What is the solution to the radical equation?

  - 1 = 2

What is the inverse of the sentence, "If Sam leaves, then I will stay."?

The logical inverse of an if-then statement p -> q is

~p -> ~q

For us 

p is "if Sam leaves" so ~p is "If Sam does not leave"

and q is "I will stay" so ~q is "I will not stay"

Therefore the inverse is:

If Sam does not leave, then I will not stay.

The element lawrencium has a half-life of 10 hours. What fraction of 1 ounce of lawrencium will remain after 4 days 4 hours?

4 days and 4 hours is 4(24)+4 = 100 hours 
so our quantity is halved 10 times over the time period: 

 



so its 1/1024 oz

Determine Algebraically whether f(x) = 1 + x + x^2 is even, odd, or neither

A function is even if f(x) = f(-x), but for our function

f(-x)=1-x+x^2

so it is not even.

To be odd -f(x)=f(-x), and for our function

-f(x) = -1-x-x^2

and so it is also not odd.

Therefore it is neither.

Find the twentieth term of the arithmetic sequence with a1 = 15 and d = 4.

For an arithmetic progression we use the formula:

n=20, a1=15, d=4








:)

how can i decompose this partial fraction(4x^3)/(x^3-x^2)

This is not a "proper" decomposition problem. Typically the degree of the denominator is greater than the degree of the numerator...

but...we can still simplify...
notice that this expression can be factored:

from here we notice that by polynomial long division (don't know how to show using this editor) that:

so our expression simplifies to...



:)

find a if a(a-8)=20

a(a-8)=20

so a= 10 or a=-2