1. Algebra

    Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible: Vertical asymptotes x = -4, x = 5; x-intercept (-2,0)
  2. Probability

    Find the probability of obtaining between 50 and 55 tails inclusive when a fair coin is flipped 80 times. (answer accurate to four decimal places.)
  3. Chem Help

    For the reaction, XBr2(g) X(g) + Br2(g), if a container is charged to an initial concentration, [XBr2] = 2.00 mol/L and the system allowed to react and come to equilibrium, if Kc = 4.0 x 10-8, what is the concentration of X(g) at equilibrium? This is what
  4. Calculus

    A bacteria culture contains 200 cells initially and grows at a rate proportional to its size. After half an hour the population has increased to 360 cells. (a) Find the number of bacteria after t hours. (b) Find the number of bacteria after 4 hours. I
  5. 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
  6. Math Help!

    1.Find the percent of decrease. Round your answer to the nearest tenth of a percent where necessary. 75 to 60 A. 20% B. 30%*** C. 40% D. 50% 2. Find the percent markup. Round to the nearest whole percent. Store's cost: $100.00 Selling Price: $160.00 A. 50%
  7. Math Help!

    1.Find the percent of decrease. Round your answer to the nearest tenth of a percent where necessary. 75 to 60 A. 20% B. 30%*** C. 40% D. 50% 2. Find the percent markup. Round to the nearest whole percent. Store's cost: $100.00 Selling Price: $160.00 A. 50%
  8. 12th Grade Calculus

    1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve? At what point on the curve does the curve
  9. Physics

    How do you set up and solve this question Ben (55 kg) is standing on very slippery ice when Junior (25 kg) bumps into him. Junior was moving at a speed of 8 m/s before the collision and Ben and Junior embrace after the collision. Find the speed of Ben and
  10. 7th grade science

    Sorry! this is alot of questions. Science is not my best subject but i still do well in it but the questions are really hard for me pleas help answer this. What might you ask yourself in drawing a conclusion about an experiment? Why is scientific inquiry a
  11. Emergent computer tech.

    1. What file is being called by this IMG tag? (1 point) answer= SRC 2. What type of link is used to call this file? (1 point) answer=need help with this one 3. If the user loads this graphic in a text-only browser how will the browser describe it? (1
  12. Calc

    The time interval T, in minutes, between patient arrivals in an emergency room is a random variable with exponential density function p(t) = 0:125e^-.125t. What is the average time between patient arrivals? What is the probability of two patients arriving
  13. Interior Design

    please check my answers? Your client wants his dining room to be a cozy, dark, nighttime room where he can entertain just one or two people for casual, intimate dinners. The room won't be used during the day. The unfurnished room has a low seven-foot
  14. Algebra

    1.In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open
  15. Math (calculus)

    Prof gave us this question to practice but I do not know how to solve it. If you know please provide step by step with the answer so I can understand it. Thank you very much :) Suppose a rocket is launched from the ground with 10 seconds worth of fuel. The
  16. Math

    I haven't done factoring in ages I'm trying to factor this X^2 - 2X + 8 If i remeber correctly sense the leading coefficent is 1 the factored form is in this format (X-A)(X-B) which would give you X^2 -AX - Bx + AB or simply X^2 -(A+B)X +AB so then in my
  17. French

    Could you please check these thanks. Directions: Complete the following with croir. 1. Il------- que tout est moins cher pendant les soldes. Et vous, vous ---------- ça aussi? Answer 1: croit Answer 2: croyez 2. Julien -------- que l'examen va être
  18. math

    1. Find the LCD of 3/5 and 1/6. a. 5 b. 6 c. 11 d. 30 2 Add the fractions and write your answer in lowest terms. 2/5 + 1/9 a. 1/15 b. 23/45 c. 3/14 d. 19/45 3. Subtract the fractions and write your answer in lowest terms. 4/5 - 3/8 a. 1/40 b. 1 7/40 c.
  19. Maths

