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what does 0.6666666666666667 equal in a fraction??

=2/3

Tan(82)=Height/204

7.11537=H/204 cross multiply

H=7.11537 x 204

H=1,451.5 feet - the height of Empire State Building.

First, figure out the volume of the wooden block before immersing it in water:

V=5 x 5 x 2=50 cubic cm.

Second, figure out the volume of the block that is under the water surface:

V=5 x 5 x 1.55=38.75 cubic cm=volume of displaced water=mass of displaced water.

Density=Mass/Volume

D=38.75/50 =.775g/cm^3. And so, I would say "D"

Alan: Please verify this. Thanks.

Hello IronDome!

Does f(x) = sin1/x have a tangent line at x=0. Explain why or why not.

You mean f(x) = sin (1/x) ?

f(x) = sin (1/x) = sin (x ^-1)

f'(x) = cos (1/x) * (- 1/x²)

There is no tangent.  1 / (x = 0) and (-1/(x=0)²) is not defined.

1/0 is not defined.

Greeting asinus :- )

   !

By "outside of the circle", do you mean "Circumference"? If so, then we have:

Circumference=Diameter x Pi

2.9 =D x 3.141592 divide both sides by Pi

D=2.9 / 3.141592

D=0.923 inches - the diameter of the circle.

Thanks Alan: I tried both!!!!!!!. Here is your suggestion:

http://www.wolframalpha.com/input/?i=(+r%5En+-+1)+%2F+(r+-+1)%3D364,+r%5E(n-1)%3D243,+solve+for+r,+n

Where is the "diagram"?.

4 x 2 =8 square feet-the area of the garden.

Sqrt(8) =2.828 feet-the length of each side.

Find the derivative of the following via implicit differentiation:
d/dx(f(x)) = d/dx(3 x-2 x^2)
The derivative of f(x) is f'(x):
f'(x) = d/dx(3 x-2 x^2)
Differentiate the sum term by term and factor out constants:
f'(x) = 3 d/dx(x)-2 d/dx(x^2)
The derivative of x is 1:
f'(x) = -2 (d/dx(x^2))+1 3
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x:
f'(x) = 3-2 2 x
Simplify the expression:
f'(x) = 3-4 x
Expand the left hand side:
Answer: | f'(x) = 3 - 4x

Sqrt(1/96) =1/(4 sqrt(6))=1/(4 sqrt(2)*sqrt(3)) x sqrt(3)=sqrt(3)/[4 sqrt(2) sqrt(3)]. Cancel sqrt(3) and multiply by sqrt(2):

sqrt(2) / (4 x 2)=sqrt(2)/8.

See the answer under your first question.

Up thrust from water = 8.84 - 6.86 = 1.98N

Upthrust = volume displaced*water density*g, so volume displaced = 1.98/(1000*10) m^3. (again using g = 10m/s^2) → 0.000198m^3

volume displaced = volume of crown, so

density of crown = mass of crown/volume of crown → (8.84/10)kg/0.000198m^3 → 4464 kg/m^3

Nearest supplied answer is A.

Simplify the following:
(x^2+9 x+3) (x^3-4 x+7/x)

Put each term in x^3-4 x+7/x over the common denominator x: x^3-4 x+7/x  =  x^4/x-(4 x^2)/x+7/x:
x^4/x-(4 x^2)/x+7/x (x^2+9 x+3)

x^4/x-(4 x^2)/x+7/x = (x^4-4 x^2+7)/x:
Answer: |  (x^4 - 4x^2 + 7)/x (x^2 + 9x + 3)=x^5 + 9x^4 - x^3 - 36x^2 - 5x + 21/x + 63

Thank You so much:) can you pelase help me with my next few questions?

no i can't.... :(

" I don't get it and neither does W/A!!!!!."

That's because you entered r^(n-1) in the numerator of the first term instead of r^n -1

i.e. the "-1" is subtracted from r^n, it isn't subtracted from the n.

Tension in rope when out of water 2.7g ≈ 27N

When weight is submerged in water it experiences an up thrust equal to the weight of water displaced. This reduces the tension in the rope, so the only possible answer of those supplied is D.

(To do the calculation:

Volume of weight = 2.7/2500 m^3. This is the volume of water displaced, hence the weight of water displaced is (2.7/2500)*1000*10 N. (Taking g ≈ 10m/s^2)

Subtract this from the 27N to get something close to 16N)

.

 (x^2+9x+3)(x^3-4x+7/x)  =  

x^5 + 9 x^4 - x^3 - 36 x^2 - 5 x + 21/x + 63

I assume you can take it from here

78 = 2 x 39  = 2 x 3 x 13

97   is a prime itself

The first term of a geometric series is 2, the nth term is 486 and the sum of the n terms is 728. find r and n.

We have two  things we can work with, here........first......the sum of the series 

728 = 2 [1 - r^n] / [ 1 - r]

364 = [ 1 - r^n ] / [1 -r]

364 -364 r  = 1 - r^n

364r - 364   = r^n - 1

364r  - 363    =  r^n    (1)

And, second.......the nth term

486  = 2(r)^(n-1)

243  = r^(n-1)

243  = r^n / r

243r  = r^n     (2)

So....equating (1)  with (2), we have

364r - 363   = 243r   simplify

121r - 363  = 0

121r = 363       divide both sides by 121

r = 3

And using (2)

243(3)  = 3^n

729  = 3^n  

And n = 6

Sorry.....I get the same result as Melody........check

Sum =  2[ 1 - 3^6] / [ 1 -3]  =  728

And the 6th - and last -  term is given by

2*3^(6 -1)  =

2*3^5  =

2* 243  = 

486

I'm not sure of the answers generated by WA........for instance.........their calcuation for "n"  results in a decimal approximation......it should be an integer!!!!......I'd go with the solutions Melody and I provided

I think you might mean "operations"....the four basic operations are addition, subtraction, multiplication and division......

CPhill: Can you please look at this Wolfram/Alpha "solution" that Melody got? I don't get it and neither does W/A!!!!!. Thanks.

http://www.wolframalpha.com/input/?i=(+r%5E(n+-+1))+%2F+(r+-+1)%3D364,+r%5E(n-1)%3D243,+solve+for+r,+n

3/5 - 4/15   =

9/15  - 4/15   =

5/15  =

1/3

[ log√8 + log √125  - log √27 ]  /  [ log 2 + log ³√5  -  log ³√12 ] =

[ log√8 + log √125  - log √27 ]  / log ³√8 + log ³√5 - log³√12 ] =

[ (1/2) log 8 + (1/2) log 125  -  (1/2)log 27 ] / [ (1/3) log 8  + (1/3) log 5 - (1/3) log12] =

[(1/2) log 2³ + (1/2) log5³ - (1/2) log 3³ ] / [ (1/3) log 2³ + (1/3) log 5 - (1/3) log12 ] =

 (3/2)[ log 2 + log 5 - log 3] / [ (1/3) [ log2³ + log 5 - log 12] ] =

(3/2) [ log ( [2 * 5]  / 3 )  /  [ (1/3) [log [2³ * 5 / 12 ]  )  =

(3/2) log (10/3) /  [(1/3) log (40/12) ]  =

(3/2) log (10/3) / [ (1/3) log (10/3) ] =

(3/2)  / (1/3)  = 

(3/2) * (3/1)  =

9/2  =

4.5