AK (alphakappa)

Race #3267

View Pit Stop page for race #3267 by alphakappa — Ghost race

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Official speed 82.72 wpm (125.34 seconds elapsed during race)
Without ending ping 82.85 wpm (189 ms delay sending score to TypeRacer’s server)
Timerless 83.05 wpm (306 ms elapsed before first character typed; 124.84 seconds elapsed during race)
Timerless minus one 82.95 wpm, ignoring the first character typed
Race Start October 3, 2023 5:03:51pm UTC
Race Finish October 3, 2023 5:05:56pm UTC
Outcome No win (3 of 5)
Opponents 1. kerp434 (91.09 wpm)
2. missingkeys (84.49 wpm)
4. rakin000 (76.11 wpm)
5. chradora (71.22 wpm)
Accuracy 95.6%
Points 223.35
Text #4940058 (Length: 864 characters)

Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed of a falling object change as a function of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Characters typed Calculus is a tool that helps us understand how a change in one quantity is realelated to a change in another. How does the speed of a falling object change as a funciton tion of tieme? How does th ee level of water in a barerel change as a function of the oamount of liquid poweured into it? We see change occurring in earlnearly everything we ibobserve i n the world anduni univeres,ese, and powerful modern instruments help us see more and more. In this sefcction we intriodudce the ideas ofaver f average andin instrananteaneous rates of change, and show that they are closleely realtlated to the slope of a curve at a point P on the cuverve. WEee give precise vdevelopments to tof these important conecpcepts in the next chapter, but for new owe we use an informal apprioacoach so you will see how they lead naturally to the main didieaidea of this cahhapter, the limit/ . The idea of a lmiiimit paylays a foundational role throughout claalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 306 262 368 206 122 90 164 133 120 92 87 35 117 86 94 66 152 147 87 82 100 49 68 43 59
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 161 102 65 144 115 116 129 65 138 98 47 174 88 111 224 286 105 85 77 110 64 84 37 134 110
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 147 85 147 17 367 63 91 70 105 63 101 85 57 124 172 104 219 239 159 174 160 80 80 107 93
Character r e a l e -e -l -a l a t e d t o a c h a n g
Milliseconds 45 188 94 73 102 125 234 148 130 203 24 134 93 102 109 107 35 54 92 109 129 73 131 8 260
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 128 161 142 87 68 93 86 113 150 128 86 79 102 210 148 182 145 81 133 67 115 70 104 101 79
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 81 27 549 94 213 159 87 95 80 62 74 30 111 378 101 105 130 97 63 27 55 108 282 140 117
Character c t c h a n g e a s a f u n c i t o n -
Milliseconds 126 225 86 201 80 49 104 75 82 66 74 135 106 92 72 219 201 104 121 200 14 54 54 55 251
Character -n -o -t -i t i o n o f t i e -e m e ? H o w d
Milliseconds 139 161 147 144 97 127 22 45 42 132 46 67 143 59 143 272 96 80 275 103 288 217 92 69 130
Character o e s t h e -e - e l e v e l o f w a t e
Milliseconds 111 110 128 34 99 111 115 139 162 129 54 56 132 20 102 97 121 85 227 91 59 140 73 115 113
Character r i n a b a r e -e r e l c h a n g e a s
Milliseconds 92 68 105 459 72 58 98 34 185 344 169 401 38 65 111 78 122 83 77 77 63 50 89 53 124
Character a f u n c t i o n o f t h e o -o a m o u
Milliseconds 78 91 87 100 472 73 32 241 75 16 36 89 135 47 83 130 90 59 47 220 347 182 62 125 107
Character n t o f l i q u i d p o w e -e -w u r e d i
Milliseconds 111 31 81 92 89 29 169 70 212 171 89 109 134 181 83 245 142 190 146 165 52 97 108 80 345
Character n t o i t ? W e s e e c h a n g e o c c
Milliseconds 69 82 119 70 173 77 259 159 158 229 165 93 70 158 87 103 93 119 27 136 66 91 106 124 202
Character u r r i n g i n e a r l -l -r -a -e n e a r l y
Milliseconds 136 98 163 51 49 88 79 119 67 63 149 83 74 102 237 139 148 161 77 82 79 72 99 158 52
Character e v e r y t h i n g w e i b -b -i o b s e r v e
Milliseconds 129 132 90 99 117 110 101 55 90 21 163 167 19 157 343 0 346 137 176 40 120 74 375 241 79
Character i - n t h e w o r l d a n d u n i -i -n -u
Milliseconds 101 165 130 261 80 73 70 91 54 86 120 108 72 114 185 74 106 50 26 264 135 123 193 161 147
Character u n i v e r e s , e -e -, -s -e s e , a n d p o
Milliseconds 108 146 113 123 74 136 127 104 6 136 33 212 157 144 178 123 45 63 189 75 87 45 99 60 113