    Use the binomial series to find the Taylor series about 0 for the function f(x) = (1 + x)−3/5, giving all terms up to the one in x4. I have the answer; f(x)=1-3/5(x) +12/25(x^2) -52/125(x^3) + 234/625(x^4) but i am not sure how to work out the interval
  20. Literacy

    Please check my work, thank you. Question 1 – 4: Access the Library of Congress library Catalog. Then, find the information to answer the question. 1. What year was the oldest copy of Ralph Ellison’s Going to the Territory published? A. 1952 B. 1986 C.
  21. math

    The math team in addville travled to subtractville for a math compertition. The bus averaged 40 mph from addville to subtractville but adveraged 60 mph during the return trip. What was the adverage speed of the bus for the entire trip? Thats the story
  22. Math

    I've got quite a few problems. Please answer any of them in whole or in part. Thank you in advance. (For the record, you're not doing my homework; you're helping me understand it. These problems were not assigned.) (1). Determine the discontinuities and
  23. Waste Disposal and Recycling

    1. Which of the following types of waste should not be recycled at home? The answer is A: Expired Medicines ____________________________________ 2. Which of the following is NOT a method of disposing hazardous wastes? The answer is D: Disposing of them in
  24. Physics

    Two charges are placed on the x axis. One of the charges (q1 = +9.3 µC) is at x1 = +3.4 cm and the other (q2 = -20 µC) is at x2 = +8.9 cm. (a) Find the net electric field (magnitude and direction) at x = 0 cm. (Use the sign of your answer to indicate the
  25. Math- Reiny can you help me with this question

    I know how to do the work, but the way the question is worded I am not sure the answer. The math works comes out to -2 which is b but if you want the number less than -2 the answer is c. Which are they asking for . This is my work. Which is the value is in
  26. Social Studies

    PLEASE ANSWER! PLEASE ANSWER! PLEASE ANSWER! Identify two problems resulting from urban sprawl in the western region of the United States. If these problems are not solved, what will the outcome likely be?
  27. Math

    So she saw 461 dolphins that are 5 year so we don't need to estimate on this problem. So I did 461/5 is 92 is the answer. Then the said how many did he spot per summer in the 5 summers he worked so I think we need to divide the answer which is 92 and the
  28. Dimensional Analysis

    eLydi wrote 4 1/2 pages of her science report in one hour. What was her writing rate in pages per minute? My answer: ( ihavetwo, tell me which is right, if any are?) answer 1: 0.075 answer 2: 13.33
  29. Physics

    a ball is dropped from the top on an 80-m high building. what speed does the ball have in falling 3.5 s? I keep getting the answer 34.3m/s but it is counted wrong. I found an answer on Chegg that say 29.4 m/s but I can't figure out how they are getting
  30. Geometry

    Hello, Can someone please tell me if I have the right answer? Thank You my answer: 1.59m If an area in the form of a circle is to be roped off by a rope 10m long, what will be the radius of this area? Round your answer to two decimal places.
  31. trig

    Is the answer to this problem correct? I'm not sure and I want to make sure I do well on the test. Evaluate the following logarithms given log 4/log a = .321 The answer my teacher gave me was 0.963. What is the reasoning behind the answer?
  32. 5th grade word problem math

    the teacher asked the students to add up all the numbers from 1 to 100.It only took carl a minute to come up with the answer. Can you figure what carl did to come up with the answer and what is the correct answer.Hint: there is a pattern.
  33. Algebra I

    Hi, I would like someone to explain to me the process to get to the answer of these questions. (The answers are in the back of the book, but I don't understand how to get them myself): QUESTION ONE Warren has 40 coins (all nickels, dimes, and quarters)
  34. Math

    1)The sum of a number and 17 more than twice the same number is 101. Find the number. 17+2n=101 17-17 101-17 2n=84 n=42(answer) 2)Evaluate: 5-/a+5b/ if a=-12 and b=2. 5-/-12+5(2)/ 5-/-12+10/ 5-/-2/ 5-2 3(answer)
  35. Physics

    x = 2t^3 - 21t^2 + 60t - 30 is the motion of an ant where x is his location on the number line at time t seconds. 1) When is he going to the left? Answer: between 3 to 5 seconds 2) When is he going to the right? Answer: between 0 to 2 seconds 3) What is
  36. Chem Question?

