CPhill

$10380.72.....the value "declines" because we're multipling an initial value by something between 0 and 1 (.82) five times.....a "depreciation" problem, maybe???

It depends.....let's suppose that your "stuffie"  holds 2 cubic units. Let's suppose that the first item that you put in has a volume of 1 cubic unit and each additinal item has 1/2 as much volume as the previous one.

Then the first few items have a total volume of

1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 = 1.9921875 cubic units

And we could, theoretically, put as many items in the "stuffie" as we wanted to as long as each successive one had 1/2 the volume of the previous.

(This also answers the question, "How many angels will fit on the head of a pin????")

If you take Calculus, you'll see that we approach a "limit" here....I'll keep you in suspense as to what that limit is......maybe you can guess it !!!  

(It also proves that seemingly "frivolous" questions sometimes prove to be more interesting than first thought!!!)

Here's a slightly easier "formula" to use which doesn't involve the need to solve for "time" first.

v² = u² + 2 (a) (s)......where v is the final velocity, u is the initial velocity, a is the acceleration due to gravity and s is the initial position. Note that "u" is just "0" in this problem, since we're just "dropping" something. So we have...

v² = 2 (9.8m/s²) (61.6m) =

v = √(2 (9.8m/s²) (61.6m)) = 34.747 m /s...which is exactly what Melody found, too.

Since the motion is "downward," this, of course, is "negative."

Your choice !!! 

Let me append something to this...Melody's method might be of more interest, because it gives a more complete "picture" of the situation.

You cut a piece of ribbon into 2 pieces so that one piece is 24 inches longer than the other. The longer piece is 4 times longer than the shorter piece.

I'm assuming that you want to know the lenth of both pieces.

OK.....call the length of the shorter piece "x" and the length of the longer piece "x + 24.'

Then 4 times the length of of the shorter piece = length of the longer piece. In math terms, we have

4x = x + 24       Let's solve for x.......Subtract the "x" from the right side.....This gives

3x = 24   Divide both sides by 3.....this gives

x = 8 (inches).....This is the length of the shorter piece.

The longer piece  = x + 24 = 8 + 24 = 32 (inches)

That makes sense...... 32 inches is 4 times longer than 8 inches and 24 inches longer than 8 inches !!!......  

What is the answer to this?: cos43=15/b

Well...let's just "solve" for b. Multiply both sides by b and divide both sides by cos43. This gives us

b = 15 / cos(43).

Technically, the "43" represents 43 "radians," but I have a feeling that we're dealing with degrees, so I'm gonna' stick a little degree symbol on it !! (My former trig teacher used to become "unglued" if someone didn't specify "degrees!!!!") So we have...

b = 15 / cos(43°)  ≈ 20.5

And there's "b"        

what does it mean when you say classify a real number?

We have two broad classes of numbers, real and non-real

The real numbers include, well, those found on the "number line"

We have several categories of "real" numbers:

1) Natural numbers....usually known as "counting numbers"....1,2,3, etc. "0" is sometimes included, too. If "0" is included, these numbers are sometimes referred to as "whole" numbers.

2) Integers....basically...all the natural numbers, "0," and the negatives of the naturals...i.e.,   ...-3,-2;1,0,1,2,3... These extend to infinity - both positive and negative - on the number line

3) Rational numbers - basically, anything that can be expressed as a fraction... 2/3, 4/5, etc. All the integers are rational because I can express something like "10" as 20/2 or 80/8, etc. "0" is rational, too, because I can write  it as  0/1, 0/2, 0/3, etc. Also, repeating decimals are rational.

Note that all integers are rational, but not all rationals are integers !!! Thus, the "integers" form a subset of the'"rationals."

4) Irrational numbers - Any real number not capable of being expressed as a ratio. These include things like (pi), (e), etc. Any positive number that cannot be wholly taken out of a square root is also irrational. Thus, SQRT(5), 6*SQRT(3), etc., are irrational. Also, non-repeating decimals are irrational.

Non-Real numbers - You will encounter these in "upper" maths. They're known as "complex numbers" or, more familiarly, "imaginary" numbers - a poor name, because we can actually graph them on a "complex" plane!!! These include things like 3 + 6i, 4i, -5i, etc., where the "i" is the "imaginary" part. Any "negative" square root is also  "imaginary" (complex).

I think I've covered most everything. Here's a website that presents a nice picture of what I've presented. It may even throw in a few "extra" things, too !!!

What are you looking for .....area??.......finding angles or sides??......right triangle properties??

A coin had a value of $1.17 in 1995. It's value has been increasing at a rate of 9% per year.

I assume you want to know its value now.

To calculate this, we have

A_n = A₀ * (1.09)ⁿ

Where A_n is the value after n years, A₀ is the original value, and the exponent n  is the number of years.

So we have

A_n = 1.17* (1.09)¹⁹

See if you can go from here......

what is 8.94 rounded to the nearest tenth?

Look at the "hundreths" digit. If it's 5 or greater, we "round up.' If it's less than 5, we "round down."

In general, we use this rule for rounding to the nearest value specified. Look at the next digit - If it's 5 or greater, we "round up.' If it's less than 5, we "round down."

 Now, see if you can figure this one out........

On a map, the distance between two cities is 5.25 inches. The map scale is 1 in =25 mi. To the nearest mile, what is the actual distance between the two cities?

Well...1 inch would be 25 miles. ( 1 x 25)

2 inches would be 50 miles.  (2 x 25)

So, to find the number of miles, we have....... (inches) x (25 miles per inch)

See if you take it from here.......