1. Precalc(attn Bobpursley)

    Hi i posted this before but I wanted to ask Bobpursley a few questions on his reply 1)For the first function you used cosine when they ask for sin, why is that? Also why did you put .5 in the beginning and end of the function? 2)For the second question why
  2. Jiskha

    I typed several questions and answers regarding the subject of Geography, and suddenly, as I was waiting for a reply from Ms. Sue, it seemed as though my questions were deleted from the webpage where all of the other questions are posted. I do not know
  3. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means f inverse of 1 doesn't
  4. Math - derivative of sinusoidal (check)

    a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative. This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=-sin(x) however in the fourth
  5. Pre-Cal: Word Problem

    I'm having a lot of trouble on this word problem. Can someone help me plz? To define the inverse sine function, we restrict the domain of sine to the interval ______. On this interval the sine function is one-to-one, and its inverse function sin^−1
  6. ATTN bobpursley

    On Thursday October the Second, you gave a reply to "martha" regarding the movie chariots of fire. I have posted a response there of my own because I feel that your feedback was misguided. Could you please read my message and then get back to me?
  7. Physics recheck

    Let f be the frequency, v wav the speed, and T the period of a sinusoidal traveling wave. The correct relationship is: a)f=1/T b)f=vwav + T c)f=vwavT d)f=vwav/T e)f=T/vwav My thoughts: Since frequency is equal to T=1/f so f=1/T. Vwav is connected to f by
  8. Pre-Calc

    I am really struggling with how to do these problems, I posted them a few minutes ago but the answers/work shown was incorrect. 1) a) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos
  9. another precal

    i have two questions for you to check please! 6cos^2x+5cosx-4=0 where 0degrees < or equal to 0 which is < or equal to 360. I got that this factors to (3x+4)(2x-1) so the answer is x= -4/3 and x= 1/2 ?? right? and the second question: determine
  10. Trig

    In ABC, vertex C is a right angle. Which trigonometric ratio has the same trigonometric value as Sin A? A Sin B B Cosine A C Cosine B D Tan A
  11. trig-reply to Reiny

    RE: (- sin (x/2) /( 2 sin (x/2) + cos (x/2)) is an alternate representation for, 1 / ( 4 tan (x/2) + 2 ) Thanks for your help, sorry I posted 3 times, I thought you didn't understand what I needed. I really do appreciate your time spent. just for your FYI,
  12. Reply to grant about a regression problem

    This is a reply to the question posted here http://www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
  13. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 +
  14. trig

    Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity = sin(145-75) = sin
  15. Physics - Frequency

    This is in reply to a previous post, I'm not really sure whether replies to posts that are several days old are viewed by anyone, so I'm reposting just in case. In reply to bobpursley's post, I just want to ask, how would you know how long it takes for the
  16. DEAR REINY

    dear reiny i am sim who posted 4 questions this morning i am in dubai and my final examinations are after 13 days and by the way those questions were not my homework or assignment those were some sums which we get on our school website and i had a doubt in
  17. Math 2nd question

    Express as a single sine or cosine function (note: this is using double angle formulas) g) 8sin^2x-4 I just don't get this one. I know it's got something to do with the 1-2sin^2x double angle formula. It's the opposite though? :S h) 1-2sin^2 (π/4-x/2)
  18. Trigonometry

    IM STUCK ON THESE :( 1. What is the equation for shifting the standard sine curve +2 units horizontally? A. y = sin (x + 2) B. y = sin x + 2 C. y = sin x − 2 D. y = sin (x − 2) 3. What is tan-¹ √3/3 ? A. π/4 B. -π/3 C. π/6
  19. Trigonometry

    IM STUCK ON THESE :( 1. What is the equation for shifting the standard sine curve +2 units horizontally? A. y = sin (x + 2) B. y = sin x + 2 C. y = sin x − 2 D. y = sin (x − 2) 3. What is tan-¹ √3/3 ? A. π/4 B. -π/3 C. π/6
  20. Algebra II

    Part 1: Using complete sentences, compare the key features and graphs of sine and cosine. What are their similarities and differences? Answer: The sine graph will always pass through (0, 0), While the cosine graph wouldn't. If the graph is 2cosx, it will
  21. drwl / bobpursley please check

    I had posted three questions at 1:48pm, 2:40pm and 2:41pm and I am having problems with them. Can you please check them for me. Thanks! Repost if you are not satisified with the responses.
  22. ok (my posts mysteriously vanishes...)