    I answered this question already, but would like you to check if the answer I provided was right. If for some reason my answer was not right please provide me with the right answer. 1)The air in the inner tube of the tire of a racing bike has a pressure of
  37. Algebra

    Please let me know if i answered these correctly thanks 1.Which property of the real numbers is illustrated by the following statement? 4(3x) = (4 ∙ 3)x answer: distributive property 2. Which property of the real numbers is illustrated by the following
  38. grammar

    Dangling Modifiers If your baby does not like cold apple juice, it should be heated. Your answer: 1. Dangling Modifiers When they are fresh, eating oranges can often keep away the cold virus. Your answer: 2. Predication Our plans for tomorrow should begin
  39. college

    Using the Library, web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 50 gallons of gas. By setting up and solving a proportion involving x, find the value of x
  40. Chemistry

    Nitrogen & hydrogen goes react to form ammonia gas as follows: N2(g)+3H2(g)-->2NH3(g) At a certain temperature & pressure, 1.2L of N2 reacts with 3.6L of H2. If all the N2 and H2 are consumed, what volume of NH3, at the same temperature & pressure will be
  41. Calculus

    When an electronics store prices a certain brand of stereos at p hundred dollars per set, it is found that q sets will be sold each month, where q2 + 2 p2 = 41. a. Find the elasticity of demand for the stereos using implicit differentiation. b. For a unit
  42. Calculus

    When an electronics store prices a certain brand of stereos at p hundred dollars per set, it is found that q sets will be sold each month, where q2 + 2 p2 = 41. a. Find the elasticity of demand for the stereos using implicit differentiation. b. For a unit
  43. MATH PLS HELP

    19 WorkPad Note: In questions 19-21, remember to show all of the steps that you use to solve the problem. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your
  44. Math help please *calculus*

    ok im having a bit of a problem rationalizing denominators. i have 2 to the root of 3 +4 divided by the root of 3. I have tried multiplying the top and bottom by the root of 3 and the answer, but then i get stuck at this part. Do i multiply 4 by 4 and make
  45. Biochemistry

    I'm desperate and I cannot find the answer to this question.... As the name implies, globular proteiens tend to have a roundish, globular shape. What types of side chains might you expect to find on the amino acid residues that face the outside of a
  46. Physics

    Write True or False. If False, Explain why! 1. In a position vs. Time graph, a line whose slope is negative represents an object that is slowing down. Answer: I circled True but it's not. Can you explain why my answer is wrong. 2. An object can have a
  47. Algebra

    Can someone verify if my answers are correct? Solve. 1/x+6-1/x-6 My answer is: -12/x^2-36 Solve. 1/x+5+2=5/x+5 My answer is: -3 Subtract. Express your answer in simplest form. 13x/30-4x/15 My answer is: x/6 Can someone verify if my answers are correct?
  48. math,correction

    add 5y-4 and 2y^2-8y my answer is: 2y^2-3y-4 classify the following, if possible 7x^2+10xy+y^2 a)not classified b)trinomial c)monomial d)binomial My answer: trinomial Write using positive exponents, and simplify if possible (-3x)^-2 a)(1)/(6x^2)
  49. Trigonomrtry

    I had asked help for a question and Steve gave me this answer on how to set up equation 20-x/6.11=tan28 degrees The answer is approx 16.75 ft. I still don't know how to do this! When I do it I get different answer. Could you please break this down step by
  50. Math, Algebra.

