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Use the calc on the home page.  

On the forum calc

inverse tan is atan

If you have a division problem like these,  then subtract exponents; the answer is  x^4.

 x^10 / x^6  =  x^4

x^8 / x^8  =  x^0  =  1

x^4 / x^7  =  x^-3      which is the same as 1 / x^3

[a^5·b^3] / [a^2·b^7]  =  a^3·b^-4  =  a^3 / b^4

If you have some specific problems, please ask...

√(-v + 27)  =  v + 3

To get rid of a square root, square both sides:

  -v + 27  =  (v + 3)²                         (v + 3)²   =  (v + 3)(v + 3)  =  v²  + 3v + 3v + 9  =  v²  + 6v + 9

  -v + 27  =  v²  + 6v + 9

Since it is a quadratic, get all terms to one side; add v to both sides and subtract 27 from both sides.

  0  =  v²  + 7v - 18

  0  =  (v + 9)(v - 2)

So, either v = -9 or v = 2.

Checking answers, 2 works but -9 doesn't.

I believe that the way to find this is to divide the peak voltage value by √2.

The graph of 140sin(100πt) has a maximum value of 140 (since the maximum value for sin is 1).

140/√2  ≈  98.99 ≈ 100

If p = 2/3 and q = 1/3,

then p² + 2pq  =  (2/3)² + 2(2/3)(1/3)

                       =  4/9 + 4/9  =  8/9

When you multiply fractions, multiply the numerator times the numerator and the denominator times the denominator.

If you draw a right triangle ABC, with C the right angle. Let point A be the location of the plane and location B be the locaion of the station.  AC will be the height of the plane (5.9 km). The angle at B is 78.6°. Side BC represents the distance from the plane to the station (both in the air and across the ground).

For angle B, the side AC is the opposite side and BC is the adjacent side. If we want to find the length of BC, let's use tangent, because tangent = opposite / adjacent.

tan(78.6)  =  5.9 / BC

Cross-multiply:  BC · tan(78.6)  =  5.9

Divide:              BC  =  5.9 / tan(78.6)     --->     BC  =  1.19 km

Speed of the plane  =  distance / time  =  1.19 km / 10 sec  =  0.119 km/s

0.119 km/s x 60s/1min x 60min/1hr  =  428 km/hr

To what decimal location are we to round the answer?

To have 10^18 twenty times, you have 10^18 x 20, which is 20 x 10^18  or 2 x 10^19.

You want to find the number that, when multiplied to 10^-18 will give you 2 x 10^19

Equation:  10^-18 · x  =  2 x 10^19

Divide both sides by 10^-18:          x  = 2 x 10^19 ÷ 10^-18

When you divide numbers with the same base, subtract the exponents:

                                                    x  =  2 x 10^(19 - -18)

                                                    x  =  2 x 10^37.

There's a lot in here; if you have any questions, please ask!

Use the distributive property:

(x + 3)(2x + 7)  =  (x)(2x) + (x)(7) + (3)(2x) + (3)(7)                                                                                                          =  2x² + 7x + 6x + 21                                                                                                                                =  2x² + 13x + 21   

-2x(x + 3)  =  (-2x)(x) + (-2x)(3)                                                                                                                                  =  -2x² - 6x

2x² + 13x + 21 - 2x² - 6x   =  7x + 21

To find the square root of a fraction, write the problem as a fraction of square roots:

√(25/36)  =  √25 / √36  =  5/6

pi has an infinite number of decimals; it is not infinitely large (as in, larger than all possible numbers)

Also, what the calculator gave you was an approximation, not an exact value.

The square root of 24  =  √24  =  2√6  ≈  4.898979486  is the number that, when squared, makes 24.

$13 + ($14 + $11)  =  ($13 + $14) + $11       Associative Law of Addition

Use the distributive property:

(x + 3)(2x + 7)  =  (x)(2x) + (x)(7) + (3)(2x) + (3)(7)                                                                                                          =  2x² + 7x + 6x + 21                                                                                                                                =  2x² + 13x + 21   

-2x(x + 3)  =  (-2x)(x) + (-2x)(3)                                                                                                                                  =  -2x² - 6x

2x² + 13x + 21 - 2x² - 6x   =  7x + 21

-1 = -16/16

-1 + 5/16  =  -16/16 + 5/15  =  -11/16

x - 11/16  =  6/16

x - 11/16 + 11/16  =  6/16 + 11/16

x  =  17/16

They will be easier to compare if we convert both of them to decimals:

12/49 ≈ 0.244897...

1/4 = 0.25

Is it clear which one is larger?

You can set up a proportion:  AUD / NZD  =  AUD / NZD

     1 AUD / 0.931 NZD  =  x AUD / 788 NZD

Cross multiply:  1 · 788  =  0.931 · x

                                x  =  846 AUD

Substitute the various value for t in the equation;  y(t) = (1/4)cos(6t)       cos is in radians

t = 0:     y(0) = (1/4)cos(6·0) --->  (1/4)cos(0) ---> 1 ft

t = 1/4:  y(1/4) = (1/4)cos(6·1/4) --->  (1/4)cos(1.5) ---> .0176 ft

t = 1/2:  y(1/2) = (1/2)cos(6·1/2) --->  (1/4)cos(3) --->  

I think that you need to word your question better.

Translation  (This is in Polish)

calculate the value of the first space velocity for the Moon. Assume that its mass is 81 times less than the mass of the Earth, and the radius of 3.7 times smaller than the radius of ..

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I am sorry I do not understand what the question is.   What is 'first space velocity'?

Perhaps you could try rewording it.          

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Tłumaczenie (To jest w języku polskim)

obliczyć wartość pierwszej prędkości kosmicznej na Księżycu. Zakładamy, że jego masa jest 81 razy mniejsza od masy Ziemi, a promień 3,7 razy mniejszy niż promień ..

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Przykro mi, że nie rozumiem, co jest pytanie. Co to jest "pierwszej prędkości kosmicznej"?

Być może warto przeformułowanie go.

do it on the calc on the home page.

you can use the  $${\sqrt{{\mathtt{x}}}}$$    sign and then hit 7

or you can type in

sqrt(7)                  

And the question is?