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ur welcome melody ! 

I am not sure what you want but Rosala has answered you. Thanks Rosala

$$3+4^{-1}=3+\frac{1}{4^{+1}}=3\frac{1}{4}$$

The answer is just $$Volume = \frac{4}{3}\pi (\frac{h}{2})^3$$

For part a) just plug in 12 cm for h.

It is possible to do this the hard way, by calculating the bead volume for a non-zero radius hole, and, strictly one should do this in order to prove that the bead volume is independent of the hole radius.  However, since the question here specifies that the volume is independent of hole radius, why make life difficult?!! 

How much wood could a woodchuck chuck if a woodchuck could chuck wood??"

Type this into "wolframalpha" --for a cool answer!

Breaking news......the bird and nest have been found safe......the mother claims that she temporarily went off on a "tangent".

That's great! I thought the puddy-cat ate the bird.

common now ! stop ! 

With β = 10*log(l/l_o)  then l = l_o*10^(β/10) 

a) l_conv = l_o*10^(60/10) or l_conv = l_o10⁶       l_pain = l_o*10^(130/10) or l_pain = l_o*10¹³

Therefore l_pain/l_conv = 10¹³/10⁶ = 10^13-6 = 10⁷ .  That is, the intensity at the pain threshold is ten million times greater than at conversation level.

See if you can now do part b)

1b.)if it was necessary to have at least one female and at least one male in the three positions, determine the number of ways the three positions could be filled (use permutations)

no of all female permutations  is 6P3

no of all male permutatuons is 4P3

total number of permutations 10P3

therefore number of permutations that are not all one s*x are 10P3-6P3-4P3

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2.) There are 10 students, 6female, 4 male, from which a committee of 3 is to be chosen.

a.) Determine the total number of ways the three positions could be filled?    ₁₀c₃=120

b.) if it is decided that the committee cannot be made up of only males or only females, determine the number of ways the committee could be made ? 

Okay I am assuming this time order doesn't matter.

so the number of combinations will be 10C3-6C3-4C3

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Probability is not my strongest area but I am pretty sure they are correct.

Hi kitty,

I'm sure your answer is correct - you rarely get any wrong - but that is not a binomial expansion.

$$(x+7y)^3= (7y)^3+3*(7y)^2(x)+3*(7y)(x^2)+(x)^3

And you can take it from there.$$

The binomial theorem (for a cubic expansion) says:

(a + b)³ = a³ + 3a²b +3ab² + b³ 

If you substitute x for a, and 7y for b in this you should get the result shown by kitty<3. 

The following graph should help with part 1).   (Hint: you can't have values of x that make the functions infinite).

For part 2) note that csc = 1/sin and sec = 1/cos 

For part 3) multiply through by sin²x*cos²x (and remember that sin² + cos² = 1)

its 2 ! anything else ! 

heres the help :

45 + 21^2

=45 +441    ( 21 * 21 = 441 )

=486 is the answer ! 

I'll get the same answer but it the working might look different.

$$(x+3)(4+2xyz)\\\\
=x(4+2xyz)+3(4+2xyz)\\\\
=4x+2x^2yz+12+6xyz$$

Perhaps start by looking here.

I wish people would be more careful when they enter their questions.

Members can edit theirs but non-memebers need to take exceptional care!

I susupect it was suppose to be 4 and the zero was meant to be a bracket but not to worry the technique is very similar.

I think you have done it back to front from what is usual.  But the answer (to the question that you answsered) is still correct.

243=(2/3)^5

Can we then say

$$log_{(2/3)}243=5$$

I don't know that I have seen fractional bases before?

Looks okay but  i think it said 3/4 inch needed at one end.

Otherwise it looks really good.

Thank you NinjaDevo

Good sports lover but it would have been a bit better if you had subtracted 9 from both sides as a first step.

A good answer Ninja!

You know  this has been going around the forum since before I was born - and that was quite a while ago.

BUT for all you new people,  here is 'the' clip.

You're very welcome:) I'm sure your math teacher will explain radians soon.

Thank you so much Kitty - I have never heard of radians before.

Hello helpmeplease,

That is a common problem with trig functions on calculators. Check that your calculator mode is in degrees, not radians.

Radians are just another way of measuring an angle in pi, so they will show up as small decimal answers.  For most problems you want to use degrees.

On my Ti-84 graphing calculator, I go to "Mode" then go down to the third row and select "Degree" On this site's calculator, you can select "Deg" or "Rad" in the bottom left corner:)