    2. Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. If she gives each person 1/3 of a box, how many people can receive chocolate? 13, 17, 19, or 21? I believe that the answer is 19. Take 6 1/2, divided by 1/3, and get 19 1/2. Since 19 is
  51. Math

    I have the problem: A triangle has a base of 3.6 cm and an area of 22.32 cm squared. What is the height of this triangle. The teacher gave us the answer key and I know the answer is 12.4 but I don't know how they came to that answer. I can't figure out how
  52. Math

    Hello, I need to know if I have the right answers to these questions. 2x-y=3 question is which of the following points lie on the line. is the answer 0,3 (-1,1) (2, 1) (-3, 1) (-3, ) or (1, 2) I chose the answer (-3, 1) is that right, second question: If
  53. math correctionplz

    can someone correct these also for me.. Which of the following is not a polynomial? a) 24 b) 4x^3+5x-1 c)2x-(1)/(x) d)3xy^2+xy MY answer is: A Simplify. write your answer with only positive exponents (y^5)/(y^10) Possible answers: a)y^2 b)(1)/(y^2)
  54. Math

    #1) Luis stated that when you are converting meters to centimeters your answer will be larger than your original number. My answer is yes because centimeters are smaller . (Is my answer OK ) #2) 8/9 + 1/3= 33/27= 1(12/27)= (I'm stuck here) #3) 6/8-2/6=2
  55. math

    Can someone help me answer this question? It's combining like terms, my teacher said that the first term is right but the rest is wrong. Question~~ 2x^2y–5xy–7xy–8x^2y+9xy^2 –xy^2 My answer ~~ 2x^2+-8x^2 (2-8)x^2 -6x^2 y+y+y+y (1+1+1+1)y 4y
  56. MATH

    Can somebody show me how to get to the answer? How do 2pi[((-6561/4)+2430-(729/2))-((-1/4)+(10/3)-(9/2))]=2560pi/3. My answer is always= 10184pi/12 or 2546pi/3. I don't know what I did wrong that cause my answer to be wrong.
  57. math

    Perform each operation, convert to a fraction, & then convert your answer back to a mix number. -4(7/8)x 3(2/3) I did 8*-4+7/8 & got -25/8 then 3*3+2/3 & got 11/3 then i multiplied -25/8* 11/3 & got -275/34 but it's not the right answer, the answer is
  58. Calculus

    solve (Z^2)+5=-4/Z^2 how do i solve it?? the answer is +2or-2, or, +or -i. but i really don't know how to get this answer.i tried to multiply both side by Z^2, but i think it just made it more comlicated and i didn't get the right answer at the end...can
  59. calculus

    You work for the silver there is a home with a driveway 2 miles long extending to the house from a nearby highway. the nearest connection box is along the highway but 5 miles from the driveway. it costs the company $100 per mile to install cable along the
  60. French

    Could you check this answers also thanks. Directions use the correct form of the verb faire. Je vais chercher Sophie. On va ---------- les courses. Answer: fait Vous ------- souvent les courses? Answer: faites Mon cher ami, nous -------- les courses tous
  61. physics

    I am having some difficulty with a few problems on my homework and I'm hoping to get some insight. the first one: a robotic space probe of mass 7600 KG is traveling through space at 120 m/s. Mission control determines that a change in course of 30.0
  62. Statistics

    A sample of 148 values is randomly selected from a population with mean, μ, equal to 46 and standard deviation, σ, equal to 17. (Give your answers correct to one decimal place.) (a) Determine the interval (smallest value to largest value) within which
  63. Sixth Grade Math

    Leland wants to paint a portrait for his parents using a photograph of them that is 5 inches wide by 8 inches high. He wants the portrait to be proportional to the photograph and 42 inches high. Which proportion can Leland use to find w, the width he needs
  64. MATH

    Rob can complete his bus route in 6 hours. Joan can complete her bus route in 3 hours. If they left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
  65. Algebra

    1. Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 25 tons of rock to cover the area. If each ton cost $40 and each tree is $65, what is the minimum number of trees you can buy
  66. calculus problem I have tried 100 times

    A tank in the shape of an inverted right circular cone has height 5 meters and radius 4 meters. It is filled with 2 meters of hot chocolate. Find the work required to empty the tank by pumping the hot chocolate over the top of the tank. The density of hot
  67. Chemistry-Dr.Bob, I need you!!!!

