60 is 20, so (-80)/60 = (20 (-4))/(20×3) = 20/20×(-4)/3 = (-4)/3:
5/6^(-4/3-1)

Put (-4)/3-1 over the common denominator 3. (-4)/3-1  =  (-4)/3-(3)/3:
5/6^-4/3-(3)/3

(-4)/3-(3)/3  =  (-4-3)/3:
5/6^(-4-3)/3

-4-3 = -7:
5/6^(-7/3)

6^(-7/3) = 6^(2/3-(9)/3) = 6^(-9/3)×6^(2/3):
5/6^(-9/3)×6^(2/3)

9/3 = (3 (-3))/3 = 3:
5/(6^(-3)×6^(2/3))

6^3 = 6×6^2:
5/(1/(6×6^2) 6^(2/3))

6^2 = 36:
5/((6^(2/3))/(6×36))

6×36  =  216:
5/((6^(2/3))/(216))

Multiply the numerator of 5/((6^(2/3))/(216)) by the reciprocal of the denominator. 5/((6^(2/3))/(216)) = (5×216)/6^(2/3):
(5×216)/6^(2/3)

5×216  =  1080:
1080/6^(2/3)

Rationalize the denominator. 1080/6^(2/3)  =  1080/6^(2/3)×(6^(1/3))/(6^(1/3))  =  (1080 6^(1/3))/(6):
(1080 6^(1/3))/(6)


6 |  | 1 | 8 | 0
| 1 | 0 | 8 | 0
- |  | 6 |  |
|  | 4 | 8 |
| - | 4 | 8 |
|  |  |  | 0
|  |  | - | 0
|  |  |  | 0:
Answer: | Log[180 6^(1/3)]=2.5146562...

Well, the method is easy enough, even though it is cumbersome and laborious. We can use Taylor series to find the arctangent of sqrt(2)-1. We could even calculate the sqrt(2) by hand, using Newton's method. Since we can obtain 6-7 accurate digits by doing 3-4 iteration of this method, we should obtain 1.41421356..... - 1=.41421356. Now, we substitute this into Taylor series as follows:

Arctangent=.41421356 - (.41421356^3/3) + (.41421356^5/5) - (.41421356^7/7)........and so on. Each term will give, for this value, approx. one accurate digit of Pi, so 7 terms will suffice. With patience and some slugging, we should get:0.39269906583409 X 8=3.141592526672....... accurate to 6 decimal places.

14-2+8/4  =     the division is performed, first

14 - 2 + 2  =

14 + 0  =

14

She wants to answer any 3 of 7 questions correctly......  = C(7,3)

Each question has  25% probability of being answered correctly and a 75% probability of an incorrect answer.....so......we have.....

C(7,3) * (.25)^3 * (.75)^4  = about .173  = about 17.3% chance of answering any three correctly

Actually 1 ton is equal to 2,000 pounds.

1 kilogram is equal to about 2.2 pounds

If 1 kilogram is equal to $250 and 1 kilogram is equal to about 2.2 pounds, you can subsitute 1 kilogram for 2.2 pounds and now get that 2.2 pounds is equal to $250.

Let x equal price for 1 ton or 2000 pounds.

\(\frac{2.2lbs}{$250}≈\frac{2000lbs}{x}\)

\(2.2lbs*x≈2000lbs*$250\)

\(2.2lbs*x≈$500,000\)

\(x≈$224,215.25\)

1 ton is equal to about $224,215.25 when 1 kilogram is equal to $250.

1 kg  = about 2.2 lbs       1 ton = 2000 lbs

250 / 2.2 lbs   = Price / 2000 lbs  

Price = 500,000 / 2.2  = about  227272.73

Edit for an earlier goof......thanks to gibsonj338 for pointing out my gaffe.....!!!!

The probability of 500 heads = probability of 500 tails

Out of 1000 flips, we want any 500 of them to be heads  =  C(1000, 500)

Probability of heads on any 1 toss  = 1/2   = probabiliy of tails on any one toss

So, we have

C(1000,500) * (1/2)^500 * (1/2)^500  =  about .025  = about 2.5%

Thank you very much CPhill. Sorry to have bothered you, on New Year's day no less!.

This type of integral isn't that difficult.....just tedious.....!!!!!