    I posted a reply thanking both bobpursley and dr.bob (mild criticism)... I don't see the post. What happened? Was it removed? I saw your post thanking Bob Pursley and me. Many thanks for the thanks. All of us like to think that we lend a helping hand. Both
  23. math

    Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1 1/2) Sin^-1 (sin 7pi/6)
  24. pre calc

    The Identity Function The Squaring Function The Cubing Function The Reciprocal Function The Square Root Function The Exponential Functional Lo The Natural Logarithum Function The Sine Function The Cosine Function The Absolute Value Function The Greatest
  25. Graphing trigonometric function

    sine and cosine have a period 2pi tangent and cotangent have period pi Can someone explain why? thanks a lot. well tangent is sine/cosine and there a place where the tangent function is undefined and that is where the asymptotes occur. the same is true
  26. CALC

    Let f(x) be the function e^sin(x/10). If you wanted to estimate the area under the curve for this function from 3 to 5, how many intervals would you need to use to be sure that your upper and lower bounds differered by no more than .01?
  27. To: Bobpursley

    Thanks for your reply! I have some questions about my AMERICA ONLINE service that's why I asked "How can I e-mail to America Online? Is there any website where I can write my comments or questions to America Online? (Like Feedback) I found a website on
  28. sine and cosine

    Simplify and write the trigonometric expression in terms of sine and cosine: sin x + (cot x)(cos x) = (1/f(x)) f(x)= ?
  29. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin
  30. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin
  31. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then.
  32. Calculus - Second Order Differential Equations

    Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i,
  33. to bobpursley

    My classmates friends want me to post their questions as well.Thats why there are multiple names is there a problem. Yes. You are posting duplicate or even triplicate questions. That is silly. If we have answered one, the answers to the others follow.
  34. gnozahs

    I removed about ten questions you posted this morning. There was no indication of what you had done, what your thinking was, or what you wanted from us. We are not going to do homework for you. If you want hints on these calculus questions, say so, or ask
  35. Science-bobpursley

    Thanks for helping me with al those parts bobpursley. If you have time, can you also check my questions please. Thank you very, very much in return. My post is on the second page.
  36. Math sin/cos

    On a piece of paper draw and label a right triangle using the given sides, solve for the unknown side and write the trigonometric functions for angles A and B, if a=5 and c=7. I already found side b which equals 2 sqrts of 6. Now I need to find the sin/cos
  37. Trig

    Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v sin u. cos (v -
  38. Physics (CHECK)

    One student is pushing on a chair with a force of 260.6 N directed at an angle of 30 degrees above horizontal while a second student pushes on the same side of the chair with a force of 21.0 N at an angle of 15 degrees below horizontal. What is the
  39. Spherical Trigonometery

    I am trying to apply the formula cos c = cos a x cos b + sin a x sin b x cos C to find the length of c in my spherical triangle. I am working with 2 examples in a book in which the answers are given. In the first example all the sines & cosines calculated
  40. physics Again

    bobpursley can you please check my reply to your post about my question? I am not sure if I did my equation correctly. Thanks
  41. Trig

    Solve in terms of sine and cosine: sec(x) csc(x)- sec(x) sin(x) so far I have: 1/cos(x) 1/sin(x) - 1/cos(x) sin(x) I am not sure where to go to from there. The book says the answer is cot(x) or cos(x)/sin(x) Thank you in advance.
  42. Calculus

    Hello, Could somebody kindly check my answer for the following question? Find the derivative of the following function: h(x)=3e^(sin(x+2)) h'(x)=3'(e^(sin(x+2))+3(e^(sin(x+2))' h'(x)=0(e^(sin(x+2))+3(e^(sin(x+2))(cos(1)) h'(x)=3cos1(e^(sin(x+2)) I would
  43. Math HELP!

