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3√ (128x^7) = 3√( 64*2*x^7) = 3*8√ (x^7) = 24x³√ x

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√(45x^5y^3) • √(35xy^4)  ....let's simplify this one separately and then combine what we've got

 √(45x^5y^3) = √(9*5*x^5*y^3)= 3x²y√(5xy)

√(35xy^4) = y²√(35x)

So multiplying both of these, we have

3x²y³√(175x²y) = 3x³y³√(25*7*y) = 5*3x³y³√(7y) = 15x³y³√(7y)

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√50x^6/√2x^4   ........we can write this as √(50x^6/(2x^4))  ....and simplifying, we have

√(25x^2)   = 5x  .........pretty easy, once you simplify, huh??

pi * pi = (pi)²  ≈ 9.87

This question is worded a little funny...

I think they might be asking "What percent of 544 is 544-121?"

Here's how you would solve it if that's what you mean:

$${\mathtt{544}}{\mathtt{\,-\,}}{\mathtt{121}} = {\mathtt{423}}$$

So really, our new question is "What percent of 544 is 423?"

$${\frac{{\mathtt{423}}}{{\mathtt{544}}}} = {\mathtt{0.777\: \!573\: \!529\: \!411\: \!764\: \!7}}$$

Or rounded up to the nearest percent, about 78%

Just type abs.  e.g. abs(-6) It will appear as |-6| = 6

$${\left|-{\mathtt{6}}\right|} = {\mathtt{6}}$$

Your question doesnt make sense!

And if u want to subtract 554 and 121 then this is the answer

554 - 121 = 423 ANSWER

I'll do a few for you:

I assume the first one is √(36x²) = √36*√x² = √6²*√x² = 6x

4√(32m⁷n⁹) = 4√32√m⁷√n⁹ = 4√(4²*2)*√(m⁶*m)*√(n⁸*n) = 4*4√2*m³√m*n⁴√n = 16m³n⁴√(2*m*n)

B. This is a tricky one!  5√(-5)*5*√(-2) = 5*i*√5*5*i*√2  where i is the "imaginary" number √(-1)

Since i² = -1, we have  5√(-5)*5*√(-2) = 25*i²*√5*√2 = -25√10

Thank you Will and Melody!

Yes she is.

Rose98 is very polite too.

This is like finding a lily in a Russian snow storm.

7up

Like this?

Still don't get the same values as you quote!

Thanks Alan, Confession time i made a mistake in what is posted. The first equation at the end should also have

0 - V2/15. Those denominators are all resistors in the circuit.

The actual answers in the book are V2 = 32.34v  V3 = 40.14v though in my novice state with combining equations i can't get those answers.

The first way you wrote out the second equation is exactly the way the author has written it in the book. The second one is out because i forgot to include that part of the equation in my rush to post it!

Thanks for replying.

You can use the mod function on the calculator here.

$$\left({{\mathtt{132}}}^{{\mathtt{28}}}\right) {mod} \left({\mathtt{19}}\right) = {\mathtt{1}}$$

NB You have to enter it in the form mod(132²⁸,19)

Hmm.  I'm not sure Maple agrees with me.  I based my reply above on reasoning about the two terms separately, and in this Maple agrees with me - see the first plot below (I've just used the natural log; a different base only alters the scaling, not the domain).

However, when I get Maple to plot the difference of the two terms it gives the following (which is identical to ln(x+8)):

So, Chris, it looks like the mathematical software big-hitters (Mathematica and Maple) think it's ok to combine terms before worrying about domain validity!

I'm guessing here, but perhaps this is asking for the probability density given by Student's t distribution at a value of 0.01, with 15 degrees of freedom.  If so, then it's 0.392.

In general, try to give more explanation so we know what you are asking - we're not mind readers!

Volume of one cylindrical peg = pi*r²*L  where r is the radius and L is the length.

Here we have r = 0.5 inches = 0.5*2.54 cm = 1.27 cm,  and L = 2 inches = 2*2.54 cm = 5.08 cm

The volume of one peg = pi*1.27²*5.08 cm³.

The mass of one peg is given by volume*density = pi*1.27²*5.08 cm³ * 8.05 g/cm³ = pi*1.27²*5.08*8.05 g

So the number of these you can get out of a block of mass 157.4kg is 154.7*1000/(pi*1.27²*5.08*8.05)

$${\frac{{\mathtt{157\,400}}}{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{1.27}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{5.08}}{\mathtt{\,\times\,}}{\mathtt{8.05}}\right)}} = {\mathtt{759.605\: \!010\: \!502\: \!234\: \!142\: \!2}}$$

Rounding down, this is 759 whole pegs (and this assumes we can reshape the block as necessary!).

Note that 157.4 kg is 157400 g, and I've converted to grams because the density is in terms of grams/cm³, not kg/cm³.

In many computer programming languages 9.0e9 can mean 9.0*10⁹ or 9 billion (often written as 9.0E9 as well). 

Indeed, this is what the calculator here thinks!

For these, just use the on-site calculator

$${\mathtt{3.453\: \!125}}{\mathtt{\,\times\,}}{\mathtt{703}} = {\mathtt{2\,427.546\: \!875}}$$

Look at these answers - they should help

769=40a+(1.5a×5)

a=16.1894736842105263

But if you round it because it's a large number, this is what you get as an answer:

a=16.189

769 = 40a + (1.5a * 5)

(1.5 a * 5) = (7.5a)

769 = 40a + 7.5a

769 = 47.5a

769/47.5

$${\frac{{\mathtt{769}}}{{\mathtt{47.5}}}} = {\frac{{\mathtt{1\,538}}}{{\mathtt{95}}}} = {\mathtt{16.189\: \!473\: \!684\: \!210\: \!526\: \!3}}$$

16.189 = a

deleted deleted All answered.

7%=7,000,000,000

7,000,000,000*15=105,000,000,000

In my calculations, the answer is $105,000,000,000 in profit in the year 2015.

Fixededd :P

Yeah. It's kind of cool.

thanks DS.  Do you have Chris's specs?