Question
The gas mileage M (s), in miles per gallon, of a car traveling s miles per hour is modeled by the function below, where
.
![M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50](data:image/png;base64,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)
According to the model, at what speed, in miles per hour, does the car obtain its greatest gas mileage?
- 46
- 48
- 50
- 75
Hint:
Hint:
We need to find the speed at which we get greatest gas mileage , which is the value of for which the function M(s) is maximum.
The second derivative test to find extremum of F (x) is as follows:
C O and a point x = c is called local maxima if
0, then the test fails.
The correct answer is: 48
Given,
Gas mileage is denoted by M(s), in miles per gallon,
Speed of the car is denoted by s miles per hour.
The relation between gas mileage and speed is given by
![M left parenthesis s right parenthesis equals negative 1 over 24 s squared plus 4 s minus 50](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALoAAAAjCAYAAAAjZxB6AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAA+tJREFUeNrtnE9IFUEcxweRh4gE0SGigyCPkAgRJEIkIpCIiIjAg0SnQCIkoouHkOggiKeQCCTCg4dAJDpIBCEhIvIuIhHyCDx0Ei8RHuIhD7bf4G9h3zg7b3b3ze667/uB78HZGXf2t7/9zW/+qBAgKZdI06QdmAIUmSXSBMmDKUA7AEcHcHQA4OgAwNEBgKMDUDhH91hHpE1SGSYHRY7oHaSnpG2YPBuk8Wct685yfTh6fGpwufQZIG1FbLPJ7eDo0blBWofbJYsSo03qyOt1HkKDTjsY8V5DpI2COLgql1xge/el8Gx3M55kewapnCG9I1VYC1x2gjL/greGG/eQfpN+BMoG2fBx2GCHB3bIczWr7Oyuke96NweObssa6Z7yka7pKt4XxweT9g2/bIHrfAyUzZEmYz7Iswh5fbsjnftLWJRykFbJd/34lDj6GGleU/6GNK4WviJNkaqkayEpi4zkr7mez1fS9ZAOvOQRoM6dnlKuD4d9dW2KyV7SyftTmj+MBN6LF7O/aTr6CumWpvwmX2tgmaP6DCtIN+kXpyl+PZ9DUinECO9DrvmUuH3U/MwTxdugaWavJM8fpW6JA1pvk7Y27zctR/8T0g9ZdqAWSke+yNG8qlybDzh/lev51A2rKqMWnTxCII9kL9cRfVZJRb0M+hu89xEHQzmiveC5g0rd1r/kCsq/wM/7gWFSDmM/SZ2aeqabyLxpW5kgpO3oSUYFz7Hi2svlcw9oFha8hO+3FaNzJy9aTHOg7Y/g6A37DTKKf1cmIlOBlGUopJ4pdfEnUBvcpgepi9WE02Qv1xFdLsuVI7R11V8TMhdX9xAOQnywS01d5Mx0UZl4VnjWOmOoJ/nGUT+MLs75HmmuYTIazV6uHT1OYHHR32bUNJPR2yEfxYqag08oqYyMtLs8bITVk9gsL34gPdSUT3J7YGevNHL0OG1b3V8TV0h7StkDnhirLAplefET6Y5SaUmc3MzR1Wu2YXSVP5hzmmvYMIpmrzw6uov+Bv1tmANvB0ftPXZsFZk+PefAXOJVoXXd8kyX5TKOrt6WaDy38pcNVOcO6NZ/i3IEoBXY2CsrvAz7O8ZzxDr73jJ/WDrO8shS4wWTBRfzhqIf6hrhXO+QV4l2LIfqrM+KAAc8Efbb+XOaXD/PrHOu50eIy/yhjhva5OGsCACJ6RWNh9tU8nBWBICWUDOkOjZnRQDIPcNCv9pke1YEgNwjV54qQr9RZntWBIBcI5exPgv9sdAoZ0UAyC197ORh/2oi6lkRAHKH3BSR28zdhjrtdggNFIzz4nhXrjNGWzg4ODWsivT+jA2AzEiSjsDRc8B/BqdleULDAPwAAAEBdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPk08L21pPjxtbz4oPC9tbz48bWk+czwvbWk+PG1vPik8L21vPjxtbz49PC9tbz48bW8+JiN4MjIxMjs8L21vPjxtZnJhYz48bW4+MTwvbW4+PG1uPjI0PC9tbj48L21mcmFjPjxtc3VwPjxtaT5zPC9taT48bW4+MjwvbW4+PC9tc3VwPjxtbz4rPC9tbz48bW4+NDwvbW4+PG1pPnM8L21pPjxtbz4mI3gyMjEyOzwvbW8+PG1uPjUwPC9tbj48L21hdGg+J7MOmwAAAABJRU5ErkJggg==)
We need to find the value of for which M(s) is maximum.
We use the second derivative test.
First, we find ![M to the power of straight prime left parenthesis s right parenthesis](data:image/png;base64,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)
![M to the power of straight prime left parenthesis s right parenthesis equals negative 1 over 24 times 2 s plus 4 plus 0](data:image/png;base64,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)
That is
![M to the power of straight prime left parenthesis s right parenthesis equals negative s over 12 plus 4](data:image/png;base64,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)
TO find critical points,
![M to the power of straight prime left parenthesis s right parenthesis equals 0](data:image/png;base64,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)
Which gives
![negative s over 12 plus 4 equals 0](data:image/png;base64,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)
Solving for , we have
![s over 12 equals 4 not stretchy rightwards double arrow s equals 48](data:image/png;base64,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)
The only critical point, we get is s = 48 . So, we check if M (s) has a maximum at s = 48
Now
![M to the power of ′′ left parenthesis s right parenthesis equals negative 1 over 12 text for all end text s](data:image/png;base64,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)
So ![M to the power of straight prime left parenthesis s right parenthesis less than 0 text for end text s equals 48](data:image/png;base64,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)
Thus, M (s) has a maximum at s = 48
The correct option is B)
Note:
We could have also used the first derivative test to find the local
maxima. We need to find critical points and then check whether the
function is increasing or decreasing on either side of the critical
point. If the function is increasing , i. e ., on the left side
and the function is decreasing, i. e ., on the right hand side, then we say that is a local maxima.
Related Questions to study
Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z
Given a rectangle ABCD, where AB = (4y-z) cm, BC = (y+4) cm, CD = (2y+z+8) cm, DA = 2z cm. Find y and z
Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.
Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.