    I posted a few questions and then went back and posted how I thought they were supposed to be answered. Could someone please locate my earlier questions and tell me if I am on the right track?
  44. To Fay1985 - math

    Your post was removed. Please tell us your thinking on the 25 questions you posted. Attempt some answers, and we'll be glad to help you. Also -- I don't believe that you posted complete information for many of the questions.
  45. Math CONTINUATION OF QUESTION FROM bobpursley

    Thank you for answering the question before bobpursley, I understand how you did the deriv of inside, outside, but how do I now do the second derivative since you have the extra -18x^2 in the numerator?? Thank you very much! (I suppose I have to brush up
  46. pre-calculus

    Rewrite the following expression as an algebraic function of x sin(arccos(x/2)) I know sine is y, which is opposite over hypotenuse. I also know that arccos is the inverse of cosine. I'm confused on what the question is asking and what to do with the x.
  47. maths

    Choose the two options which are true for all values of x 1) cos (x) = cos ( x – pie/2) 2) sin (x + pie/2) = cos (x – pie/2) 3) cos (x) = sin (x – pie/2) 4) sin (x) = sin (x + 4pie) 5) sin (x) = cos (x – pie/2) 6) sin^2 (x) + cos^2 (x) = pie would
  48. Thank you (bobpursley)! (no reply needed)

    No reply needed.
  49. MATH

    1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x - sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the double-angle formulas. 3.)Use the half-angle formulas
  50. Computer Questions

    I posted some computer questions and my answers on Saturday. They should be on somewhere between pages 2 through 10. would you please check my answers for me? There are about 16 questions and answers. Thank you!! It will say "computer questions" Thank you.
  51. Calc

    Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the x-axis as a 2pi scale. The two functions appear to cross three times between x = 0 and 2pi. (including 2pi) Now,
  52. math help

    Posted by grant on Saturday, May 12, 2007 at 9:20am. The table shows the depth (d metres) of water in a harbour at certain times (t hours) after midnight on a particular day. time t (hours) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 and the in the next column
  53. Pre Cal

    how would i find the degrees of cos x= 3/2 if (0 <or= theta < 360)? i've tried putting it in my calculator with cosine^-1 but im just getting err:domain. Please help! The cosine function only goes from -1 to +1. There is no solution to cos x = 3/2.
  54. Calculus

    The motion of a spring that is subject to dampening (such as a car's shock absorber)is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion for a point on such a spring is
  55. math 140

    I have two questions posted that has not been answered please help. The questions were posted on March 18 please help.
  56. math

    how to define arc cosine(cosine x) for -360 deg<x< 360 deg?? a proper conceptual approach to the solution will be appretiated.. The function Cos(x) is equal to 1 at x = 0 and it decreases as a function of x until x = pi (=180 degrees). There the
  57. Calculus

    How do I graph sin and cosin example: graph y=-4sin(x + 3.14) Your function is the sin function shifted by pi units to the left. You need to study the sin function and know how to graph it. There should be a picture of it in your text, it's a very commonly
  58. Math

    The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D)
  59. Calculus

    Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then. How would I show the sequence of values, any help
  60. algebra 2

    Posted by hellogoodbie on Saturday, January 16, 2010 at 3:24pm. Posted by hellogoodbie on Saturday, January 16, 2010 at 2:59pm. How is this problem done? IF f(x)=2x^2-8x-3 FIND f(-2) algebra 2 - bobpursley, Saturday, January 16, 2010 at 1:42pm Put in for x
  61. MATH

    The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D)
  62. MATH

    The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D)
  63. Math (Trig)

    sorry, another I can't figure out Show that (1-cot^2x)/(tan^2x-1)=cot^2x I started by factoring both as difference of squares. Would I be better served by writing in terms of sine and cosine? Such as: [1-(cos^2x/sin^2x)]/[(sin^2x/cos^2x)-1]=(cos^2x/sin^2x)
  64. Pre-Calc

    1) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos 18° − sin 12° sin 18° And Find its exact value. 2) Use an Addition or Subtraction Formula to write the expression as a
  65. Throughout your life,who has impacted your life?

