CPhill

Let's see how jboy314's answer was derived.

The "formula" for the monthly payment is given by:

M = P(1+r)ⁿ r / [(1+r)ⁿ-1]

Where

M = the Monthly Payment

P  = the amount financed ($20000)

r = the montly interest rate expressed as a decimal = .069/12 = .00575

So we have

M = (20000*(1+.00575)^60*.00575)/ ((1+.00575)^60 -1)) = $395.08

We seem to have a "variable length" pendulum, Jedithious !!!

We'll use 31cm and call it good.......(Sorry, I forgot that the question requested to the nearest cm!!...my bad)

1.   30% = .30 in decimal form

     "Of" means multiply

     "What Number" is "x"

     "Is" means "Equal To"

So we have

.30 * x = 14.1      divide both sides by .30

x = 47    and that's the "What Number"

2. I assume you want to convert 81 cm to inches......so we have

81cm *  (1 inch/2.54cm) = about 31.89 in.       .....notice that the "cm" "cancel" abd we're left with the desired unit (inches)

The radius is (1/2) of the diameter, so (1/2)* (11.6) = 5.8

Anonymous has answered correctly if we were setting the original expression = 0. That wasn't indicated in the question, but it may have been intended......I can't say......

Using the distributive property, we have

6a(11a) + 6a(5)  =

66a² + 30a

I've been giving some thought to this one....I believe Melody is correct.....our previous answers were incorrect with respect to allowing repeats.....I think that the answer is WAY larger.......

I see this as a "slot" problem with these considerations........

1. Choose any 4 of of 7 "slots" and let each slot be occupied by any one of 26 letters. Notice that order isn't a consideration, since, for example, "slots" 1-2-4-7  are the same as 2-1-4-7 or 1-4-2-7.

2. For each arrangement above, the other 3 "slots" can be occupied by any three digit combination utilizing numbers 0 through 5.......there are 556 of these possible combinations.......(000 through 555).

So we have:

C(7,4)* (4^26) * 556   = 87,640,048,748,629,852,160  combinations  !!!

Whew!!!....that's a pretty big number!!! (Note that the 4^26 part contributes to most of the "bigness".....)

Anyone else have any ideas on this??

Let x be the number of adult tickets sold and let y be the number of children's tickets sold.

So     x + y  = 8400

And the number of adult tickets sold times the price for each plus the number of children's tickests sold times their price = $40,000   or, in equation form

6x + 4y = 40000         Now, if we subtract x from both sides of the first equation, we have that y = 8400 - x

And substituting for y in the second equation, we have

6x + 4(8400 - x) = 40000    .....simplifying, we have

6x + 33600 - 4x = 40000

2x + 33600 = 40000    ..... subtract 33600 from both sides

2x = 6400     ...... divide by 2 on both sides

x = 3200    .......so this is the number of adult tickets sold

And using y = 8400 - x,  we have y = 8400 - 3200 = 5200   ..and that's how many children's tickets were sold.

Let's add 16 to both sides.....this gives

x^2 - 8x + 16 = 0     factoring, we have

(x -4) (x-4) = 0

So, we only need to set one factor to 0....this gives that x = 4

The pendulum is 31.114476537214339461859 cm. long

To see this, note that when the pedulum swings 40 degrees from the vertical, the horizontal component is now 20cm. So, to find the vertical component in this position we have

20/tan 40 = 23.8350718518921531 cm long

So the total length of the  pedulum is just √(20² + 23.8350718518921531²) = 31.114476537214339461859cm

To see that this is true, note that when it swings back to vertical, the vertical component changes from

23.8350718518921531 cm to 31.114476537214339461859 cm (the full pendulum length, there is no horizontal component in this position!!!)

So the difference in this length minus the  the vertical component length when the pendulum is swung 40 degrees from the horizontal is just 31.114476537214339461859 cm - 23.8350718518921531 cm =

7.279404685322186361859 cm or about 7.3 cm !!