geno3141

Generally, it means the amount of mass divided by the amount of volume.

For example, the units might be grams per cubic centimeters.

I would argue that if you want the equation to have a positive root, then x must be positive.

But if x is positive, then both x^15 is positive and x^5 is positive.

Adding two positive number to the number 2, your answer must be positive; thus, it can't be zero.

(proof by contradiction)

10^-2= 1/10^2 = 1/100

If you have a whole number with a negative exponent, place the whole number in the denominator and make the exponent positive. 

Write the answer as 1 over the whole number with a positive exponent.

One way to do this that will work for other questions of this type (that is, for other number of terms and for other sum) is the following (but it won't by a 'pretty' answer:

Since we want 50 terms, add the first 50 whole numbers: 1 + 2 + 3 + ... + 48 + 49 + 50.

There is a formula that allows you do add these quickly: n = number of terms, f = first term, l = last term:

     Sum = n(f+l)/2

Since n = 50, first = 1, and last = 50:     Sum = 50(1+50)/2  --->  Sum = 50(51)/2  ---> Sum =1275

But the sum is 1275 and we want a sum of 2000, we need to 'scale up' every number.

How much? Since we want 2000 and not 1275, the scale factor will be 2000/1275 or 80/51.

Let's multiply each term by 80/51; this will then multiply the answer by 80/51 (and 80/51 x 1275 = 2000).

The terms are 1(80/51) + 2(80/51) + 3(80/51) + ... + 48(80/51) + 49(80/51) + 50(80/51)

or: 80/51 + 160/51 + 240/51 + ... + 3840/51 + 3920/51 + 4000/51

The first prime number is 2, but 2 doesn't divide into 1225 evenly (no remainder).

The next prime number is 3, but 3 doesn't divide into1225 evenly either.

The next prime number is 5 and it does divide into 1225 evenly:

     1225 ÷ 5 =  245

       245 ÷ 5 = 49

But 49 = 7 x 7; so all the factors of 1225 are 5 (twice) and 7 (twice).

      1225 = 5 x 5 x 7 x 7

5 + 0 * (5 - 5 ) / 0     --->     5 + 0 * 0 / 0     --->     5 + 0 / 0

0/0 is an "indeterminate form"; that means that it does not have any specific value (adding 5 will not change this).

It can also be called "undefined".

If you are in an algebra class, answer as "undefined".

If you are in a calculus class, answer as "indeterminate", because, if you have more information, you may be able to find the specific value for that situation.

I assume that you want it written in lowest radical form.

Factor the number, using perfect squares.

Since 4 divides into 28:    28 = 4 x 7

√28 = √4 · √7     --->    √28 = 2 · √7       --->     √28 = 2√7  

I don't have an answer, but I believe that it is answered at: en.wikipedia.org/wiki/Earth's_magnetic_field

I am assuming that you are trying to graph a rational function;

    that is, a function of the type: f(x) = P(x) / Q(x).

Case 1: If the degree of P(x) is less than the degree of Q(x) then the graph as the x-axis as a horizontal                                asymptote.

Case 2: If the degree of P(x) is equal to the degree of Q(x), then the graph has an horizontal asymptote                   which is found by the equation;     y  =  a / b    where a is the leading coefficient of P(x)                                                                                                     and b is the leading coefficient of Q(x).

The degree of a polynomial is the highest exponent of the variable.

Example of case 1: f(x) = (3x + 9) / (4x² - 14)

                                        here the degree of P(x) = 1 and the degree of Q(x) = 2.

Example of case 2: f(x) = (7x³ -4x + 9) / (-x³ + x²)  ---> asymptote is y = 7 / -1   --->   y = -7

In other cases, there will be no horizontal asymptote.

413 = 7 x 59      (and no no other prime factors)

499 is not evenly divisible by either 7 or 59.

Therefore, the fraction 413/499 cannot be simplified into another common fraction.