geno3141

If you have a problem such as   a·cos(A) / b·cis(B)

you can solve it as:   (a/b)·cis(A - B)

For this problem  a = 12      and  b = 4·sqrt(6)  so  a/b  =  sqrt(6)/2

and                      A = 7pi/6  and  B = 3pi/4        so  A - B  =  5pi/12

Therefore, the answer is:  sqrt(6)/2·( cos(5pi/12) + i·sin(5pi/12) ) 

[a·cis(A)] · [b·cis(B)  =  a·b·cis(A + B)

Multiplying  3sqrt(2) · 2sqrt(5)  =  6sqrt(10)

Adding  pi/12 + 4pi/3  =  17pi/12

Answer:  6sqrt(10)cis(17pi/12)

Question #2:  X' inersect y'

-- the area cannot contain any of circle X and cannot contain any of circle Y

-- which picture leaves all of circle X and all of circle Y unshaded?

Question #1: 

A union B consists of all those that are in set A as well as all those that are in set B (just don't count

anyone twice:  8, 14, 17, 16, 9, 15.

A intersect B consists of only those which are in the overlap of A and B (14, 17 ).

A' consists of all the numbers that aren't in A (16, 9, 15, 13, 10, 11, 12)

The probability of randomly choosing a number that is in A' is the number in A divided by the total 

number of numbers; you can do this!

This is not meant to be snarky, but you need to "write" the essay, not "right" the essay.
 

I believe that there are five sections to the First Amendment; write a paragraph about each of them.

Start with an overall paragraph (it can be quite short), then the five points, then have a closing paragraph.

None of the five paragraphs need to be long. Can you make each of them a summary of the right and an explanation of the right?

For problem #1:  y  =  5x

To figure out what happens when x doubles, choose a beginning value for x (perhaps choose 10) and put this number into

the formula:  y  =  5(10)  =  50   --->   So when we start with 10 for x, we end with 50 for y.

Now, to figure out what happens to y when we double x, let's double our value for x (now it's 20) and put this

number into the formula:  y  =  5(20)  =  100  --->  So when x is 20, we end with 100 for y.

Now, let's compare our final value of y (100) with our first value of y (50).

Is 100, 50 multiplied by 2?

Or, is 100, 50 multiplied by 5?

Or, is 100, 50 divided by 2?

Or, is 100, 50 divided by 5?

5.7646075e+17  means  5.7646075 x 10¹⁷

                           moving the decimal point 17 places:  576,460,750,000,000,000

2)  a)  The "Men" section is one-fourth of the circle  =  25%

     b)  The "Children" section is a little more than one-half  =  55%

     c)  The "Women" section is more than one-fourth (25%) but not really close to one half (50%)  =  35%.

          Or, another way, it's a little more than one-third of the circle.

1)  Half of the pupils choose Math  --  True; the Math area is one-half the area of the circle.

     Most of the pupils really like their school  -- Can't say; that's not part of the picture.

     More pupils chose Science than PE  -- False; the area for science is smaller than the area for PE.

     How many students did not choose Science or PE  -- 10; 20 chose Math; half of that chose PE (10) and

                                                                                           the remaining area is the same size as that for PE.

1)  There were 71 students who studied either:  only Spanish, only French, or both Spanish and French.

      14 studied only Spanish; 25 studied only French; so, 71 - 14 - 25  =  32 studied both Spanish and French

                   (this number belongs in the center section).

      The total number of students who studied Spanish is:  14 + 32  =  46.