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f(x)=9x² -2

This is a parabola that opens upward with a vertex at (0, -2). Thus the range is just

[-2, ∞) and since we can substitute anything in for x, the domain is (∞,∞)

f(x)=√(9x² -2)

Since the result of taking a positive square root is always positive or 0, the range is just [0,  ∞). And since we can't have a negative value under the square root, we can just see what makes 9x² - 2 = 0.

9x² -2 = 0

9x² = 2     divide both sides by 9    

x² = 2/9    take the square root of both sides

x = ±√2/3

So the domain is given by (-∞, -√2/3] U [√2/3, ∞)

This is actually quite a well-known recreational maths problem.  I first came across it in a Martin Gardner book xxx years ago!  However, in the usual statement of the problem it doesn't tell you the answer.

In the statement of the question here, the hint in the last sentence gives the game away.  In the limit when r is zero, the height, h, becomes the diameter of the sphere.  (In this limit the sphere has an infinitely thin hole of zero volume, so the bead becomes the whole sphere of diameter h).

Bertie is right.

Also, in the line below "Since y(0) = y₀" you have the term -2*0.  This should be +2*0.  However, since the result is zero anyway, this doesn't have any impact on the result!

455*56 = 25,480

The answer is 25,480 then.

2√3 - √27

Note that we can write √27  as √9 * √3   = 3 * √3 = 3√3

So we have

2√3 - 3√3   =   -1√3  or just  -√3

And that's it.....

1000+12+12+3+60+1+78+100+1+100+129+103+86+50+109+109+109+109 = ?

(1000+12+12+3)+(60+1+78+100+1)+(100+129+103+86)+(50+109+109+109+109) = ?

(1027)+(240)+(418)+(486) = ?

(1267)+(904)

=2171 

If I'm reading this right, we need 3/4 space allowed on each end that can't be used for stamping, and each stamping requires an area of 1 over 3/8 inches. How many will fit in a 72 inch strip?

I think this is how to solve it...

3/4+3/4+11/8(n) = 72

6/4+11/8(n) = 72

1.5+1.375(n) = 72

-1.5               -1.5     -Subtract 1.5 from both sides

1.375(n) = 70.5

/1.375      /1.375    -Divide both sides by 1.375

n = 51.272727

It asked for complete strips, so a total of 51 complete strips can be made out of this peice of aluminum.

Let's check it:

1.5+1.375(n) = 72

1.5+1.375(51.272727) = 72

71.999999999 ~= 72  ✔

To express (3x-40) (6x+4) as a trinomial, multiply the two binomials.

   (3x-40)

* (6x+4)       -Just multiply like you usually would if they were numbers 

----------------

             12x -160

+ 18x² -240x + 0      -add them up

-----------------

18x² - 228x - 160

So (18x² - 228x - 160) is your trinomial

To check it, put in a number for x on both equations.

(3(5)-40)*(6(5)+4) =

(15 - 40)*(30+4) =

(-25)*(34)

= -850

(18(5)² - 228(5) - 160)=

(450-1140 - 160)

= -850 ✔

Use n as the unknown number to solve:

n ÷ 2010 = 2.01020102010210

*2010      *2010        --Times both sides by 2010

------------------------------

n= 4040.504050405221

Let's check it:

4040.504050405221 ÷ 2010 =  2.01020102010210

2.0102010201021 ~= 2.01020102010210  ✔

A woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood.

Start by lining it up vertically.

   3X + 9

-  5X - 0   (then just subtract like you usuallly would)

------------

 -2X+9 

 So your answer is (-2X+9)

You can check this by putting in a number for x, for the simplified version and the original problem to see if it works. Let's put the number 5 in.

Original problem: 

(3(5)+9)-(5(5)-0) =

(15 + 9)-(25- 0) =

(24)-(25)

 = -1

Simplified version:

(-2(5)+9) =

((-10) + 9)

= -1

They both equal -1, so it works!

-4x+9=-5

-4x+9+5=0

-4x+14=0

-4x=-14

x=-14/-4=3.5

verify

-4(3.5)+9=-5

-5=-5

e^-ty = e^-t(t² + 2t + 2) + c, where c = y₀ - 2.

Multiply throughout by e^t.

If you want to know what factoring is, then you need to know what factors are. Factors are the operands in a multiplication. If you want to "factor" a number, X, then that means you want find some set of other numbers that yield X when they are all multiplied by one another. Similarly, if you want to factor some algebraic expression, that means you want to find some set of two or more other expressions that can be multiplied together to get the original.

Why is that?

sorry melody i didnt realize the 9 didnt show up

Translation:  I like achievement of another way to write my question is equal to the root of 1/6 but not the result but the other way to say

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I'm assuming you want to know how to express another way of saying that somethig is raised to the "1/6" power.....

It's the same as saying the "6th root" of that thing.......

I hope that is what you were asking....

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Estoy asumiendo que usted quiere saber cómo expresar otra forma de decir que somethig se eleva a la potencia "1/6" .....

Es lo mismo que decir el "sexto raíz" de esa cosa .......

Espero que sea lo que estabas preguntando ....

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The trig function that relates the opposite and the hypoteneuse is the sine...thus.....

sin(x) = opp/hyp = 4/15

To find this angle, use the arcsin function

arcsin(4/15) = x ≈ 15.47°

There is two ways you can prove this:

1. You can prove it using decimals

6.66666667 ~= 6.6666 so,

10*.6666 = 6.6666

6.666 = 6.666  ✔

2. You can prove it using fractions

10/1*4/6 = 6  2/3

10/1*2/3 = 6  2/3

20/3 = 6  2/3

20/30 = 20/30 ✔

Using fractions probably gives you a better visual.

Does this answer your question?

10*4 = 40

40/6 = 20/3  = 6+2/3 =  6.6666.......

what a face ! lol !

ok so im guessing this is 4/3*3.14*6.2^3 so doing that equation it would equal 997.799893333 does this answer your question?