All Answers 358514 Answers

2sin x  - 2

This one just makes the sin function twice as "tall" as the normal sine function and shifts it down 2 units

-cos (2x) +1

The 2x    makes the period 1/2 as long as the regular cosine graph

The  "-"  " flips" this over the x  axis

The "1"  shifts this up one unit

Here's the graph of this  : https://www.desmos.com/calculator/wtrtlgunw4

Last one 

Max  = 1

Min =  -3

Period = pi

Frequency = 1 /period =  1/pi

Amplitude  =  [ Max - Min] / 2 =   [ 1 - - 3 ] / 2  = [4] / 2  =  2

Equation of midline....   y = [ Max + Min ] / 2  ......y =  [ 1 - 3] / 2    ....y = -2/2  =  -1

One possible equation  of this function  is

y=  -2cos(2x) -1

Here]s the graph :   https://www.desmos.com/calculator/lk6hffalro

That's right too, thanksssss!!

I like the way you did that, EP....I'll  have to keep that method in  mind   !!!!

So it would be 3sqrt6?

-508° =    720  - 508  = 212°

-148  =  360 - 148  = 212°

-32 =  360 - 32  = 328°

32° =  32°

572  =   572 - 360  =   212°

Try  -508    do you think it might be?    212 - 360(2) = ?

sin 60 = opp / hyp

sqrt3/2  =  9 / hyp    

hyp = 9 / (sqrt3/2 )    and simplify......

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First one....convert   -7pi/4   to a positve measure = 

2pi -7pi/4  =

8pi/4 -7pi/4 =

pi/4

So.....tan  pi /4  =  tan 45°  =  1/1   = 1

Second one

sec pi/6   =  sec 30°

Note hat cos 30° =  √3/2

So.....the secant here is the reciprocal of this  = 2 /√3   =  2√3

                                                                                          ____

                                                                                             3

Last one 

cos 23pi /6 

Convert  23pi/6  into  degree measure

23pi /6  x   180 /pi  =       23 * (180/6)  = 23 * 30   = 690°   

And 690 - 360  =   330°

So....this is a 30° reference angle in the 4th quadrant

cos (330)  =  cos (30)  = √3/2

I don't think there's any other answer or am I missing something?

Everytime you go full circle (360 degrees  )    either positive or negative you will land back at the 212 degree mark, soooo

    212  +-  360 n           

example    212  -  360(1) = -148    is one answer.......

                  212  + 360(1)  = 572    is another answer......do you see any more?

A.   Mean is 115      s.d. = 12       100 score will be   15 points below the mean , or   15/12 = 1.25 standard deviations below the mean

Look at you table of negative  z-scores and find the number corresponding to   -1.25    z = .1056

   .1056 x 100 % = 10.56%     with score below 100

B.  Greater than 130    is    15 points above the mean    15/12 = 1.25 ABOVE the mean

     look at your positive  z-score table  for z-score =1.25       .8944   of the students had a score LESS than this

               so    1 - .8944  = .1056      or 10.56%   were higher than 130

C   calculate the z score less than 110       calculate the z score less than 130

                               z₁₃₀ - z₁₁₀   =   fraction between 130 and 100

D.   FInd z   for 75   (  115 - 75  = 40 BELOW        40/12 =  - 3.33  z  )     from neg z-score table  

E.   Find positive z-score = .9900       (9901 is the closest in my table)      this equals z -score   2.33

            2.33  x 12 s.d.    = 27.96     then       115 + 27.96 = 142.96 to be 1%

The diagonal length =  4√2.....and half of this length is 2√2

So   the four vertices  are

(-17 - 2√2 , 23)

(-17 + 2√2, 23)

(-17, 23 + 2√2)

(-17, 23 - 2√2)

See the graph here :   https://www.desmos.com/calculator/vbqihksx9w

10 p  48 m / 8 w   =   60  p-m/w

60 p-m/w  * 9 w  / 6 p    =   90 minutes

In that case,

The ending point of the path Jeff made depends on all the moves Jeff made, not the order. Consider a random 10-step path Jeff could take. NESWNNESEW (N for North, S for south, W for west, E for East.  Reduce our path by cancelling each E-W and each N-S pair, which will not change our endpoint. So our example reduces to NE. Notice that our reduced path must have an even number of moves, and it is thus possible to end at any point (x,y) where x+y is even and |x| + |y| is no greater than 10.'