    Opinions are ok but anything with identifying information will be removed. In fact, why don't you retype your question and omit the part about including name, address, et al. and we can get someone to remove your original post. ok.thanks,do you think you
  66. Physics

    An item is shot off the ground at a force of 31N and an angle of 36 degrees. In order to find the vertical force, would I use SIN, COSINE, or TANGENT? would it go 31 * COS/SIN/TAN (36) or 36 * COS/SIN/TAN (31)??
  67. Inverse trigonometric function

    How to solve without calculator 1. sin(arctan(12/5)) 2. cos(arccosx + arcsinx) Thanks. You have to know your right triangles. 5 12 13 is one. If the tan is 12/5, then the sin is 5/13. Draw a pic to confirm that. On the second: Think. Draw any right
  68. English

    1. Why do you not like becoming a journalist? Because I want to become an office worker. 2. Why don't you not like becoming a journalist? Because I want to become an office worker. (Are both questions the same? Are the answers suitable for each question?)
  69. Trig

    Simplify sin x cos^2x-sinx Here's my book's explanation which I don't totally follow sin x cos^2x-sinx=sinx(cos^2x-1) =-sinx(1-cos^2x) =-sinx(sin^2x) (Where does sine come from and what happend to cosine?) =-sin^3x
  70. Math

    Hi, I wanted to know how wanted to know if i was doing this step right for my homework. the question is Given rt=<sin(t)-tcos(t), cos(t)+ tsin(t),t^2 sqrt 3 and the whole thing is divided by two. The question is find the velocity vector and find V(pi)
  71. Math

    This one confused me since it revolved around what seemed like dividing trig function by another function Write the following expression in terms of the tangent function 2 / ((cos(r^2 - s^2) / (sin(r^2 - s^2)) = ? I know tan t = sin t / cos t. So would I
  72. Trigonometry

    Can you show steps on deriving the identity from the sum and difference formulas for cosine: sin a sin b = (1 / 2)[cos(a – b) – cos(a + b)]
  73. Math

    use the sum and difference identities to find the cosine angle cos pi/9 cos pi/3 - sin pi/9 sin pi/3 I do not know how to solve this because pi/9 is not on the unit circle.
  74. Pre-Calculus

    Write the following expression as the sine, cosine or tangent of an angle. cos 3x cos 2y + sin 3x sin 2y
  75. math

    Write the expression as the sine, cosine, or tangent of an angle. sin(2π/9)cos(3π/8)+cos(2π/9)sin(3π/8)
  76. Math

    Hi, this is a question I posted a couple of days ago and answers below.I am still really confused and unfortunately can't copy a picture into this. I thought it would be y-x but have no idea how to calculate that, but as the pistons move in towards each
  77. math

    Write the given expression as the cosine of an angle. cos 60° cos 65° − sin 60° sin 65°
  78. Manuscript on an Article (bobpursley)

    Posted by bobpursley on Saturday, January 27, 2007 at 8:56pm in response to English (Speech). Read the article. What did it say? What was it point of view? Was the author complete in the analysis? What needs to be done? How did it make you feel? So in the
  79. math

    Answer the following questions for the function f(x)=sin^2(x/5) defined on the interval .(-15.507923,3.82699075) Rememer that you can enter "pi" for as part of your answer. a.what is f(x) concave down on the region B. A global minimum for this function
  80. Math

    I recently inquired how to solve a right triangle. I was referred to the Laws o Sine & Cosine quite rightly. I have subsequently found a converter on the net which takes all the headache out of arriving at the correct answers. The thing is I still do not
  81. Chem?

    hi, i posted a question below under the same name and no one has answered it yet (i think bobpursley might have left) any help?
  82. trigonometric functions

    im compeletely lost with the trigonometric functions...can anyone explain clearly to me? Are you lost on the definitions?...where is the problem. You need to be able to draw and label all the parts of a triangle, the hypotenuse and legs. Then be able to
  83. Calculus

