geno3141

If the system is defined as the two cars before the collision, during the collision, and after the collision, there is no change in total momentum (law of conservation of momentum).

Negative exponents are handled like this:  x^-1 = 1/x  so  x^-2 = 1/x²

This problem has (2a)^-2 which becomes 1/(2a)²  =  1/(4a²)

Therefore:  (2a)^-2 / a²  =  [ 1/(4a²) ] / a²  =  [ 1/(4a²) ] · [ 1/a² ]  =  1 / [ (4a²) · a² ]

   =  1 / ( 4a⁴ )

Choose any number that you want for b ... any number will work ... and then determine the others ...

(-1)^-2  =  1/(-1)²  =  1/1  =  1

So:  1 - 4(-1)^-2  =  1 - 4(1)  =  1 - 4  =  -3

If the problem is:  (2p + 3q)/q  =  3/8

cross multiply:  (2p + 3q)(8)  =  (3)(q)

simplify:           16p + 24q  =  3q

subtract 24q from both sides:  16p  =  -21q

divide both sides by q:       (16p)/q  =  -21

divide both sides by 16:           p/q  =  -21/16

If you have an exponent to an exponent, multiply the exponents together:

--->   (5⁴)²  =  5^{4 x 2}  =  5⁸

You can think of it this way:  the first exponent (the 4) tells you how many 5's you have in each group; the second exponent (the 2) tells you that you have 2 groups. When you have 2 groups with 4 in each group, you have 2 x 4 or 8 items; in this case, you have eight 5's multiplied together.

When graphed, the equation  p = x² - 25x + 5000  is a parabola, rising from the vertex.

Since it has a minimum point and opens upward, the problem is to find the vertex (which is the location of the minimum point).

This can be done in several ways: one way is to graph it, another is to use a formula, and a third is to "complete the square".

The following explains how to complete the square:

First, move the constant term to the other side:

--->   p - 5000  =  x² - 25x

Second, divide the coefficeint of the linear term by 2, and square the result:

--->   -25 ÷ 2  =  -12.5

--->   (-12.5)² =  156.25

Third, add this value to both sides:

--->   p - 5000 + 156.25  = x² - 25x + 156.25

Fourth, simplify the left side and factor the right side:

--->   p - 4843.75  =  (x - 12.5)²

Fifth, determine the vertex:

--->   x = 12.5, y = 4843.75

The minimum value is the y-value:  4843.75

Since there are 1000 metres in a kilometre, multiply 2.4 x 1000 to find the number of metres.

True (assuming that the time is long enough to have interest calculated upon interest -- more than one period of time).

The problem (x⁵y²) / (yx)² can be written as:  (x·x·x·x·x·y·y) / (y·y·x·x)

and can be simplified by cancelling out the same factors in the numerator and denominator to end with:  x³.

(Or, since you are dividing, subtract the exponents from the same factors.)