Find the area of the polygon in the given picture,
cm, ![MB equals 4 cm text and end text MA equals 2 cm](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARoAAAClCAYAAACDWDKuAAAgAElEQVR4nOydd3xUVfr/3+dOSyZlMum9QOhNCF1QaVJEEaRXAbGi0mzr97v+9rvuqiuIrCgWVIpUqVItiAVBd0Wk95pCEkIaqVPu+f0xmZCEoJQkZMK8eeVFMnNn7r3nnvu5z3nOc55HSCklVYBEokq1Kr7KjRs3tQxFKAjEjX++Co/FjRs3bipFe6sPwI2bqkMghPO5K5FSUiXmupubxi00buoGQoCtmLyCQiw2FUWrx8vbG50iqRrngJubwS00buoACtJyiWM7v2D55l2kZBXhHRRN1/7juLddFN5acHsPby1uoXHj8ghh4/zub1jz9WnC73yIAdFG0g9v55tFC7Erk3ioYxi4JypuKW6hcePSCKEgLGf4z4/HMUR05sH7uxOqAI2CKTqzkN9++Jl27QYRq7itmluJe9bJjYsjICOVE8WFKDGRBCoSFRVpjKRJK1+0luMkXnC4cNzcOtxC48b1kRJ8PDB6GdCW/AkCoQgQEvfU063HLTRuXB//IKJVLdazyWRKgUYoCEsapw7nYSWGUP9bfYBu3D4aNy6NlCp4xtChZQSL1mxmRYigW7MAsvZ+xfZDFpqP7EScQWJ3WzW3FOFeguDG5RECWZTNqZ8288nGn0jOysMnIIJO/cZzf5d4TAaB6g6muSludgmCW2jc1AmEEGArICMjm4JiG1oPI37+gXjpJKpbY24at9C4cUOJ0CBQytwMErtbZKqImxUat4/GjcsgSuaonR3e+b+KipQSVbVjkxIhBBqNxr30oBbhFpoaxrnor6zPwHkDVZFxWSeoKCoSiaqq2Gw27HZ76U9hQSGp51NJSkoi8VwimVmZBPgHMHDQQIJDg2/lKbgpg1toahJpp6igACsGjEYDChKkSnFhETapxcOov63iDRyiK64wySUSm92GzWbDYrFgs9rIu5RHSnIKp06d4uzZs6SlpZGSkkJGRgaWYgvFxcVoNBoKCgrIysri3NlzTJk2hdDQUOzSfovO0I0Tt4+mphAaNEWJfPHev1h2uB5Pv/IkHSMNKPbzfDf/c34taMjwqfcSXgdTG5S1TsqKil3ayc/PpyC/gMLCQgoKC8jNziU9LZ3Ec4kkJiVyIf0CWVlZ5OTmIKQjCE9v0BMUGERgYCAhISHExsYSHReNr8mXlctW8uEHHxIUGMS9fe5l+ozpbrGpAtw+GpfCSt6FfE5t/5q193ai3gPtCdXayb94kQv5edgQuHQYq7gsJmU7pYpKTnYOly5dIjsrm9zcXC5mXiTrYhaJ5xJJTkkmJzuHwsJC8vPy0eq0GI1GPDw8CAwKpF79eoSFhRERGUFYWBiBwYHodLpyP3qdHpvdRkBAANHR0YweM5qtW7by7jvvMvnpyQSHBrsfhLcQt9DUJFIilBh6DW6ALfVrftoXygOtDGg0CoriWotxhBAolQz0cnJySEtPIyU5hYsXL5J+IZ2MCxmcTz5Peno6mZmZqKrDeWs0GgkKCsJsNtOkaRMCAgKIjIokLCyM0NBQAgIC0Oq1KIqCoihX7NNp+8mSf06/jU6v474H7iM2Npa3Zr2FoihMfW4qJl+TW2xuEW6hqVEkEoEupjMPdjzMjp2HSIlpitDUDpFx+kyASs1k5w1ts9nIzc4lOTmZxMREMjIyuJB+gQsXLpB5MZPz58+TmZmJRqMBwGg0EhERQVy9ODp07kBISAjRUdEEBQUREhJCQGDAH+6v9G8psVP5EEiUWTWpShWDwUDf/n1JS0/jww8+JDg0mHEPj8Pby9s9jLoFuIXmFiBVlcg7BtF0z3J++FWDl03U6OriyqaJVRwzOmV/rBYreZfyOHvmLMnJyaSmpnLx4kUyMjLIz88nNyeX/IJ8jJ5GjF5GfH18CQ0NpdUdrQiPCMfkZ8JsNmPyNeHv74+3jzd6nf5yO5T8q1Iro2T4pqoqGqHhwUEPUlRYxPp167EUW5j0+CS8jF5uy6aGcQvNLUBKFa0IomWHRmz54jt+OlaEiOQmXG2Vc7VZHavNisViodhSjKXYQlFREVmZWZw5e4ZzZ8+RnpZOVmYWqampFBYWYrPasFgt+Pj4YDabMQeYia8fT2xsLGGRYXh7e+Pt5Y2XtxdeXo6fsoICZUSlJOalunDkCb48pDKbzYwaO4rC4kLWr1+PXq9nzMNj8PH2cYtNDeIWmhpFotrs2OwqKoLQRh1o2/C/zJ/5BZGPdORGpeZqgmKz2ygsKiQvL4/CgkLyCvLIycrh9InTnEs8x7mz58jMzCQtLY3CwkI0Gg2KRsFsNpdaJmFhYTRu1JjI6EiMXkZ0eh16vR6dTodBb6h0aloib9nwpOzwDxzCY/I1MfGRiXjoPfjoo4+wWq1Mesxh2biHUTWDW2hqCimRihdRLZqiMQejQyK1JhreNZDJ04tJiY7EA7XcnJOoMJ66mv+ksKiQ3NxcsjKzyMrOIjc3l+ysbNLOO2JNEhMTuZR3iby8POw2O97e3nh6euJr8iW+QTx33X0XERERREZFEhoWipePF1qNFp1Oh1ajRat1OGQF4goHbK2zCioxllSpYjKZGDF6BBarhfXr1qPT69w+mxrELTQ1hoqqD6bTsAeRKGikigpoAxvx0HN/QUWDtsKQonSIIR03dlFhERkXMriQcYH09HSysrK4ePEiWRlZpKenk5aWRkFhAVJ1hOGbTCZMfiaiYqIIDAwkLDSMgMAAIiIjCAgIwNfki6IoDkumZGZHEZXP6tQ6QbkaVzEKpZT4m/0ZP2E8iqKwds1akDB2/Fi8vLzcUdnVjFtoahSBVqcDyi43EOh0nqX3h0RSbCnm7OmzJCYlcj7lPBcuXCApKYnMjEwuXrzIxcyLoIKn0RNPT08CAwOJiIigabOmBAQGEBAQgNlsdvzvb8bkZ/rDYKtSQZEuJCh/wNVCHlWp4ufnx9jxYwFY8OkCbHYbEydNxNvotmyqE7fQ1DAVn5yKULDZrHy//Xt+/PFH0i+kk5udS26u40dRFLy8vPDx8cHf35/GjRsTGhZKcEgwfmY//Pz8MPmaMJlMeHt7l9+X85+UV7356hx/cpqqVDGbzIweOxqbzcbqz1fj7+/P4KGD8TB41AmhrY24heYWIoSgsKCQzZs2M/PNmdhsNlq0aEFUdBQN4hsQHhGOn79f6dSxc0bHaDSWd3jW0IyOSyAqjwEqiypV/P39mThpIpdyL7F0yVJMfib69u2LRqtxt2E14BaaW4QiFLJzslm5dCUff/wx5xLPMXTIUKZMm0JAYAAeHh7o9frKBcX91L068upDp3KbSYnZZOaRSY+Qk5vDB+99gCIUetzbAw+927Kpam6nxcK1Bo3QkJeXx8JPFrJ48WJ69urJ3XffjY+vD8GhwZh8Tej0OlSpYpf20h9Vui2WP+U6IgTs0k5UVBRTp08lNi6WN15/g21fb8NqtV4x4+fm5nALzS0gMyuThZ8sZN3adYwcOZLJT08mMCAQ1a6i2tVSv4qbG0D++dCpLHZpJzoqminTp9CqVSvmfzCfrVu3YrFY3GJThbiFpgZRhEJiYiJzZs9h9erVDB8xnLEPj8XobbzVh3Zbo0qVBvUb8PyLzxMVHcX7773P9m3b3WJThbiFpiYQjuFS6vlUPpz3Idu+2cYjjz7CmHFj8Pb2xm53T6tWGTeoC6WWzbQpxDeIZ9bMWWzbtg2LxVIutsjNjeFuwWpGCIGQguMnjjN79mx+3/M7U6ZPYcjQIRiNxttn2rmGuJmpfBWVevXq8ezUZ4mPj+e9f7/HN199Q7Gl2G3Z3CRuoalGhHCE7B84eIBX/+9VDh08xLjx47j/gfvR6XTumY1q4GYywTkDFuvF1eO5F56jXlw9Pp7/Mb/8/AuyJOm5mxvDLTTVhDNJ0949e/nX6/8iJzeHF//yIgMGDUCv07tFppqoiuBEVarUr1efZ6c9S1hoGPPmzmP3r7tRVdUtNjeIW2iqASEENpuN3bt38/Zbb1NUWMSM52bQsVNHt8i4CHZpp358fSY+MhG73c5bb77Fvt/3la4jc3N9uIWmGlDtKj99/xOv/t+rCCGYOm0qnTt3RlEU97S1CyGRtE5ozUt/eQkEzPzXTH777TfHNXRrzXXhFpoqRBEK0i754bsfeOff72D2NzN12lTad2wPwl23ydVwDsPaJLRhxowZ2G125s6Zy6EDh1Dt7mHU9eAWmipCCIHVYmX7tu28NestQsJCePnll2nZqiWKxm3J1BQCUeUCoKKS0C6B5196Hrvdzj/+/g/2/LrHbdlcB26hqQIUoVBY6Fgc+Y9//IPo6GienfIs9eLrORyTbo2pMapjYanTsmnVuhXPTHkGq9XK3Hfmsn/vfrfP5hpxC00VkJefx8b1G5n7zlw639mZl//6Mo0aN3I7fW8B1WHRgENsFEWhXft2vPSXlyguLmbmv2ZycP9BVNV9nf8Mt9DcBBqhIScnh5XLVvLx/I/p2LEjz0x5hvDwcBz589zUJaR0rEFr3bY1M2bMQFVVZs+azcnjJ93Rw3+Cu3VuECEEFy5eYNHCRaz6fBU9e/Zk8rOTCQ0JdVgy7uHSLaNaqyzgGColtE/gmSnPkHEhg3nvzuPsmbNusfkD3C1zA2iEhszMTJYvXc7qlavp2asnkx6fRGiIu8bzLecaEl/dLE4ncLv27Xhy8pMcPnyYt2e/zfmU826xuQruVrlOhBAkJSfx0QcfsWnDJoYMG8KESRPw8/Nzi0xt4BoTX930bkrEpue9PXlq8lOcOH6Cf8/5N2fOnKn2fbsibqG5DjRCQ2JiIu/MeYcfv/+RgYMGMn7iePxMfm7Hb22hBiyasmh1Wnr17sXjTzzOvr37mPv2XJLPJaMRmho7BlfALTTXiCIUzp47y9w5c9mzZw+PPPYIo8eNxtvLu9pERghRUhDtT94XNVtSt1ZT0aIp00bVsjspMXgY6NW7F48+9igHDx1k3nvzSExKdE97l8EtNH+Cs7Mc2H+Af73+L/bv3c/ERybSt19fjJ7GahIZAVLFarFQXGzBJq8sJoeU2K0WLMXFFBcXY7Wqbv9zORwCrdqsFBcXY7Haqi24TkqJTq+j7319eeLJJ9izZw9vv/U2qSmpbp9NCe7k5H+AQCCl5MihI8z810yKi4uZ/vx0OnfpjMFgqB6REQLsORz/cSsr1u8iw2alfpehPNi7C9F+IKVDhHKPfMXC1d9wLM2CIn2Jb3cvg0fdSYROg+qcdSlZQS5Kk5pLhFAQznMrqYwpSrdRUV1drUqGTkKqWNMPsXr1GrbvS8cc2JJ+kwbSJToAWe66iZLUEjjaQ0ooEYcyr5aWHHa00ZWN5BSb3v16I5F8+P6HvDPnHZ58+kkiIyNv+6G1W2iughACVVU5sPcAc2bPoSC/gKnTp9Kxc0fHe9VkyWg0NlKP7WTT2oMEJXQjQX+Wnd9v4ivvQEb0aYa3RmJXbaQc/JFUu4mEHp2JMmrxDYnBWxGlQiEE2Cz5ZFzIokjV4GM24+2hxZafS7HdQm5+MXovE36egpzsHCzo8DX742vQunYyLoljuGS7yP6dezlxwUzX/i3J+XUHqzb9h2YTe2PWi9L8MlItJjP1IpesEqOvH36+HtjzLmFVreRcKkTovfD39aAwN5s8K3j5+WM26ivftZTo9Xp69+mNIhTmvjOXeXPnMXX6VAKDAm9rsXELTWUIsFlt/PeX/zLvvXnk5+fz/IvP07Z9WxBUX4cRIKwWsjMuUtDybsYN70GgPhdt8sv8fiGRAlszfDQAeaQm2vHyDCUmJoIYf2+CwqMxaewlT1uBtGdy5IdVLProB5IsWuL7DGdQt2jOrVrE7iKV40dPo4toTfcWwRzevYMTWZ7cOehJHh/UAk8BLrs0S1BS59yHenf35ZHuPoQGeHLSkMrvK45zdnR3zHp9yaZWkvetZ8HbWzlwsYCgtn0ZOeZuircsYVdmHoeOnsHmFck9HVuRdXwnu0/k0LDHJKY8fBcBBlFprJTTZ9O7b2+sVisfvv8hCxcsZOKjE2/rSQO30FRACIFqV9n10y5mz5pNUHAQzzz7DK3btkajqebiYlJiw0C9dg/yZIIBf71K1pmfOXrem9BGEXjpHH1bFl/gzIlz7Pj9IEdP7Mbs40+b7iO4r0czAj0VFOykHf4PX39xkOaTXmKSVyLfHCkgJSWJU8lJ5Lcczf8N92HLhx+z+TdPnpg0A/vuL/ly2y6O925KK2+Ny1o1jusjkRoP/IKDkZaLHN6xnS+/PYjhjvuI89CXDIgk1qzDbPn0G7z7P8qrDW3s+vU0SYkpFKec4qixJzNeHsrRjZ+x+OtDjH7qCe7N/Znly//Dvv4J3BXhw9VsP6dl07N3T9IupLFu9ToUjcK48eMIMAfclmEQbqEpgxACq9XKrh27eHfuu4SEhjBt+jQaNGpQcyVQhILBwxcDxaQc3MYXy7dS1Lg7/To0wKiUeAukFzEd+jDxvmZ06tyAwoPb+Pb7dexv3oBusUaQBeSkZpBqbUr3hHgampsQ08bKpfMHyDTFEtOhDfWbetG6YSMUj6Y0bdWMvIu/4fV9Mjm5Kni77tSsw2nukBIAe3E2Z48dISVXR0Sohcx8FV8/DQIVy8VznMiMp8cdDYmPDyCmcXsK85PZ/n04XTom0KhJPPoTe7lHhZatWxKamoLZdpqcTDsy/I+PQ5UqPj4+DB8+HNWusmbNGrQaLWMfHovJZLrtLBu30JSgCIXCokK2btrK/I/mEx4ezoznZtCgYQPHuqUae8ALoIjEvZtZtOBbbPUfYOzQHsT5KiWuW4lijKD7uIdLpwxzgrxRtClk5jk7r8PxKxUDWkUAWjwMCsUaBUXRotc6vkuj0eFp0HLZ4YnrL50ond52OMCFTz36TJhG5147WTbzU7af6MrYtn6Ojq/asQs9Oo1AItDrPZAWDYpQMOg0jvYWWjwNAo3idKZzzW0kpcTf7M+oMaOw2+ysXbMWm83GxEkTMfmabivLxi00OESmoLCAjRs28unHn9K8eXOemvwU0bHRNdwZBIqwcX73Jt6fu5bCZsMYc39bTPZscguM6BUVm11BW3iGjduP4hnThHaNAslMs6LTNSEyRIOjgpoB3wA/AuR2Dhy5h4DgHHZ/dwYRoqMYiVriMVbtduwlK4+lLCle5+pCI0AIDUreeXZ+tYezmmh6tIsi72IOxcKbQL3icEAJBb1/JDHGTRw+lEgTj4sc/u4Al/x8yYPSNpJSxW4vcbJLed1tZJd2TCYTYx8ei4rKF2u/QKfTMWbcmNvKsrnthUYRCrmXctm8cTOLFi2iTUIbnnzqSSIjImv+iSMAWzGJh/7Lf46eQ3tpA3MPbkDx8KHDg2Po7JvH74dVOjzYhCj9eZYtWM+yPIXA4GbcO2QgzQP1OKwTLUFN29Gj90lW/PtVvkJDZOve9G4VQbHZjFGvAAKDrwlfL08UQGf0wRzsh4frjppKKPHAGEyEeCeyeeU7bFpox9srlIRuw+jewAuNkCAFusBm9B3bkc/mv8uLi6z4x3Wi/7AG6M1mCjx1CEBn9MbXJNAJUHSemIP9MequLzZGSomfnx9jxo5Br9Wzft16bHYbD094GLPJfFtYNkJWkePBFYvPO0VmwccLWLtmLZ3v7MzkZycTFhpWY+eiCIXMrEz++pe/4uvry0svv4Biy+f8xVwsFhuqBKFoMQWH4ae1kZsPfmFmDJZskpPTyCmwY/D2JywyFG/tZateCLAW5nD+7Hny7Fr8wyMI8NFSmJ2L4u2Hl0FQmJODVRjw8jWiFuZyKceGZ6AZT63rRbQKIbBYLLz/7jw+X7WKFas+JyLIRGpyIhdyLGg9fAmNjsDscTnOSCBQ1XzSTieRWSjxCQojNMgba3YWNk9ffDy1WPMvUWAFo8kXrS2fnIuF6Mz+eBmU647/U4RCTm4On3z8CevXrGfw0MGMnzAeo5ex1mdgvJkyNnAbWzQaoSEzO5NPPvqEDV9sYNDgQYweO/rWzwoIBW//CBr4R1R4Q6ICPn4OR6P08CemfkCZd+3lgu2kBJ2nmdjG/mU+L9EHBkPJtka/QEcImlTRGv0IMgpU7K49fBKOwDqkClovwmIaE1byVsVgO4lEaLyJiG9CROkWEkNAMJRsa/D2wwPHEErqfQgM872ira8VVar4+foxYcIEtIqWlctXAjB+4ni8jF4u96C+Hm5LoVGEQubFTBYuXMiWLVsYMWoEQ4cPrTUrsP/IOiw9OqnyZ0cqK9lGlnlFSnupBVTZtq6PxP5nN++ftlGZpR1V0EZ2acfX5MuI0SMoKi5i44aNhIaGcv8D96M36Gu9ZXOj3HZCowiFpKSk0sWRg4cMZvjI4fj51g6RcXOTuMB9KqUkKCCIsePGkp2VzfyP5mMwGOjTrw86bd2sYHpbrfjSCA0ZGRm8/dbb/PTTTzwy6RFGjxmNr6+vW2TqCi7iXrJLO6EhoTz25GM0bNSQd+a8w5dbv8Rmt9XJhZh174yugiIUjh47yhv/fIMjh4/w4ksvMmDgALy9veusuXo7Irn5krg1hV3aiYmKYdqMaTRt1pS5c+ayddNWCgoL6pzY1K2zqQRneoXDhw4z842ZHDhwgMeeeIwevXqg09dNM/V2xrFa3UXMGhxiExsTy9NTnqZps6a8//77fPP1N3XOsqk7Z1IJoiRNwpFDR/jbK38jNTWVV/7fK9zX/z4MHga3JVMHcdZgciVUqRJfL55pz00jNjaWee/O46utX2GxWupM8qw6KzSOFACSPb/tYfas2RQVFfHSX16iQ+cOoLjL09ZZXPS+tEs