if tan(theta) = -3 and cos(theta) < 0, then tan(theta/2) = ?

so

so

 (we take the negative case because cosine is negative for this example)
now

Therefore...


which simplifies to

find the unknown length in the right triangle one side is 9m and the other side 15m.

If we assume that 15m is the longest side then a side of 12m will give us a right triangle (why?)

:)

simplify: 53-[3(8+2)+5(9-5)]

53-[3(8+2)+5(9-5)]=
53-[3(10)+5(4)]=
53-[30+20]=
53-50=3
:)

find the slope of the linear equation y=3x-6

Since this equation is written in slope-intercept form, we can see that the slope is the coefficient of the x term. The slope is m=3

for the sequence,describe the pattern, write the next term, and write a rule for the nth term 1,2,4,8.

This sequence is the powers of 2, so the next term is 16 and the rule for the nth term is

notice we subtract 1 from n (why?)

:)

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

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

Is it a function?

given the relation {(-4,-2),(1,-4),(3,0),(4,3)} determine if this relation is a function
a. yes it is a function because each x value has only one y value
b. no it is not a function because -4 appears twice
c. no it is not a function because each x value does not have a unique y value
d. yes it is a function because each x value is unique

by definition of a function:
a. yes it is a function because each x value has only one y value

Find dy/dx at the point (0, 1), if y^5 = (x + 2)^4 + e^xln y − 15 Amy.

Saying that 4 < sqrt(x) < 9 is equivalent to saying what about x?

typically we want to write inequalities in terms of a variable, so we rewrite it in terms of just x:

:)

7 raised to 5x-8 and 5 raised to x+2 if product of these two is equal to 30625 then how to find value of x

:)

Solve: x= 3 + sqrt(3x -5)

.

Solve: sqrt( 3x+3 + sqrt(x+2)) = 5

.

Radicals/918343: 3 = x-2√x

divide by a polynomial: (x^4+2x^3-6x^2-7x-41)/(x^2+x-10)

Find all zeros of the polynomial: P(x)=(x^2+4)(x^2+x)-(x^2+4)

 

solutions are
, 
and

Find the exact zeros (show your work using synthetic division and\ or factoring )F(x)=x^3-7x^2+13x-3.

What is the leading coefficient of -3x^2+2x+5x^3 ?

The leading coefficient is the coefficient of the term of greatest degree (regardless of the position of that term) so it is 5

Solve: 8|2-9p|-2=14

8|2-9p|-2=14
8|2-9p|-2+2=14+2
8|2-9p|=16
8/8|2-9p|=16/8
|2-9p|=2 

case 1)
2-9p=2
-9p=0
p=0 

case 2)
2-9p=-2
-9p=-4
p=4/9