    You can mix 100.mL of 1.0 M HCl with 100 mL of 1.0 NaOH, both at 25 degree Celcius. The temperature of your calorimeter rises by 5.98 degree C, and its heat capacity is 100 J/degre C. How much energy is released per mol of H2O formed? My answer: 6x10^6 J
  68. To DrBob202

    Bob, This is what you said to do but i'm still not getting the answer which i have to get to V=20ft cubed. I've done the converting but i can't get to the answer because 4ft is 48inches. I've tried it with feet and inches and i still can't get to the
  69. Physics

    The heating element of a simple heater consists of a 2.2m--long, 0.70mm--diameter nichrome wire. When plugged into a 120 V outlet, the heater draws 7.5 A of current when hot. I found that the wire's resistance when it was hot was 16 ohms. Now using this
  70. U.S. History to 1865

    I think that I have the answer to this question but I am not so sure. My answer is On the principle of first national doctrine but I think that I need to answer more. Here is the question: How might have the Gutierrez map's indication of where Native
  71. math

    first multiply first 2 digits, wrire answer side by then multiply1st and 3rd digits write answer next to earlier answer. Then add both answers and minus middle digit of the question
  72. math

    On a TV game show, a contestant makes $800 for every correct answer but loses $500 for every wrong answer. After answering 26 questions, Sarah broke even. How many questions did she answer correctly?
  73. MATH - PLEASE HELP!

    Need help with combining like terms How do I figure this out... 11+5t^2+t+6t If anyone can help I would really appreciate it. I helped BELOW!!!LOL See the answer below which I posted as a correction to the answer provided by Margie and Dr Phil. The correct
  74. calculus

    updating previous question so easier to understand im using chain rule to answer this question: f(x) = -5 sqrt(x^2 - 4x + 1) what is f'(x)? tried to use calculator to get the answer to base my answer off of but this is a nonreal number. does this mean i
  75. MATH

    On a TV game show, a contestant makes $600 for every correct answer but loses $500 for every wrong answer. After answering 22 questions, Sarah broke even. How many questions did she answer correctly?
  76. physics

    I found out how I was messing up and getting the wrong answer. I entered (-30) squared + 49.5 squared then took the square root of the answer getting 39.37 instead of 57.88 which i figured out was the right answer, I didn't enter all in my calc at the same
  77. Math-Algebra 2

    The surface area of a golf ball is 8.92 in ^2. The surface area of a softball is 53.78 in ^2. Find the ratio of the volumes of a golf ball to a softball. Surface Area = 4π r^2 and Volume = 4/3π r^3 I'm not sure if I did this problem right, but I think
  78. Brief Calculus

    The position s of a point (in feet) is given as a function of time t (in seconds). s = −10 + t − 15t2;  t = 8 (a) Find the point's acceleration as a function of t. s''(t)= I know this answer, it is -30 (b) Find the point's acceleration at the
  79. Calculus

    Find the inverse of each relation: y = (0.5)^(x+2) and y = 3log base 2 (x-3) + 2 For the first one I got y=log base 0.5 (x+2)...but the answer in the back of the textbook says that it is not x+2, but x-2. Can someone tell me why it would end up being x-2
  80. Fitness (Check answers)

    6) Gang member often have weapons and are involved in violence. TRUE OR FALSE ~ (my answer is TRUE) 7) Being disruptive in class and getting angry easily could be sign of abuse. TRUE OR FALSE ~ (my answer is FALSE) 8) People with high self-esteem are prone
  81. Language Arts

    A. Bostians find themselves at odds with colonists in the other colonies as a result of the conflict in Lexington. B. Despite the lost of life in Lexington, Governor Gage continues to be a conciliatory and lenient presence in Boston. C. After shots are
  82. Calculus

    A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the original dimensions of
  83. Radicals3

    State the restrictions on the variables and then simplify each of the following expressions. A.) X root 12x^4 The answe is 2x^3 root 3 but I don't know how to get the answer it. B.) (3x root x^2)(2 root x^5) The answer is 6x^4 root X but I don't know how
  84. French

    Could you check these thanks Part 1 Directions: Vrai or Faux? 1. --------- Les passagers récupèrent leurs bagages avant d'embarquer. Answer: vrai 2. -------- Les passagers récupèrent leurs bagages après avoir débarqué. Answer: faux 3. -------- On
  85. math

    what is the number feared by the pythagoreans I googled "number feared by the Pythagoreans" and checked the 3rd entry. This is what I found on that web site. Find the number feared by Pythagoreans, since it lies halfway between the only two integers that
  86. French