7kRGRTH9uOo0aNWL2W7P56suvsFltdUJs6qbQlKR5+OGHH5g1cxYWq+WyyIBLzEy4uUFc+NqqUqVeXD2envI0jZs05sP3P+Srr76i2FLs8mJT54RGEQqqXWXnTzuZ9eYs9Ho9M56bQbuO7RwZMt2WjJtajIpjGDXjuRnExsby6cefcmj/oWqrwFlT1CmhUYRCcXExX235illvziI4KJgZL8ygRcsWjg3cGlP3qeEqCFWNlLLUQTx58mSMnkZe/+fr7P51N3a73WXFps4IjSIULMUW1qxew9x35hIbF8sLL71Ao8aNXM456ObGcUVncGWoqMQ3iufZKc+i0+l4/bXX2btnr2NxvguKTZ0QGmcumRXLV7DgkwW079ie6c9Pp2GjhoB7uHQ7IZxrnVwcZ4G61m1b8/yLz6MoCrPenMXe3/c6NnCxU3R5odEIDfl5+Sz9bCkfvP8B7Tu25/HHHycmOsYdI+PGtSl5Pra6oxUvv/wyQgjefONN9u7Z63I+G5cWGiEEWdlZfPTBR6xauYoHBz7I408+TkhYiFtkblPqytCpLKpUaXFHC2Y8NwOAf/z9H/z+2+8On42LmDYuKzRCCHKycvhk/ids2LCB+++/n0cfe5SI8Aj3UOk2xlVuvOtFSknrhNZMmz4NKSVvvvEm+/fur9YqnFWJSwqNRmhISU5hzttzWL1qNSNHjWTU2FH4mHzcloybOosqVVontOb//e3/oaoqb818i8OHDruEuLqW0IjLaR7mzZ3Hrp27ePLJJxkyfAi+Jt9aackI4aiEqBGaSn8EAo1GU0VPJYFSyT6U2t8PS6js+K/v4J3O4HL/X+XHJRHQomULnnvhOaxWK2+89gZnz5x1rIuqxafkUvloBIKUlBTmzJ7D/v37efKpJ+l7X1+0Om2tFBkAq8VKWloauTm5jhcqdAZFKGRnZ5OZmYmPj8+N70gIZHEmR/fu5/CZdCwluXN9wurRolVrInyVWttGDgSKtJJ19gA7fj9NQZENrSmKFm1aUD/EG3GNx14XfTQVsUs7rRNaM/mZyfztlb/x1sy3mPH8DCKjI2vtubuE0AjhqAy9f/9+Pv7wY/bt3cfUaVPp278vWm3tFRkhBEcOHeGjDz/i2LFjKIpSUr+5pBxrSVlWi8XCqVOnCA4Jxmq13ti+ULDnnObrTxbz4yUP6jcKwaM4h4ztP3MiRWHkoAT8tfZa2g0FQtpI/W0rK1b/wFHhSZBeS1baD/y8vz1jxw2iWYj3NZXPtNls5GbnsmbVGgICAirtGxJH4qm27dvi7+/vksNtIQQdOnVg+ozpzJo5i9mzZjP9uelERt6CpPrXQK0XGqcJfOjAId5+623S09J58S8vck+3e2q1yIDDAjt48CA///wzAwYOIDAwEFUt36mFEOTn57NpwyaAm3siSUBE0m3EQ4zq3wpfNZMfP/mYHccPkF6cQKAO7LWwuYRQsV46ybfLt5MedDfPPN6HBr4G0g9uZdmi9ezcfQfRve7ApPvjXL1SlRQVFZGVlcXaNWsxelaS9FtAfl4+qqryzzf+SZc7u1TvyVUTUkq0Wi3de3UHAe/NfY9ZM2cxffp0wqPCa919UauFxrkCe/+B/bz91tvkXcrjxZdepGvXrqiota4xKyJxdHyj0cj4CeOJjIisdLucSzmcO3MOTw9P9LrKC8hf8z6lhUuZGaSmpVFgSSe50IAxJIJAD1lLk44LkDbyzuznx/xQ+o3tREOTJwqS0GbdGT0phExdKDqh/qkECyEw6A0EBQfx9LNPExwcjKygTIqisG/vPj784EMyLmRU32nVAFJKdDodPe/tid1m551/v8Ob/3qTGS/MIDIyslZZarVWaIQQ2O12ftn1C++9+x4FhQVMmTKFO7ve6agCUEsHARVxOh5tNhvAFWatIhRsNtsVls6N7Utis55l25L3ObwrEA9bPmfPS9r0b4pGEbWzxQSggrRYKAoNJ9jkgaY0qbiekAYJhMC1VWcQoDfo8fL2olPnToQGh1a6mU6nw7zSXMUncmuQUqLVaOnRqwcAc96ew9w5c5n8zGQio2qP2NRKoVGEw3H57Tff8t6772E2m5k6fSptEtoANzm8qGGkrKGa3YCUAq0uiq4PdaV/z6b4SCsnv1/Kz6m/cyytJ53CauHQSQJCoDUHE5l1hLxLxdhLo6g7JssAACAASURBVF6tZJw9To42mLCQQDw0f37lVemwdG02W6XVJDRCg9VqrTU3YFWgShWDh4F7+96LVqPl7bffZtabs3jhxRcICw+rFT6b6pvedk4jlnvpz6cVhRDYrDa2f7ud9997n/DwcJ5/6XnaJLQpdaC6EjU9jSrwICgyjgb16lO/fjxRgX7opaOgXO1EgtDgERhGA06xY9tuzhbaUFDIPLWLFfPn8c3eZIqlck3ncC1rnerKeqiySCnRaXV069mNJ596kuPHj/P27LdJTkn+g5SglU37V8/xVZtFI+127FIiFGcch0S121GlQNFUXuVPCEFRYRFbN23low8/Ijo2mmemPEOTxk1cwidTGaXP4Brq16o8z471i8k+GYmnmsuF5DzCmz9AnD/U1me4RKD3aUi3hzqQtGYb7845SKRRz4XTx7jk14xxLePw1anXVLTtWqa3XbEfXQuqVNHr9fTt3xeAWTNn4T3fmyeeeoKAgIArrDgp7dht5YvqKRotmmoIvKp6oRECRS3g+K7NrPgxk4T+A+jXIoyivPP8vHYJe/Kb8eDDPYjxKD9jpAgFq9XKF2u/YP78+XTq3IlR40ZRv179WmH63TTV3LclEsU3iq5D+uF1NBWrAkgzjbt2psOdbQnSX19x+hpFSqTQEdV5ABMDw/ly11HyCq3EtO1P+64daR7pc01T21B3lyBcK6pU0Wg09OzTk8zsTJYsXoKn0ZOJkyaWqfMtUISNjGM7WLH0G05eKkajAFo9Ue0eYFjvtgR7a6pUkKvBohEIWcT5g/v4csUJNE1a061FKIW5h/h6zbccttjoOvoeYsruWkBBfgGbN27m4/kf0/Wurkx+erIjDsKF/DEVEYhSs1VRSv6vYMYKhCO+psR0dcba3FAGfM8Q2vQcSJueFd+QJa6QWn4TaoyENrmbcU3uLveyRP6pRVjajoq4/PtV2tF5LZztUZeqDTjxNHgyePBgiouKWbN6DQLBxEkTMZlMqFIiUMk6c4y9/82iwchuNDIZsOSfYc/Xm9gRHkm/DpF4iKq7+6rPGSwCiPA4gb3oHEn5bfDNSqPYNxKfSx4oZUYTEsjNzmXVilV88MEHdOnahWHDh6HRacjMygQum7plg9zKIpGOQLiSHB7O352BftWOcxcV9i2EIC8/D5vNRnZ2NiaTCZvtcrJpKSWK4ogMLioqQqfVkZWZhdVqvTwEkGUa6mo3W7n3yo+zyz2VZEndozLHV5arteHlj8vSxEtltyv7ful3UP56VXYdnI7yiuHzpd8pcFg7Vz3XMp8RAqvVSkF+gaO9s7Ixehqxq/bLx4xjhiY3NxebzUZeXh55+XkUFxeXuyblvr9Moqkr3qsuKuyzsvareH0q206raOndpzfp6eksX7YcvV7P6LGjMfmZHTuRBvzDmtNryGBaGxTIP0zBz69zIiWLQnsUxiqMu6o+H41UiIwygU5w5mQmEUcvEFQ/iKwjOkrvTCEoKizki7Vf8Pe//x2rxcr5lPP8e86/QTrMQGenK42mVR03Z+kNJC5/Xdm/nTexKtUrL4aU5SJ0y77n7MjObUp/L3mv9DMVtys5RueMmbNDHjt6jFOnTvHGa2/g5+eHalfLRQYrikJRYRG//PILGo2GS3mX0Ol0lzu05KrfXfY95zEIRaBRNNjsNgSiXBuCo00tNgt6rd7xZC/p1KXtVOZGlqpEKKLStijXXpQRnyv6QZnrJcq8JhQsVgt2acegM1zxnc7zdV5DVVXL7aOyCGtVVTl08BCnT53mtVdfw8fH57JYl6BoFFKSUzhx4gQLFyzk510/Y7Vay51LxfMse36VHWdl7XFFW1XSlyrtZ87zKvOaIq6hH5c4dstdR0Cj1ZCTnUNGRgYz/zUTnU7H+IkTMOgFQrGSc+EI365bS7KvB5bUg+wvjKBthD8eStU+oqvPopEq2oBw9BaF/OSDHEs1EOLtwVnd5eG2wBEynpef57jJii+Rn5+Pf4B/yXeAFJdP19lZyzm1JOWfcmVaR5VqaWco/b6Sjud8rbL3yv1d8XfncZTdTlzeTnW6XEteql+/PjGxMeh0Oux2e/nvAFRVRafX0alTJxCg1WivuDmc5+c8n3KvlzSk8zPnzpzj0KFDJLRNIDg4uFR0EY4hQ0ZaBr/+91eaNG1CTExMaUeteL4Vj7PsMZW+Jitpk4pP/LLXq0ybocD58+fZv38/rVq1IiIiotw1EIogKSmJAwcO0LJVS8LDwst9T7nr5/xbQHx8POHh4XgYPRxDBFH+mFS7naDgIPr27YuiUUqXfJQ7fll+H1ecc4W+ckX7UeE7rtaXKu6nzHmU/f6r9mPK/1/22IRwLNZNSkri9z2/k5ycjI+PT4nFbMOg14Cwk5d5il+3Q5KnFkWjpcF9Q+jWMgxPzbU536+V6o2j8YqknqGYwnM/cMongTuKi9GV6ZyqlHh7ezNk6BD0ej2rPl9FaGgoo8eMpk3bNmg0VeuQuhWUDj0qdsTyW6GUePql+ucRsFfbj6qqrFuzjrn/nsv056bTrm27co50jdCwc9dO/vLCX5gwYQL3P3j/LWtjjdDwxYYvmPXmLJ6a/BTde3YvdxwaoWHDhg28NfMtJj8zmXvuvueaJgWsFitFBUV4+XihaASOe/SyIlec8XT1/lUR55C4IL+A3bt3s3jRYrRaLXfddRcDBw2kT78+eHp5AMVIuweh8d154P8m0M5sRJGg6LRoxGVjoKqoNqFRVRVV1RMWaOHLjQcp6nYnBh8DdlvxFTdSUHAQYx4eQ1xcHAs+XcBbM99ixMgR9LmvD95Gb1ypnvKNYrdakShodbob+rxzmKTValEUBa1W6/i9TKiUgoJWp0XRKGi0GnQ6HRpFc0vaVkEpd6w6ra7ccSgo6HS6q57L1dDr9Hh5eSNsWez7djNrv/ydfL0WRdox+IVy54CJ3NPYdE1LGlyJkqQY2FU7J0+eZMXSFWzauIn8gnwGDx7M4CGDadO2TcnwSpYOy6RU0On16HV6FOedVg0NU01Co+Dp44t/gBeBsUEE+rXEL9yMv2rCP6AIQ4V5euf8f/ee3YmKjmLx4sW8//77HDlyhGHDh1Evvp5LButdGwoaLvCfdRs5Ym1E70GdCPWQ12+2lnQcZ2RsZcObcn6Akm1KTe6apuKxVDwOceUQ7VqO0zH00KCx5XD8l/2cvOBJ9xEdCLQXkX1+P9vffxf1safp2dTrmlNP1Hacy1jSL6SzecNm1q5Zy5kzZ2jXvh0jRo2gY6eOmHxNpX3DMT4U6D298A+S6JTLQ6/qapGqFxqpoireNO1zP1HFWszBBoZPqY/G7INBjeaReBV/jytXXTsdXA0aNeCZKc/QuFFjVq5YyZnTZ5gwcQJt2rbBYDDUqdBxKJktSTlB0un/sr3QlxYZRYRFesANXnJFKH86jX25w916/vRYbnSWR4IifIlr3oa+ffs41ksVtOSL+cvZ/c1vJDTsQqBWlAtWczWcteVzcnPYtXMXixYuYs9vewgPD2f6c9Pp268vISEhpQ71y0hUqSW0TXfGxtkxGfWIahQZqCaLRqLBJygUExIViVe0T8lv3viYBKqsPC+Ks8MFBQYxYvQIGjVqxNy5c/mfl/+HcePG0X9Af8z+5lpzk9w8AoV8Dv12nFSiaGzMJOnUORqHN8ZT3FjuGGfbVIwVubzHy/E6tYE/OpZyTvcbRFXt2AApVRRjOPH1g9i7+XeSc+8kyL+WxxX9Ac5iiUePHmXZZ8tYt24der2eUaNHMWzYMGLrx6LT6FBRK304SwQG30CifK9+P1Yl1Ti9bcfpurv8m+RaYnydU3QJ7RN45W+vsGLpCpYvW86RI0cYMWoELVq2uHUmf1UiFOSlJI6fT0WN6U1fr2/47MgxmraIp4FZwX4D5ydwOIUzL2ZyMfMiNqut9D2dzhGnY7fZa03blQojSrkZRqDUh1R1KGh1Bjz0Bdhd0DAuu0br6NGjfLnlS5YtW0bmxUz63dePgYMG0rZdWzyNnsCVmQIqIqV6TfdjVVArV2/D5aFUbFwsk5+dTNPmTVn62VL++eo/GTNuDF26dMHH18elncQClZyU0+z7YQt7PS6SqjnLd8m59OzWmVhzADfipi0sLOTixYvMe3ceoaGh5dJPKIrC+fPnKSgoQKvV1tj6q6shhCA7O5stm7eQlJRUfkmKorD7191kZGTcZESz49YUQoA1i5Skc6R4NMTP6HrWjKqqZKRnsGPHDpYuWcrevXtp17YdU6ZMoUevHgQEBgC1cyat1goNXG4wb29vBgwYQFxcHJ/M/4RX/ucVhg4byoRJEwgMCHTNBZdCQVEvce5cGhmiHd07N8HTWp++xV9xLCmN9nGB+GuvLzLT6VRVFAU/Pz9HRr8Kj26z2UzPnj1p3rz55QDAW0RQUBCREZHs2rmL33b/Vu49IQRpaWlcyrt0w0IjVTtWWzHFdisWtYiMgz+x/ZsTRD08gQhjRb9F7cTphym2FPOfX/7D/I/m89327wgODmbatGkMeHAAkZGRpTOztfU+qNVC48TZIVq0bMHLf32ZNZ+vYfXq1SQlJzF+4niat2iOVqN1iY7jRCCwZKeTlppOo/HP80S3IDTYOBubxuu/HeVCszj8g6/PKSyEwMPTA7O/mfETx9OhQwestitzEGs0GgwGwy21BlVUmjVvxszZMykoKLjifY2i4ccffmT5suU3dl2FBk9TIYfXf8r/nN2Mh90CWi2N+zzBiE4R6Knd09vOYZIzn/SSRUvY9s02ci/lMnLkSAYPGUyLVi3Q6/QusejYJYTGiSpVggKDGD9xPNGx0SxasIiXX3qZCY9MoEfPHmVWp9Z+BCqFBVZQI+nYzuSwRoSKufldNP3xEGmZBdQLdqS0vL7vdSwk9DR6YjAY0Bkqj8u51U8+WRKs2bxZ86tuk5qWioeHx/U7hKUduz6IjiMeJfKuDIrsjhBcrYcv4fUbEex5A+EDNYhzyUFycjJbN29l+fLlJCcm07FjR0aNHUX7Du0d09WoLtPfXUpowOHg0uq19OrdiwYNGrDgkwXMmzuPo4ePMnLUSOLi4lxiKKVKiTE0js4PRaP10iBQUaUGY2hHHp52B4rRC3ETFtr1xJ7cKqSUZSYKyqMRGse6sBs9fqHDFByLOTi2/D754wTntxQBGjRk52Sz44cdLPlsCbt37yY6JpoXXnqB+/rfR2BQoCPNrYsIjBOXExqgdKFefHw8r/ztFRYsWMDypY5ZqcmTJ9OmbRu02to/lFK0ejy9BcjLZrwQerzNBkc4wA3eELVZXK6Hmz2PsjOftRmnH8Zqs7Ln9z18vvJzli1dhp+fH+MnjGfkyJHExMYAXHW6urbjkkIDl5+GGp2G0WNH06RpExZ8vIBX//4qgwYPov/9/R3OUNSbjsWoNpypIMq/eNNBZLU+78w1UlfO449wJuE/deYUm77YxOrVq8nJzmHQQ4N4aPBDJLRNwMPTw+UsmIq4rNA4kVLiYfCg852diYqMYtmyZSz9bKmjkuWTTxJXL6401cHtwu10rq6KM6VD1sUsvtr6FStWrODA/gO0adOGqdOmctc9dxHgH+ASboBrweWFBi7PSsXExPDMlGdo1qwZ7819jynPTGHq9Kl0uasLBp3B5Z8Ktxt14QarSNnp6t2/7ua9d99jx487CA4O5vkXnqfvfX2JiIxAEUqd6q91Qmic2KUdTw9P+vTrQ/369Zn7zlxe/+fr9NnTh5FjRhIaElqrYw2qApcuYF+BiucihKbM+u2SBaS34sBuEOeygSNHjvD5is/ZumUrNpuNkaNHMmLkCBo2bIhBb3BZP8wfUaeEBi4nZ27StAkv//Vl1q1ex6aNm0hKTGLMuDE0a9EMvU5f5y6kk9q0YLIqcCTtEoCdzHMH+e2341xCS0TzDrSIC8VTcw2F5W4xTivm9JnTfP3l16xevZrkpGTatWvH8BHDadehHSY/k0vOJl0rdU5o4HKEbHhYOI88+giNGzfmg3kf8L//878MHzGcQYMG4eXlVScvqnPRZF1CKHbyz+9j6wfL+DnLhl6mkffdGYZMHM3dzf3ROLMaCgVNuXUVKpLKS/s4qc7pbqfAZOVk8f2337PksyXs2rmLhHYJvPiXF+l7X1/8zY5sknXtAVGROik0TlTpSJN5T497CI8I55OPP2HhpwtJSUph1OhRhEeFA3XTF1AXcFgzChpLNicOnOBX2YIpr40gRp5kyT9eZ8+hdrRu1JkAvWM1sq3oHN+v2MhPR9LwqZfAvQ/ejdfp3zmTfJbfzqaSY/Gi/T3d8E3dxTd7kgm4ox9De7Uh2EiVio1TYCxWCwf2H2DxosVs2bwFLy8vnnjqCYYOG1qaY6muWtYVqdNCA5dFpEmTJjz3wnN8tfUrVq5YybHjxxg2Yhhd7+rqCMd3i02tw2GZSVTVQHjTuxka50+cSYMl24rAiJdOjyPDhEDastm3eQU/HrMSHBZC1rk9fPlLME1Pb2LZf7Np3LktPhm/8d5r+2nTrS0xZhvbF2wgJjaC3q3C0FXRkgRFOBy9SeeSWPX5Kr788ksy0jPo378/Dzz4AAltE/AyetWZ2aRrpc4LjRO7tBMUFMTgYYOJiYth0YJFzJ45m/PJ57n/wfvx9/O/7S6+KyCkRNV5ERTRmCAkRbln2LFmFUc8W/JAywb4ah2RSGpOIrt/yiHwrsGMG3AHxedPk2oTpJ71Irppc4aMG4nP4WAuntxCi15DGRh9kqxt8zh3+iJFLcPR32SeXEU4EmFmZGTw5ZYvWbF8BSdOnKB58+ZMnjyZrnd3JSgoCImsk0P2P+O2ERq4nDK0S5cu1Iurx5LPljD/w/kcOXyEMQ+PoXHjxqXrTFyZuiKWl1NLOiyb/Mz9bPr0M35Oj2bApCG0j/dxLNMQAmxFFOhDiPDzQYvAGFYPM/lkCk/CAvzwMOhA70t0aCAhZk9sGgW9RkVaSiKwb9Ct5Vz8mJeXx+7du/l4/sfs3LGTiIgIps2YRr/7+hEaFlon+tXNcFsJDVwuPRIeEc5jTzxG/fr1WbZ0Ga/+7VXGPDyGu+66C6PR6NKdoq44g4UQIAQCK/mpe1i7YDF7Lc0Z8tgwOtTzRsGRuEkAQu+JtzWF1MxsipAUnDtBYk4Rl6SjtrSUgJSodhVVdWTuU6XkRstMOwXGarVy8MBBNm7YyPp165FSMmToEIYOHUrjpo3x8PQAcOn+VBXcdkIDl2elfH19GTBwANGx0Xy26DPmvTOPk8dP8sCDDxAVFXXznaNicbsaoq5YNABCKFCczYGtG5m37CdiuoXw8xefsNtgoFGX++jcJAJPrUSYYujYI5y129cz78h2rDkWAlp1IEIo5eedysXl3HilbrvdztnTZ9n2zTZWr1pNYmIiXe/qykODH6JT5054+3gDdeta3Ay3pdA4UaWKolFIaJtAZEQka9esZc3qNRw4cIDHHn+MVne0uqEIzVInpl1FClGSjrL8IklH1U21dF1TXQq0qyqclRpU9IS06MnoR+tRbBclqTNEaTVHpATFm0bdH6JX0XfsOXURY0ICXXu2xZBoIkr44StUlPAGdB7kgb9JQaMLo+uEYYiGoRjEtZUYUYSjnnd+QT7ffP0Nixcu5tf//kqLVi148eUX6d27N0HBQXW4YseNc1sLDVx+4oSGhTJm3BhiYmL4fOXnvPp/rzJsxDB69uqJn9mv3LZ/hpqfwq4N61m3bR8WTw8a93yY4b3vwN/gqP6nCEHyzkXMW/MfMvJBUf1J6DeQgQNaYy6TjV6UeRrLkhqYovQfJQnfxeVtRMkWdUSwHOehIgy+xCZ044mE8u/Lkgha6fgDjSGMjgNH0an0XQnmtkQ4F6oGRNHq7mikVJEE0br/vVD2O/7gOASCS3mXOLjvICuWr+DHH3/EoDfwzJRn6HtfX+IbxJcmX3OLzJXc9kLjRJUq3t7e9OnXh5i4GJZ+tpQFnyzg+PHjjBg5gpjYmGt4Uiko5HLw52/Z/ksuLfs/hF/2PnZsWcX26CgeaBWAVkiktHFu306swXfQu1VT/LRaAmLC8CwnMpKinDRSUzIoUrwIigjFV6dSlJNDnrWI7NxivANCCTBYSE2/iF3vS1BQMKIOzZxVrIJQWm647PvlX0DFXuE6lVkfL2WZSWyJeg2WqrNm0rlz5/h8+eds2rSJnJwc7rr7LoYOG0qbhDZ4e3nXyWUDVYlbaMqgShWhCJo2a8q056axecNmVq1axbGjxxg7diyd7uyE0dN49aGUEIjCQrKsGgK792PM/a1Qc+O4dOhVTqdfwkogWlQQGSSftqMza9EqEq/gQCKjw/EUJVGqQmDJP8WOVcvZuO00BToDcb2H80Bzwe7lK9mvGMlOPIsISSAhVs/Jw7+TWhTE3YMn4a3V1B2LpoJ1dq0CWhVC67RiUs6nsO3rbSxftpxzZ8/RsmVLXvzLi7Tr0I7AwEDgz6sNuHELzRU4O6m/vz9Dhg8hLi6OhQsWMvut2SQlJdH//v4EBFxl+b60Y9f707bbg7RWDChYOXPkF05eiqFNqC86ZzmRomSOH0lkV85FEo/54e0XwT0PjKdPl3p4awWKLOTkzzvYeUSl10v/oFnBr2w9WUB2dh4n03II6D+WaWNymP/P+eww3MeLU6dycs0X/Pf73fi1Mtzq4gZVh6h5Z6ozqje/IJ///PIfli1ZxrZt24iNjeWJp57ggQcfIDw8/Lafrr5e3EJzFaSUGAwG7ux6J9Ex0SxcsJCVK1Zy+tRphg4bSnyjeLTaKytuomgwGHQIcjjy45ds2LKfgF4P0bWRGR0luWqtvrS8fzQJLe+kQ4swUn9Ywje7N3Cs2bMkBAmw53EhtRCbVwtaNg8lRvTj0bZ20g58R1RoQ+LbNCMs6hJtGzYgqlUzYurVozDME+2ZbPLzQ255GZWqpKasM+d+iouKOXzoMBvWb2Djxo0ADBs+jCFDhtC0eVN0ekcOZrfIXB9uofkDnLWlomOieeqZp2jUuBGrP1/N66+9zshRI+lydxe8jd4VTGcBxRfYs30VqzefIqb7GB7q2xI/g0RFoAhQjbF0HxuHQa9HAxSb9dhEJnlFTo0QpV/lmI5VULAhAUVo0CigqhJF0aLTCsp5Hhx5uOsGNXEeoqR4nZQkJiWybs06Nn6xkePHj9OjVw8eGvyQo4aYj0+dTzFSnbiF5k9wxtyYzWYGDhpIfP14lny2hDlz5nD06FFGjxmNOcDs2BaBYs1m39YFvPvZPqL7P8HdbUOxX7pArjShtVuxSQWPrN9YuDWJ+u0SaBnuQ3KKFj/fRoQGOlyXQutFUKgnut/3sW9/R6R6jB0/XcAc75AbZ19XVbsj+AxH1UFVVeuSMQNU79DJacVkZmbyw3c/sHTpUvbs2UPLFi15c+abdO7SmdCw0Ntq8WN14Raaa0RKiVanpU3bNoSEhbBq5Sq2btnK2bNnGTVmFC1atkCv1WMvyuXM8cMcSUokY+snnN5mQesbzL3jn6bBhQMcyw2gR/94mhp/YuncjSwo1BMe14mBYx8k1rPEJBcexHS8m05nlrDub8+zytOPlr0G0SJIS35gOp5aAWjwCgjE4uWBgoKHjz+BIZ7ka6g7Q6dqOg+nH+ZS/iX2793PsiXL+P677zF4GHj88ccZMHAAcfXi0CgatxVTRbiF5jpw1F6SREREMOGRCTRs2JBFCxfx2j9eY/iI4fTs2RNfnxC6jvkrDfsXYLc5ZpEUnZ6A8CCMMe0IsenwNvrTecA4ItpeIL9YYPQLIjwyAL1zeltKdF7R3PnQI8R1uECxxkhwVAR+OjvRkU3Q+ekRGj/aDBmB3eCNBzoadhtIeAf46vtv686NUQ2nIYTAZrVx6uQp1q9bz9o1a7FYLHTv0Z2Ro0fSpFkTfLx83NPVVYxbaK4X6Yjn8PHxoXe/3sTExbDss2V8+P6H7Nu7jwmPTCQ2Jg7/kIofU5EY8S2J3xDeIcQ3Cr38boWgMSkFnn6hNPALK/N58AvyKinFosE7IAhREozm6RuAh6+Kh3Jzq5BrG1XlDHZG9aanp7Nl8xaWLlnKqVOn6Ny5Mw8NeYiud3fFZDIhqLtZ7m4lbqG5QVSpIoSgcZPGTJ0xlS/WfcHnKz8n40IGQ4YPoXOnzugNFVOGyjJOW/VPaw5Vtk3Z8ixSlgs/Q1Udf9eVOJqqmN52xsPk5uby866fWbNqDTt+3EF0TDTPTn2WgYMGEhISgqJRSv1xbqoet9DcBM6bIMA/gFFjRhETF8OCTxY48twMP0/f+/tiMpnKbevmOpA3LprOz1mtVg4dOOTwqW3dSlFREYMGD2Lo8KE0a9bMEQ9Th6KpaytuoakC7NKORqvhnm6OlKFrVq5h8eLFHDhwgDHjxtCoSSN3gFcN4lw2kJSUxKaNm1i/dj1paWl06NCB4SOG0zqhNWazGVW6Tu1qV8ctNFWIlJKGDRvy1DNPUb9BfRYvXMxr/3iNhx9+mM5dOmPwMFS/2Mi6Yz1d74yPU8wvZFxg5w87WbJkCfv376d+/fr871//lzu73klYmMPn5Rb9msUtNFWMlI48Nw8OepB69evx6fxPee2frzF0xFD639+f0NDQ6i3Tq9QdH821nkfZ1dUH9h3g8xWf8/XXX2MymXhk0iMMGDiAmJgYdDqdW2BuEW6hqQZUqaLT6Wjbti3RUdEsXbKU5UuX8/tvvzPx0Ym0vKOlI8dsdVgedcmiuYbzcA6TThw/wdp1a1nz+RosFgs9e/Vk6LChJLRLQK/TI0tm9tzcGtxCU004U4YGhQTxyGOO2lKLFy3mjX++wfCRw+neszsmH5PbR/AH/FH+O6cVk3o+lS2bt7B27VpOnTxF+/btuX/A/XTr1g0fXx8Ujds3VhtwC0014nwie3t507tfb+LqxbF4wWL+Peff7N+/n3EPjyMyKrLKM7LVlaFTZTrjPLf8vHy+/fZb1qxaw65du4iM4dfzDAAACdNJREFUiGTK1Cn069+P8PCSel3uqN5ag1toagDnE7Vx48Y8O/1Zwj8PZ+3qtaQkpjDx0Ym0btMajUZTZU/euhILUlEkFKFgsVg4fvw4Sz9byuZN/7+9e41t8rrjOP59HvuxHefiUBI7CbnYiR0XUkgglDQwQVlQYaCqlBaIaMetUDFVU7UXvWitehEvNvXFVNH7BmlLaSd1haZlgLaqop1WjY6tZIE4JAHikAQScnEuxAnx5exFcEppO1pusb3zeRklVhT7+eV/zvmfc/YjhGD16tWsrlyNy+3CqBlllRiFZNDcRJG7pTY+tJGS4hK2/347W5/fysrVK1mydAnpk9Ovy0OiiPioaCIHX6nq2HzWqVOn2PfnfVR/WE3XuS7K55Wzbv06iqYXkZqSShi5XB2tZNDcZGERxmg0Uj63HKvVys63d1K1vYqmxibWrl2LvcCOTr3G6iY+cmZ813TH2Q4O7DvAW2+/Rc2RGoqKiti0eRMLFi4gM2tsuVoGTHSTQTMBIufcuFwunnzqSQ7sPcCOqh2cPHGStRvWcufCOzFol29fiG+XziupqACEwiGGBod49ZVXaW9rx5puZf3G9VSuqcRhd6CgyK7eGCGDZoIIIQgRIiEhgRUrV+BwOtjxhx288JsXaD7VzD333ENGZsbVTWhG+XMXWTGKBAWM/T2Gh4c53XKakydO0n6mnYOfHuT06dOkW9NZvnw5qypXUVxSjGbQbmwvknTdyaCZYJHqZuasmTzx6yeo3l3N3uq9NDU28cDaBygqKkKv/3FvUzROBkcqFiEEgUCAYDDIhZELtLe3U19fj/eUF2+zl/b2dnp7e9E0DZvNxqO/epTb59zOnLI5WFLlvrFYJYMmCkQenNycXLZs2UKhq5CqqiqeefoZ1q9bz5KlS0hMTPxBQylFUVCu9p7X6+TSigXG5k9GR0cZGRmhq7OLmiM11NbW0tjYSMfZDvoG+jBoBhwOB2V3lFFcUowtw0Z6ejrp6emYE8yy4S7GyaCJImERxmAysHjpYuz5dt6sepNtL26jtbWV+1beR3ZONvC//6NHbne82SKn1sHYeT39/f0MDAzQ09tDg6cBj8dD3bE6znWdIxQMoaoqdoedZcuWMWv2LLJzsrGkWki1pJJgShh/XbmSFB9k0ESZyDk37qluHnv8Mfbs2UP1nmrq6+t5aPNDlJaWXrnn5kbnjDK29BwJFgBfn4+Ojg66u7tpa22jtqaW+uP1dHV1YdSMJCUnkZGZwbyfzKO4pJg8ex4plhTMZjMJCQnolIvHZiK+HSwXQ+zSOi1MKK4O+Ip3MmiiUKQiSUtPY+OmjTidTt7Z+Q7PPv0s6zesZ/HSxaRaUr83bG5UZ3DklDqAgcEBmpubaW9rp621jXpPPXV1dfT392M0GLFl2MjPz+euxXcxbdo07HY7adY0NE1D07TxkIoMib7/Uj4VNejndO1BPjncwnBAIWfmfObffhu3GEKEZNjEBBk0USwswuh1eioqKnA6nbz2ymu8tO0lPB4P6zasoyC/4DuXd4Vy9U/f5fMrEf5hP95mLw0NDXibvTQ1NnH06FF8Ph8Gg4EpU6ZQMrMEt9tNobuQgoICMrMyv/E6kYoFfmDfi6IggsMc+3QXf9z/b/o0C4lqH55jTfgGt3DvIjcW/cXbPaWoJoMmykWqlty8XJ565ik+/uhj9nywh63PbaVyTSVz580dv3Mo4sd0Bl++1BwMBgkGggyPDNPibaHuaB0tLS14vV7OnjmLz+dDM2jk5uTys6Vjl9tPyZ5CdnY2WVlZaHptPFCubfJ27Dcaav0P+z9uwLJwA4/fX04qg9R98Aov/uUTcgps/NSVglznjn4yaGJEWIRJTkpm5aqVOPIdvLvzXV7e9jLNJ5tZft9yMjLG7h+60jERl1csgWAA/7Af/3k/3V3d1B2ro/ZoLSdOnKC3t5ehwSGMJiN2h52KigrcU91jK0LWdGxWGyajCfi6WrluDXQKKOEgg52NeNOms6m8iFQEgiScC+bj/OuHeBva8Dtvw0xIRk2Uk0ETQ0IihF7TU3ZHGc58J++9+x7v/+l9jh8/zuaHN3PrtFvR6XWoqvqNn7t0biUswgycH6Cvv49+Xz/1dfUcOnQIj8eDr9eHEAKTyYTL5WL+/PmUzi7FlmkjJSWF5KRkjAbj+Ove2BUhBREOM9jfgz8pHbNeN/51JclGvgUGQhcICuJmy0U8k0ETYyLVQuScm0L3WM/N8889z4M/f5Ch80MoqjLe5Keg0NPTQ2dnJ50dnXibvRypOYKnzoN/yI9er8diseByuSgqKmLGjBnk5uWSkpqCyWjCYDB8HVI3dalZoKgqyZbJJA4G8AdDEBjm/EiAQGiAzvNGknQm9Cpy5BQDZNDEqLAIY040s+iuRWRNyWLXO7t44/U30Ol19PT0UHOkhrNnztLS0kJTYxNNjU34fD5MCSZsNhuls0spdBXidDpxOp1YJlnQNA29pkenjlUPE9okJ0CoeiyZUym6sJ+D/2zAvtDKyS8+5+9HPLRMnsoqdzYJhGXOxABFXKfuLtm5OTEijXLnus+x+/3d7Hx7J8eOHSMvLw+TyYTZbKagoIBCdyF2h528vDwcDgfWDOv4fE1EZEI5alr8FQVCo7Qe3s+u6s84MzrKua9OMjQyQGDqbJaseITNi90ka7KoudEuHX5fDRk0cUJVVPzDfr7611d8eehLNE0jNy+XrKwssnOysWXY0Kv68UnbqAmTK1FUlKCf9rov+LymjYCYTKF7MgOD3ShpxcybnkuiXgbNjSaDRhqnKGP9s4FQEL1O940PRkwfp/AdncFjBCH5mbsprjVo5BxN3FAQgUHOtLbS1tHH6MU9TwIzmfkO7FmT0EXlvu4fQAiufIGwFM1k0MQJRVEJ9TXy4e+2sbdhgEmZFgxCMNonSJtTwdpf3M+syWbkIEOaCDJo4ogIC0LBbJY8fDerl80gRcCFlr/x8uufcfCzJm69fyaJQja3STefDJo4oyg6dHodOr0eHaCZNDRFgZBcBpYmjgyaOKIogsBoE/tf/S2H901CHRlmMJSMs2wRaxa4MMueE2mCqFf+FilWCKGg01uZuXAZlZV3M8sa4oxPY/rcedyWkYISq6tOUsyTQRNnVHUSzpIyFi5azsZHfskK5yiHP/8Hp4aD6OSeIGmCyKCJJ0IQDgUJBgOMAkkFs7n33lmMHP2IXbu/pGdYyDdcmhByjiZOCASK2cqMinJ0jjQ0BGEM5JcvY02vytHREQZGBLckKHKFW7rpZGdw3FNQEIQvXusiSVfjWjuDZSUdb771WRAIRUGd4CtYpP9vcugUb76rPhUxuvVAihvXbegkSZL0ff4LERtJArXB6a0AAAAASUVORK5CYII=)
Find the area of the polygon in the given picture,
cm, ![MB equals 4 cm text and end text MA equals 2 cm](data:image/png;base64,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)
![](data:image/png;base64,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)
A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.
A man bought 3 paise and 5 paise denomination stamps for Rs 1.00. In total he bought 22 stamps. Find out total number of 3 paise stamps bought by him.
A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.
A ball pen costs Rs 3.50 more than pencil. Adding 3 ball pens and 2 pencils sum up to Rs 13. Taking y and z as costs of ball pen and pencil respectively. Write down 2 simultaneous equations in terms of y and z which satisfy the above statement. Find out the values of y and z.
In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.
In a town there are 2 brothers namely Anand and Suresh. Adding 1/3 rd anand’s age and suresh age would sum up to 10. Also adding Anand’s age together with 1⁄2 of suresh age would sum up to 10. Find Anand and Suresh ages.
From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?
From a cylindrical wooden log of length 30 cm and base radius 72 cm, biggest cuboid of square base is made. Find the volume of wood wasted?
