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cosx = -4/9     in quadrant 2 and 4

arccos (-4/9) = 2.03 R   and 4.25 R

it's part of an assignment that is due in a few hours

Are 3.14 and 3.142 both supposed to be pi?

What if all the solutions have 9,18,or 6 as a denominator?

ok i put the part in

(a + b + c )/3 = 9

c-4 = a    c = a+4

b+3       = 2/3 ( a +3)        b = 2/3( a+3)  - 3       Sub the red in to the top equation

(a + 2/3(a+3)-3   +   a+4 )/3 = 9

2  2/3 a   +3 = 27

8/3 a = 24

a = 9               then   c=a+4 = 13  y/o                 and b=5

**** deleted ****

csc is   1/sin    in quadrant III   and IV   sin is negative, so there should be two answers'

1/sin = -2 sqrt3/3

sin = 1/(-2 sqrt3/3)

arcsin = -60 degrees    and   240 degrees       or     240 and 300 degrees   or  4pi/3    and  5pi/3     this is   3x

divide the answers by 3     4pi/9   5pi/9      (edited)  

For k = 4, both equations reduce to x = y, so the answer is k = 4.

First, we choose the two girls to stand next to each other.  We can do this in 5*4/2 = 10 ways.  There are then 8 ways to choose the two places where they stand next to each other.  There are 7 other people on the soccer team, so there are 10*8*7! ways to arrange the team members.  Answer = 403200.

1980 a^9 b^11 c^4 

f = fancy                  total cost  28 f

(7-f) = p = plain       total cost of plains 15 (7-f)      summed, the costs are 131

28f      +     15 (7-f)      = 131      solve for f, the number of fancy shirts..... then plains  =     7-f

Amplitude 4

   4 cos x

Shifted down 4

   4 cos x       - 4

Shifted pi/4  right

  4 cos(x- pi/4)   - 4

Working alone and at a constant rate, Machine A takes 3 hours to create a widget. Machine B, working alone and at a constant rate, takes x hours to create a widget. Working together, Machine A and B take 12 hours to build two widgets. What is the value of x?

Machine B is 3X slower than machine A

3 + x = 12        x = 9  

0.3^2 = 0.09

0.4^2 = 0.16

so 

sqrt(0.16) = 0.4

sqrt(0.09) = 0.3

So 

\(0.09\le x <0.16\)

0.16-0.09 = 0.07

probability is 7%

Actually this is not quite right because I have assumed that the first non zero is in the tenths place value but it could be in some other place value.  So the answer is slightly higher than this. If you want the exact answer you'd need to set up a series  with all possible answers and look at it.

-5e-x+17=7    subtract 17 from both sides then divide by -5 to get

e^-x = 2           can you get it from here.....take the ln (natural logarithm) of both sides.....

Here is one way that doesn't use  logs

8^5x  =  (2^3)^5x   =   2^15x

16^*(3x+4) = (2^4)^(3x+4) = 2^(12x+16)

now equate the exponents

15x   = 12x + 16

3x = 16

x = 16/3

Let be P the centroid of triangle ABC. If triangle ABP is an equilateral triangle with a side length of 2, then find the perimeter of triangle ABC.

AB = 2

PF = sqrt(3)

CF = PF * 3

AC = BC = sqrt[(AF)² + (CF)²]

Perimeter of triangle ABC = AB + AC + BC    

sorry thats wrong

First, we can choose the seats for the four mathematicians.  Then we seat the physicits, then the engineer.  There are 4! ways to seat the mathematicians, then 3! ways to seat the physicists, then 1! ways to seat the engineer.  But then we must divide by 8, because we can rotate the table, so there are 8!*4!*3!/8 = 725760 ways to seat everyone.

Example: Find the LCM of 2 and 4

You first find the GCF, which is 2.

You take 2 * 4 and divide it by the GCF to get 2 * 4 = 8/2 = 4.

So the LCM is 4

Can you apply the same concept to this problem?