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If the original side length is L inches, then we have

L^2(L-7) = 67

This gives a value for L of 8.04 inches (to 2dp).

D = (3/7)(U - 10)

Divide both sides by 3/7 which is the same as multiplying by the invert or 7/3

7/3D = U - 10

Add 10 to both sides

7/3D + 10 = U

or

U = 7/3D + 10

Let the volume of the cube be v in³ (I am studying in Singapore, so I use cm more frequently. ).

Note: a / b = a divided by b (fraction form)

v^{1 / 3} - 7 in = 67 in³/ (v^{2 / 3})

v = (v^{1 / 3})³

Rewrite equation in this form:

v = { [67 in³ / v^{(2 / 3)} + 7 in] }³

Simplifying yields:

v^{5 / 3} - 7v^{2 / 3} - 67 = 0

Shift term 0 to the left:

v^{5 / 3} - 7v^{2 / 3} = 67

Rewrite equation in this form as a - b = c, and a - c = b:

v^{5 / 3} - 67 = 7v^{2 / 3}

Divide it by 7:

(v^{5 / 3} - 67) / 7 = v^{2 / 3}

Finding v:

[(v^{5 / 3} - 67) / 7]^{3 / 2} = v

Split the fraction into two parts, as (a-b) / c = (a / c) - (b / c):

[(v^{5 / 3} / 7) - (67 / 7)]^{3 / 2} = v

Simplified to decimal form:

(v - 12.46363958)/7 = v^{3 / 5}

v/7 - 1.78051994 = v^{3 / 5}

(0.14285714v - 1.78051994) = v^{3 / 5}

0.14285714 v^{5 / 3} - 2.615640598 = v

v + 2.615640598 = (0.14285714 v^{5 / 3})

Hmm... Cant seem to find v^{1 / 3}. Will have Part 2 if i have.

It's a step-up transformer.

V_secondary = 112*1050/30 V

With no losses the secondary power will stay at 112 W.

Use the fact that power = V_secondary*I_secondary  to find the secondary current.

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Thank You that makes more sense!

One way as follows:

Multiples of 48:

48  96  144  192  240  288  336  384

Multiples of 84:

84  168  252  336

So 336 is the lowest common multiple (or least common multiple).

An alternative way is to start with the prime factors of each number:

Prime factors of 48:  2⁴, 3

Prime factors of 84:  2², 3, 7

Take the largest occurrence of each prime factor and multiply them together:  2⁴*3*7 =  336

a + b = -5               (1)

a - b =  8                (2)

Add equations (1) and (2) term by term:

a+a + b +(-b) = -5 + 8

Simplifying

2a = 3

Divide both sides by 2 to get

a = 3/2   

You could substitute this back into either (1) or (2) if you also wished to find b.

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BIN means Binary or Base 2.

Base 2 is notated like this:

x₂.

10₁₀ = 1010₂ 

1.58e-02 or 4.73e-06 which is greater???

1.58E-2 Much greater=1.58e-02 / 4.73e-06=3,340.38 times greater!.

$45 x 20%=$45 x 20/100=$45 x .20 =$9.00

Ln(35) / Ln(10) =Log(35)-base 10.

In a game of texas holdem, what are the odds that with a deck of 52 cards and 9 players are all playing at the table ( thats 2 cards each = 18 dealt to the players) would a complete royal flush be dealt to the board by the dealer?

I will assume that a royal flush is   J, Q, K, A    any suite.

The prob that is has a royal flush of spades      48C14   /    52C18       

This would be the same for each of the other suites too.   So you could just multiply this by 4

BUT

But there would be some double counting here.

The probability of getting any two royal flushes (say spades and diamonds) would be 44C10 / 52C18

This would have been added in twice so now it needs to be subtracted once

There are for suits 4C2 ways of choosing 2 suites = 6 ways

So I think we need to subtract    6*44C10/52C18

The prob of getting 3 royal flushes (say spades and diamonds and clubs) would be  40C6     /  52C18

There would be 4C3=4 ways of choosing  three suites.

Say you had S, D, C all  royal flushes.   

This hand would have been counted 3 times when counting singls flushes,  Then it would have been taken away 3 times when we were dealing with 2 royal flushes so it had better be added back in again now

There are 4C3=4 ways this can happen so we need to add back in    4* 40C6     /  52C18

Now there could be 4 royal flushes  there is only one way that this can happen.    36C2 / 52C18

This got added in 4 times when a single flush was looked at.

Then it go subtracted 6 times when 2 royal flushes were looked at

Then it got added 4 times when three royal flushes were looked at.

So it needs to be subtracted once.  because    4-6+4-1=1

4* 48C14 / 52C18   -   6*44C10/52C18     +   4* 40C6 / 52C18   -     36C2 / 52C18

(4* 48C14-6*44C10+4* 40C6-36C2) / 52C18

(4*nCr(48,14)-6*nCr(44,10)+4*nCr(40,6)-(36C2))/nCr(52,18)     =  approx   0.0449

The exact result - assuming that what I have done here is correct can be found here.

https://www.wolframalpha.com/input/?i=(4*nCr(48,14)-6*nCr(44,10)%2B4*nCr(40,6)-nCr(36,2))+++%2FnCr(52,18)

cosh(x) is defined by

\(\displaystyle \cosh(x) = \frac{e^{x}+e^{-x}}{2}\).

It does have a relationship with the trig function cos,

\(\displaystyle \cosh(ix)= \cos(x)\).

Ben:   $1400*75/(75+45)

Adam:  $1400*45/(75+45)

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If the pressure is constant you could use the fact that volume is proportional to temperature, so:

V₂ = V₁*T₂/T₁

Or, for the third, just use the fact that the three angles must sum to 180°

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It stands for "Binary", or "0 and 1"

how do u solve -(5x)^2 or (-5x)^2

-(5x)^2=-25x^2

(-5x)^2=25x^2

1,000^1,000 =10^3,000

a = 4; b = 8; c = 11

c² = a² + b² - 2ab cos(C)

11² = 4² + 8² - 2*4*8 * cos(C)

121 = 16 + 64 - 64 * cos(C)               Sqare values

121 - 16 - 64 = -64 * cos(C)              Subtract a and b from both sides

41 = -64 * cos(C)                             

41 / -64 = cos(C)                               Divide both sides by -2ab

C = cos-1(-0.641)                              Inv cos

Repeat for 1 more angle then use Pythag for the third

No thanks.

sin(44.427004000806) = 0.7

1 -> 12, increase of 11

12 -> 21, increase of 9

21 -> 28, increase of 7

28 -> 33, increase of 5

33 -> 36, increase of 3

36 -> 37, increase of 1.

1,12,21,28,33,36,37

2x + -2(2/3x + 1/3)  =  2

Distribute the -2:

2x + -2(2/3x) + -2(1/3)  =  2

Simplify:

2x -4/3x - 2/3  =  2

Multiply each term by 3 to remove denominators:

3[2x - 4/3x - 2/3]  =  2[3]

Distribute the 3:

3(2x) - (3)(4/3x) - (3)(2/3)  =  6

Simplify:

6x - 4x - 2  =  6

       2x - 2  =  6

             2x  =  8

               x  =  4