Find the area of the figure.![GE equals 14 cm comma HF equals 10 cm comma AD equals 24 cm straight & BC equals 12](data:image/png;base64,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)
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Find the area of the figure.![GE equals 14 cm comma HF equals 10 cm comma AD equals 24 cm straight & BC equals 12](data:image/png;base64,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)
.
![y equals 2 x plus 4](data:image/png;base64,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)
![y equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis](data:image/png;base64,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)
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?
Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
by middle term factorisation, we could also use the quadratic formula, which is given by
Where the standard form of equation is
![y equals 2 x plus 4](data:image/png;base64,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)
![y equals left parenthesis x minus 3 right parenthesis left parenthesis x plus 2 right parenthesis](data:image/png;base64,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)
The system of equations above is graphed in the xy -plane. At which of the following points do the graphs of the equations intersect?
Note:
We can solve the equations by other methods too, but the method of substitution is most suitable here. Also, instead of solving
by middle term factorisation, we could also use the quadratic formula, which is given by
Where the standard form of equation is
Find the area of an isosceles trapezium ABCD, if the parallel sides are 6cm and 14 cm, its non parallel sides is 5cm each.
![](data:image/png;base64,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)
Find the area of an isosceles trapezium ABCD, if the parallel sides are 6cm and 14 cm, its non parallel sides is 5cm each.
![](data:image/png;base64,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)
and
Solve by using the elimination method.
and
Solve by using the elimination method.
The sides of a parallelogram are 12cm and 8cm. one of the diagonal is 10cm long. If d is the length of the other diagonal, then which of the following is correct?
The sides of a parallelogram are 12cm and 8cm. one of the diagonal is 10cm long. If d is the length of the other diagonal, then which of the following is correct?
Cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, find the rise in the level of water.
Cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, find the rise in the level of water.
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)
During mineral formation, the same chemical compound can be come different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is a portion of the phase diagram for aluminosilicates, with the temperature t , in degrees
Celsius
, on the horizontal axis, and the pressure p , in gigapascals (G Pa), on the
Which of the following systems of inequalities best describes the region where sillimanite can form?
Note:
We do not have the exact inequalities in the option, so we choose the one from the options which is the closest approximation of the inequalities that we have calculated. There are a couple of formulas and concepts used here, such as the equation of a line passing through two points and the concept that the region below a line is given by replacing the equality sign with less than or equal to in the standard form of the equation and vice versa.
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)
During mineral formation, the same chemical compound can be come different minerals depending on the temperature and pressure at the time of formation. A phase diagram is a graph that shows the conditions that are needed to form each mineral. The graph above is a portion of the phase diagram for aluminosilicates, with the temperature t , in degrees
Celsius
, on the horizontal axis, and the pressure p , in gigapascals (G Pa), on the
Which of the following systems of inequalities best describes the region where sillimanite can form?
Note:
We do not have the exact inequalities in the option, so we choose the one from the options which is the closest approximation of the inequalities that we have calculated. There are a couple of formulas and concepts used here, such as the equation of a line passing through two points and the concept that the region below a line is given by replacing the equality sign with less than or equal to in the standard form of the equation and vice versa.