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pi is a mathmatical constant found frequently in nature, ususally associated with circles, or rotational mechanics. it can be easily calculated by taking the circumfrence C of a circle and dividing it by the diameter d: C/d=pi. The actual number itself is 3.14159265359, though it is commonly truncated to just 3.14. 

the lateral area of a cone with radius 4 cm is 60 cm. a) Determine the slant height of the cone? b) Determine the height of the cone.

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The "formula" for the lateral surface area of a  cone is given by:

A = π * r * l

Where A is the area, r is the radius, and l is the slant height.  For convenience, I'll use 3.14 for π.  So we have....

60 = 3.14 * 4 * l   Solving for l, we have....

(60)/(3.13 * 4) = l  ≈ 4.77 cm.

Now, to find the height, we can note that the height and the radius form two legs of a right triangle, and the slant height, l, forms the hypoteneuse. Something like this:

So we have, using the Pythagorean Throrem, h = SQRT( l² - r²)

So we have:

h = SQRT(4.77² - 4²) ≈ 2.6 cm.

That makes sense. It should be less than the hypoteneuse.....and it is!! It's always good to check that your answer is "reasonable!!"  Also note, that it's a pretty "flat" cone!!!

Use your feet.

What actually are sine, cosine, and tangent? Are they numbers that go on infinitely, like pi? 

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They are ratios......specifically - in right triangles - of one of the side lengths to the hypoteneuse or of one of the "legs" to the other. If we're looking at some angle in a right triangle other than the right angle, the sine is the ratio of the "leg" opposite that angle to the hypoteneuse length. The cosine is the ratio of the length of the "leg" adjacent to that angle to the hypoteneuse length. The tangent is the ratio of the length of the opposite "leg" to the adjacent "leg."

The normal sine and cosine functions have"ranges" between -1 and , inclusive. So they take on all real number values in this range......Thus, their values can be either "irrational"(non-repeating decimals like the "decimal" part of pi), or "rational" (can be expressed as a fraction) in this range,  depending on the angle.

The tangent, (where defined), has a range from -∞ to +∞. It takes on all real number values - rational and irrational. Note, that for reasons I won't go into, the tangent isn't defined for certain angles!!

Hope that helps

Re: which data set best describe by the function y=2x squared+5x

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It's a parabola opening "upward' with its vertex at (-1.25, -3,125) 

The first order approximation of f(x,y) around some point (a,b) is:

$$f(x,y) = f(a,b) + f_x(a,b) (x-a) + f_y(a,b) (y-b)$$

In your case:

$$f(x,y) = f(-9,9) + f_x(-9,9) (x - -9) + f_y(-9,9) (y - 9)$$

Fill in your values to get the results... 

I'm not actually sure what was intended either, Alan.  I assumed that we were either selecting some 10 from the 40 or that we were selecting one group of 10, then another group of 10, etc.

Your way sounds valid, too!!

(Maybe we should form a "subgroup" of  "n" forum members to study the question!!

I wonder how many ways we could select THAT??)

You would first need to use the cosine rule [ cos(A) = (b² + c² - a²)/(2bc) ] to find one angle, then you could use the sine rule [ sin(B)/b = sin(A)/a ] to find the other angles. 

a²b(3a² + 4ab²) = 3a⁴b + 4a³b³

Hmm!  Chris, suppose there are 4 volunteers where each subgroup consists of 1 participant. 

If there is one subgroup then clearly there are 4 possible choices.

However, if there are 4 subgroups, it seems to me there is only one way to do this; but your method would give nCr(4,1)*nCr(3,1)*nCr(2,1) = 24 ways!!  This would only be correct if each subgroup were given a different label and it was the number of combinations of label and participant that was required.  Perhaps the subgroups are given labels - this would be quite sensible. However, it isn't clear to me that that was what was intended here.

There are 40 volunteers for the research study on the Power Pill. Each subgroup of the study will contain 10 participants. Determine how many ways these participants can be selected and explain your method.

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If we're just talking about selecting only one subgroup of 10, then we have the number of ways that we can choose 10 people from 40. This is known as a "combination," and is denoted as 40C10 or as C(40,10).

And C(40,10) = 847,660,528 ways   (quite a lot, huh??)

Now, if you're specifying that we're choosing one group of 10 from 40 and the next group of 10 from the remaining 30, and the next group of 10 from the remaining 20...we have WAY more options....this is given by

C(40,10) X C(30,10) X C(20,10) = 4,705,360,871,073,570,227,520 ways... (This number ≈ 4.7 "septillion," as  the term is used in the U.S.)

Note that I didn't have to worry about specifying in the "formula" the combination for choosing the last 10. There's only one way to do that........"choose" all of them!!!

Hope that answers your question   

what does -6-x equal? then i can tell u

distribute so u get 3a^4b+(4a^2*b)^4b

hihihihihihihihi

42!!!!!!!!! (thats in kilometers by the way!!!)

Because the bag and the packet added on to the weight of the apples and crisps. In total, the bag and packet weighed .1 lb together while the apples weighed 1.25 lbs and the crisps weighed 35 lbs. OK? Hope I helped!!!

22! its so obvious

Potato!!!!!!!!!

Cos c= 0.6879 , who do you get c by self. whats C= ?

We're just trying to find an angle whose cosine = .6879

You can use the on-site calculatoer for this.......just hit the "2nd" button, the "acos" button, and type in the value you're looking for. "Acos" stands for "cosine inverse" - sometimes written as cos^-1(x).

So, acos(.6879) ≈ 46.54°

Be careful......since the cosine also has a positive value in the 4th quadrant, this might be a 46.54° angle in that quadrant......i.e., 313.46°   

2+2=1+1+1+1=0.5+0.5+0.5+0.5+0.5+0.5+0.5+0.5=0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25+0.25=4

42 is the meaning of life (it's from "a hitch hikers guide to the galaxy")

2.0258165153785312

potato (2)

Re: 3,6,18,72,360, what is the next two terms

Let's see if we can discover a "pattern"

3(1) = 3

3(2) = 6

3(6) = 18

3(24) = 72

3(120) = 360

Mmmmm....I think I see it now.....the terms inside the parentheses are just  "factorials" - 1!, 2!, 3!, etc.

So, the next two terms should be

3(6!) = 2160

3(7!) = 15120

That's quite  a nice series!! ...... (factorially speaking!!) 

    6 = 2*3

  18 = 3*6

  72 = 4*18

360 = 5*72

 xxx = 6*360

 yyy = ?*xxx

I'm sure you can work out what xxx is.

Looking at the pattern, what do you think ? is?  With it and xxx you can work out what yyy is.