∫(sin(x))^4   dx  =

∫ [sin^2x)]^2  dx =             sin^2x  =   [1 - cos(2x)] / 2   =  1/2  - cos(2x)/2

∫  [ 1/2  - cos(2x)/2]^2 dx  =

∫  1/4 - (1/2)cos(2x) + cos^2(2x)/4  dx  =

[1/4]x  -  (1/2) ∫ cos (2x)dx   +  (1/4) ∫  cos^2(2x)  dx

For the second integral    let  u =  2x        du  = 2 dx   du /2  = dx

[1/4]x - (1/2) ∫ cos(u)  du/2   + (1/4) ∫  cos^2(2x)  dx  

[1/4]x - (1/4) ∫ cos(u)  du   + (1/4) ∫  cos^2(2x)  dx  

[1/4x] - [1/4] sin (u)  + (1/4) ∫  cos^2(2x)  dx 

[1/4]x - [1/4] sin(2x)  + (1/4) ∫  cos^2(2x)  dx

For the last integral     ........  cos^2(2x)  =  [ 1 + cos(4x] / 2   =  1/2 + cos(4x)/2  

[1/4]x - [1/4]sin(2x)  + (1/4) ∫ 1/2  + cos(4x)/2 dx 

[1/4]x - [1/4]sin(2x) + [1/8]x   + (1/8) ∫ cos(4x)  dx

[3/8]x  - [1/4]sin(2x) + (1/8) ∫ cos(4x)  dx

As before.....let u = 4x       du  = 4dx       du/4 = dx

[3/8]x -[1/4]sin(2x) + (1/8)  ∫ cos(u) du/4

[3/8]x -[1/4]sin(2x) + (1/32)  ∫ cos(u) du

[3/8]x -[1/4]sin(2x) + (1/32) sin(u)  + C =

[3/8]x -[1/4]sin(2x) + (1/32) sin(4x) + C =

[1/32] [ 12x - 8sin(2x) + sin(4x) ] + C

Sorry, your numbers are not clear enough: what does this number mean:

4.15x10squared6 m ????????.

Thanks CPhill ! :)

3/2 of infinity=infinity!!.

I'm not sure what the term "uniform" refers to, Solveit......but here's the solution

Area of an equilateral triangle = the area of the cross-section = (1/2)side^2* sqrt(3)/2  = [sqrt(3)/4] *side^2

And the volume of the prism  is ......    Cross- sectional area * Height

So......the  volume =

[sqrt(3)/4] *(4)^2  * 8  =   [ 32 *sqrt(3) ] units^3

A certain unifrom prism is 8 units high and each cross section of this prism is an equialeteral triangle. if all of the edges of the prism s base are 4 units long, what is the volume of the prism ?

152654565^2x1564995232646.641656464645=3.6469735281386332050347224883132894200125 × 10^28  

Excellent thinking, Dragonlance.......!!!!!

Here's a pic of the cross-section of the cube within the sphere showing that Dragonlance's answer is indeed correct.....!!!

Bertie's "double and add the next digit" method is exactly the same thing we do in base 10.....consider  the number 1267

Starting from the left.....

Multiply the 1 by 10  = 10........add the next digt = 12 .........multiply this by 10   = 120.....add the next digit  = 126........multiply this by 10  = 1260 .......add the last digit = 1267......!!!

This method might be rightly called ...."multiply by the base, add the next digit"

Here's a way to understand why this "works"

(1 x 10) + 2

(1x10  + 2)10 + 6

(1x10^2 + 2*10 + 6)10  + 7

(1x 10^3 + 2x10^2 + 6x10) + 7  =   1267

Hit the "2nd" key........"asin" is the sine inverse function

asin(15/17) =  about 61.9°    or about 118.1°   if we're in the 2nd quadrant

(3/4) x 7 = 21/4   = 5 + 1/4  pints in seven days

2(L + W)  = 98

L + W  = 49

L = 49 - W

L^2 + W^2  = 41^2

(49 - W)^2 + W^2  = 1681

2W^2 - 98W + 2401 = 1681

2W^2 - 98W + 720  = 0

W^2 - 49W + 360  = 0

(W - 40) (W - 9)  = 0

W  = 40 and L = 9     or W = 9 and L = 40        [ depending upon your orientation ]

And the area = L * W   = 40 * 9   = 360  units^2