geno3141

Sorry, I didn't see that they could represent line segments, I thought that they represented products.

I htink that you are completely correct.

An example of a number in standard notation is 32,000; this same number in scientific notation is 3.2 x 10^4.

Standard notation:  0.0034   ---   scientific notation:  3.4 x 10^-3

Write each of the factors with a base of 2:

8 = 2^3   --->   so, 8^3  becomes  (2^3)^3  =  2^9         When you have an exponent to an exponent,

4 = 2^2   --->   so, 4^2  becomes  (2^2)^2  =  2^4          multiply the exponents.

16 = 2^4

(8^3) x (4^2) x (16)  =  (2^9) x (2^4) x (2^4)  =  2^17   When you are multiplying numbers with the same

                                                                                     base, add the exponents.

This looks like a compound interest problem, where $300 is invested for 10 years at 16% interest and you are supposed to find the number of times per year that it is compounded.

If you tell us the final amount, we can help you find the value of n.

I don't know why CPhill assumed that tl + lc = tc; in fact, under this assumption, x = 7, but 

t reduces to √(350/11) ≈ 5.14

c reduces to (25√11)/√350 ≈ 4.432

l reduces to (11·√350)/(25·√11) ≈ 2.48

so l isn't between t and c.

Unfortunately, I don't know a possible answer.

One way is to compare the price per ounce; the one with the lowest price per ounce is the better buy:

$2.24 / 28  =  0.08 cents per ounce

$2.40 / 32  =  0.075 cents per ounce    <---  the  better buy

(1/2) ^ x  =  32

First way:

If the unknown is an exponent, find the log of both sides:

log[ (1/2) ^ x ]  =  log( 32 )

x · log( 1/2 )  =  log( 32 )

x  =  log( 32 ) / log( 1/2 )

x  =  -5

Second way:

Write both sides with the same base:

Since  1/2  =  2^-1  and  32  =  2^5:

(2^-1)^x  =  2^5                             When you have an exponent to an exponent, multiply the exponents:

2^-x  =  2^5

-x  =  5

x  =  -5

3(x - 5) + 8  =  -14.8

3x - 15 + 8  =  -14.8

3x - 7  =  -14.8

3x  =  -7.8

x  =  -2.6

In the exponent  2/5,  the 2 means to square the number and the 5 means find the fifth root (these can be done in either order).

1024^2  =  1 048 576  and the fifth root of  1 048 576  is  16

the fifth root of  1024  is  4  and  4^1  =  16

If you have $35,000 to put on a down payment, you have more than enough to pay for the snowmobile.

However, if all that you have is $3500 to put on a down payment, then you will still need to save

$6000 - $3500 = $2500.

At $400 per month, $2500 ÷ $400 = 6.25, it will take another 7 months to have enough money.