    Could you please check these thanks. Directions: Complete with the verb mettre. 1. Qu'est-ce qu'ils -------- dans leur sac à dos? Ils ------------ Answer 1: mettent Answer 2: mettent 2. Qu'est-ce que tu --------- dans ton sac à dos? Je ---------- Answer
  87. Math

    (1 & 2) The first three points do not fall on a straight line, and there is no value of k that will make that happen. (4) To find the quadratic y = a x^2 + bx + c that passes through the first three points, solve simultaneously 1 = c 3 = 4a + 2b + c 6 = 16
  88. Spanish 3 Homework

    Hi! Can someone check these for me to see if I'm doing them right? Thank you! Directions Re-write the commands in Spanish using object pronouns. Also, the words in parentheses are saying who you are talking to. 1.) (sister) Wash the dishes for me! My
  89. Social studies?

    Please ignore my previous post. I prematurely hit the enter key. I've been watching this board all day, waiting for someone to answer my physics question (no one has yet. sigh.) I just have to say Ms. Sue is my hero. She consistently answers almost every
  90. science

    i do not understand how to answer the question if it has (N) instead if saying (kg) how would i answer, and the question is.: if the net force is 100N, and the acceleration is 5m/s squared how much mass am i moving? please answer soon!! Thank You!!
  91. Math

    What is 1 7/12 - 3/20 equal to? I tried to do this question but I couldn't quite get the answer. For the directions of the work, its says use the least common multiple as the denominator and when I came across this one, I couldn't quite get the answer. If
  92. Algebra 2

    Q: What is the value of b in the equation 4^2b-3 = 8^1-b? My Work/Answer: Set each sides base to 2 2^2(2b-3) = 2^3(1-b) cancelled bases out solved for b my answer - 9/7 Is my work and answer correct Thank You
  93. Physic

    The position of a mass on a spring is given by x = (7.6 cm) cos [2 π t / (0.82s)]. Where is the mass at t = 3.1 s? (Answer: 1.45cm) Answer is provided above. Please show all work on how to get the answer. Thank you.
  94. Calculus

    I am having trouble differentiating x^2 + 2lny = y (solving for dy/dx). I know that I need to do implicit differentiation, but the answer I get is not correct. The answer I got was (2x-2xy)/2, but the answer is (2xy)/(y-2). How do I do this problem?
  95. math ( CHECK MY WORK)

    1. on 3 tests, a student scored a total of 258 points. if the student improved his performance on each test by 5 points, what was the score on each test a. 81,86,91 b. 80,85,90 c. 75,80,85 d. 70,75,80 is the correct answer A. 2. an item costs x dollars.
  96. Geometry :(

    this maths problem is wrecking my head.... 1.find the points of interesction of the line L and the circle k in the following L:x-2y=0 K:X Squared + y squared=25 I would solve both equations for y, and then you'll have a system with two equations and two
  97. Physics

    A ferry is crossing a river. The ferry is headed due north with a speed of 1.7 m/s relative to the water and the river’s velocity is 2.4 m/s to the east. a) What is magnitude of the boat’s velocity relative to Earth? Answer in units of m/s b) Find the
  98. Physics

    I need immediate help on these questions:. 2.a small plastic ball with a mass of 0.005kg is suspended from a thread and hangs in equilibrium as shown in the drawing below when a small rod with a 2 uC charge is brought to within 3mm of the ball a)find the
  99. math

    in a big right triangle with a small right triangle inside of it. C is the length of the whole thing., R is the adjacent of the small tri. H is the oopisite of the small tri. B is the adjacent of the big tri. as well as the hypotenuse of the small tri. S
  100. physics6

    In a cathode ray tube, electrons are accelerated from rest by a constant electric force of magnitude 6.2 multiplied by 10-17 N during the first 2.2 cm of the tube's length; then they move at essentially constant velocity another 43 cm before hitting the