    1) The period of a trig. function y=sin kx is 2pi/k. Then period of y=sin^2(pi.x/a) should be 2pi/(pi/a)=2a, but somewhere it is given as a. Which is correct? 2) The period of r=sin^3(theta/3) is given as 3pi. How is it worked out? Is it because after
  84. math

    The Fourier series expansion for the periodic function,f(t) = |sin t|is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series approximation of f(t), up to the 6th harmonics when t = 1.09. Give your answer to 3
  85. math

    The Fourier series expansion for the periodic function,f(t) = |sin t|is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series approximation of f(t), up to the 6th harmonics when t = 1.09. Give your answer to 3
  86. math

    can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) (b)write down the
  87. Math sin/cos

    On a piece of paper draw and label a right triangle using the given sides, solve for the unknown side and write the trigonometric functions for angles A and B, if a=5 and c=7. I already found side b which equals 2 sqrts of 6. Now I need to find the sin A
  88. math

    Anyone can help me on this qns? The Fourier series expansion for the periodic function,f(t) = |sin t|is defined in its fundamental interval. Taking π = 3.142, calculate the Fourier cosine series approximation of f(t), up to the 6th harmonics when t =
  89. To: bobpursley or any math helper

    please help me on my questions, I have a big test tomorrow and I don't understand how to do some questions, please help me
  90. Physics

    A vertical spring with a spring constant of 450 N/m is mounted on the floor. From directly above the spring, which is unstrained, a 0.30 kg block is dropped from rest. It collides with and sticks to the spring, which is compressed by 3.0 cm in bringing the
  91. math

    bobpursley, I am confused to the equations that you have just posted. However, this is what I figured out but I'm not if it's correct. ((25+R)-B)+3N=435
  92. math (trig)

    Find sin(x/2) if sin(x)= -0.4 and 3pi/2 < or equal to (x) < or equal to 2pi Let's use cos 2A = 1 - 2sin2 A and we can match cos x = 1 - 2sin2 (x/2) so we will need cos x we know sin x = -.4 and x is in the fourth quadrant, so the cosine will be
  93. Physics

    A horse runs 15 m [N 23° E] and then 32 m [S 35° E]. What is the total displacement of the horse? I can't even visualise this... My friend told me the basic steps on how to solve it, but I got the wrong answer anyways... d1 = 15 m [N 23° E] d1x = 15m
  94. physics

    Given the position function s(t) = t cos t, find the velocity function. Answer v(t) = -sin t v(t) = sin t v(t) = cos t - t sin t v(t) = cos t + t sin t
  95. Evaluation-repost

    Reposting because it has gone down to the second page! Evaluate 1. sin(tan inverse sqrt(x^2-2x)) 2. tan (sec inverse 3y) For 1. draw a right triangle and label the opposite leg sqrt(x^2-2x), the adjacent side 1 and the hypotenuse x-1. Do the calculations
  96. Math

    Write the expression as the sine, cosine, or tangent of an angle. cos 0.96 cos 0.42 + sin 0.96 sin 0.42 Is this cos 0.54?
  97. Algebra 2 check my last answer?!

    A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. The function is a reflection of its parent function over the x-axis. Which function could be the function described? f(x)=10cos(3x)−10 f(x)=10cos(2π3x)+10 <my
  98. Calculus

    Answer the following questions for the function f(x) = sin^2(x/3) defined on the interval [ -9.424778, 2.356194]. Rememer that you can enter pi for \pi as part of your answer. a.) f(x) is concave down on the interval . b.) A global minimum for this
  99. Trigonometry

    Alrighty I have to find two real world sinusoidal functions. I found: 1. A piston in an engine moves up and down in a cylinder. The height, h centimeters, of the piston a t seconds is given by the function: h= 120 sin(πt) + 200. 2. You can find the
  100. Math PLEASE HELP

    No one was answering my questions for the first question I posted so I posted it again. answers for 12345: 1. 9 3/5 2. 4 1/2 3. 4 3/4 4. still 7 6/9 5. still 10 16/18