Character w e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 129 69 58 247 43 90 103 170 97 181 160 64 93 82 176 60 113 61 207 146 98 136 103 55 127
Character h e l p u s s e e m o r e a n d m o r
Milliseconds 135 324 113 83 107 113 107 106 53 122 39 148 71 173 54 129 34 55 129 90 99 128 162 72 85
Character e . I n t h i s s e f c -c -f c t i o n w e
Milliseconds 53 114 200 217 240 38 105 67 70 75 51 344 105 81 47 397 127 64 207 26 78 23 74 69 53
Character i n t r i -i o d u d -d c e t h e i d e a s
Milliseconds 108 163 99 229 201 119 323 195 63 393 128 371 60 80 98 88 80 16 124 134 43 194 79 169 261
Character o f a v e r -r -e -v -a -f - f a v e r a g e a n
Milliseconds 85 66 229 139 87 122 142 143 147 146 146 33 293 255 135 74 96 153 78 96 113 54 125 96 79
Character d i n -n -i i n s t r a n -n -a -r a n t e -e a n e o
Milliseconds 35 206 99 318 133 41 163 47 89 75 211 147 97 162 139 135 72 136 87 323 236 75 51 360 188
Character u s r a t e s o f c h a n g e , a n d s
Milliseconds 109 80 96 338 97 125 113 129 112 78 104 196 115 97 92 90 98 41 101 181 64 95 29 302 163
Character h o w t h a t t h e y a r e c l o s l e -e
Milliseconds 78 72 60 67 157 70 148 88 94 123 77 79 97 17 54 155 118 112 200 50 92 105 156 203 225
Character -l e l y r e a l t -t -l -a l a t e d t o t h e
Milliseconds 128 67 151 89 58 114 48 90 57 203 188 134 143 196 33 69 92 98 114 84 41 67 87 108 94
Character s l o p e o f a c u r v e a t a p o
Milliseconds 100 124 75 129 181 134 121 154 117 62 95 77 157 147 113 218 82 116 165 76 53 95 62 90 121
Character i n t P o n t h e c u v e -e -v r v e . W
Milliseconds 226 67 39 120 131 148 133 76 103 30 128 62 79 175 145 214 138 277 132 26 263 230 154 185 215
Character E e -e -E e g i v e p r e c i s e v -v d e v e
Milliseconds 84 117 300 140 32 112 102 200 65 84 81 61 153 123 122 171 96 71 112 189 221 31 183 116 101
Character l o p m e n t s t o t -t - -o -t o f t h e s e
Milliseconds 99 125 170 115 154 125 171 124 93 87 0 96 104 234 157 150 150 223 100 6 186 88 92 98 112
Character i m p o r t a n t c o n e c p -p -c -e c e p t s
Milliseconds 47 218 87 90 138 114 176 85 55 91 94 165 46 44 130 8 171 264 129 137 36 55 102 93 84
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 77 124 92 72 116 42 103 0 343 155 201 137 103 172 91 75 171 118 119 89 35 187 419 134 65
Character f o r n e -e w - -w o w e - -e w e u s e
Milliseconds 36 176 74 95 17 182 115 232 309 28 240 127 183 43 85 21 427 122 61 56 98 132 173 127 101
Character a n i n f o r m a l a p p r i o a c -c -a -o -i
Milliseconds 106 36 159 65 185 39 77 141 59 64 133 104 72 137 101 145 108 147 0 73 118 154 142 144 276
Character o a c h s o y o u w i l l s e e h o w
Milliseconds 205 47 104 163 171 60 145 71 164 63 103 50 102 82 22 196 54 115 79 171 80 132 224 81 62
Character t h e y l e a d n a t u r a l l y t o t h
Milliseconds 74 82 97 85 85 134 55 62 130 175 163 45 96 65 109 71 53 152 81 78 58 61 78 55 131
Character e m a i n d i -i -d d i e a -a -e -i -d i d e a o
Milliseconds 56 77 193 116 28 81 77 25 70 370 126 166 0 186 71 216 139 152 157 194 27 182 76 124 99
Character f t h i s c a h -h -a h a p t e r , t h e l
Milliseconds 84 41 143 57 261 118 96 153 226 137 163 131 184 84 54 129 129 82 61 166 127 66 73 29 113
Character i m i t / - -/ . T h e i d e a o f a l
Milliseconds 118 60 143 87 159 217 175 165 82 264 196 158 95 0 178 75 161 129 159 71 129 87 103 73 179
Character m i i -i -i -m i m i t p a y -y -a l a y s a f o
Milliseconds 184 11 137 253 145 165 187 0 127 301 111 97 218 138 228 131 214 65 89 120 109 100 175 215 50
Character u n d a t i o n a l r o l e t h r o u g h o u
Milliseconds 96 89 152 143 114 129 73 21 141 137 140 151 65 156 82 136 288 181 126 120 73 79 100 176 69
Character t c l a -a -l a l c u l u s .
Milliseconds 101 97 127 146 10 389 109 25 157 80 72 114 141 116 106
WPM Timing
Seconds WPM
2.51 81.38
5.01 95.74
7.52 100.53
10.03 93.35
12.53 94.78
15.04 96.54
17.55 96.42
20.05 96.34
22.56 92.02
25.07 90
27.57 90.95
30.08 91.35
32.59 90.95
35.09 90.27
37.6 89.68
40.11 91.25
42.62 90.67
45.12 88.56
47.63 88.18
50.14 86.17
52.64 87.31
55.15 88.12
57.66 89.08
60.16 88.36
62.67 87.51
65.18 84.88
67.68 84.75
70.19 83.43
72.7 83.86
75.2 84.89
77.71 84
80.22 84.82
82.72 85.59
85.23 84.05
87.74 84.25
90.24 83.51
92.75 83.58
95.26 84.03
97.76 83.71
100.27 83.17
102.78 82.78
105.28 83.43
107.79 84.61
110.3 83.56
112.8 83.4
115.31 83.15
117.82 82.81
120.32 82.58
122.83 82.75
125.34 82.72