If |x| + |y| = 0, there is one possibility for (x,y).

If |x| + |y|  <= (less than equal to) 2, there are 9 possible paths ((0,0) (-+1,-+1) (0, +-2) (+-2,0)); these solutions will form a 3x3 diagonal grid

The solutions with |x| + |y| <= 10 will form an 11x11 grid, so there are 11^2=121 ways

Sorry if I didn't explain this very well, I'm in a bit of a rush.

The cosine function is negative in quadrant ​ II ​     

cos =  x/r....in this quadrant, x is negative  [r is always positive ]

The sine function is positive in quadrant ​ I ​

sin = y/r.......x, y and r are all positive in the first quadrant

The cotangent function is negative in quadrant ​ II

cot  = x/y......x is negative and y is positive in quadrant 2

The other, leg, EF =  sqrt (EG^2 - FG^2 ) =  sqrt (10^2 - 4^2)  = sqrt (100 - 16)  = sqrt (84)  = 2sqrt (21)

Tan G  =   EF /  FG  =      2sqrt (21)   4  =    sqrt (21) / 2

Cos E  =  EF / EG  =  2sqrt (21)  / 10   =  sqrt (21)  / 5

Sec G =  EG / FG =  10 / 4  =   5/2 

A cone has a base area of 24 square inches and a height of 8 inches. What is the area of a cross-section of the cone that is parallel to the base and 3 inches from the vertex?

Cone height  h = 8

Cone base  r = sqrt( 24/pi) = 2.764

AB = h - 3 = 5

BC = 5 / tan(β) = 1.727

FB = FC - BC = 1.036482449           ( FB is the radius of cross-section circle)

Area of a cross-section is:  (FB)² * pi = 3.375 in²    

Thank you so much! Your answer to #1 is correct. I apologize for the typo, the number is 10

Let's see:

Lily = 25

Mary = 35

Amber = 35*3=105

Amber has 105 dollars.

Amber has 80 more dollars than Lily.

They have 165 dollars all together.

If x does not mean multiplication, this question does not make sense.

IF it DOES mean multiplication:

4 * 7 * 087 * 37 * 6 * 5 * 3 * 76 * 545 * 674 * 334 * 666 * 666 * 443 = number too big to calculate.

1) Without any restrictions, there are 18*17*16 = 4896 ways  that three people can be seated. Then, we have to subtract  the cases where they are adjacent.

Case 1: Where all three people are next to each other in a "boomerang" shape. There are 18 ways to choose three consecutive seats. There are then 3! = 6 ways to place those three people, which gives us 18*6=108 possible seatings where they are next to each other.

Case 2:  There are two people sitting next to each other, and the third person is not next to either of them (loner, like me).

There are 18 ways to choose two consecutive seats for the two people. There are then 14 ways to choose the third seat for the loner. After the three seats have been chosen, there are 3!=6 ways to place the three people, which gives us 18*14*6=1512 possible seatings.

Subtracting all of them: 4896-1512-108=3276 ways.

Hope this is right!

2) Can't help you since there is a typo. "After  steps". No number.

Describe clearly how you would determine the measurement of the circumference of a baseball using the width of your thumb as a referent.      

You mean to directly measure the circumference in "thumbwidth" units, rather than "inch" units or "centimeter" units? 

1.  You could use an ink pad and press your thumbprints around the ball, then count how many there are.  Some stickler would probably argue that that measurement would be in "thumbprint" units rather than "thumbwidth" units.   

2.  How about if you inked the ball, and rolled it on a sheet of paper to get the distance of one circumference in a straight line.  Then lay your thumb at the end of the line and mark off one thumbwidth, move your thumb over and mark off the second thumbwidth, and continue until you've reached the end. 

_.

Total tix sold =   12 + 4 + 6 + 14 = 36

12 A + 4 C    = $ 84

 6 A   + 14 C = $ 78      multiply THIS equation by -2

-12 A  - 28 C = - 156    and add to the first equation

         - 24 C =  -72

                 C = 3               Now you should be able to find A ...the price of Adult tix.....(sub the value of A into oneof the eqautions)

xf   =  x0   + vo t   + 1/2 a t^2      xf = 10 m      x0 = 23 m     vo = 22 m/s     a = - 9.9 m/s^2

10 =   23   + 22 t   - 4.9  t^2

0 =   - 4.9t² + 22t + 13      Use quadratic formula to find t = 5.02 s   and  - .529 s  (throw out)