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{
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 6 : FORMULAE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6_1 pgno:69"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expr=8*i-5\n",
"the number is 16\n"
]
}
],
"source": [
" #8 times a number is decreased by 5 the result is 123\n",
"#let x be the number\n",
"\n",
"print'expr=8*i-5'\n",
"x=0;\n",
"for x in range(0,100):\n",
" if((8*x-5)==123):\n",
" print\"the number is \",x\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6_2 pgno:71"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"expr=(2*n+1)+(2*n+3)+(2*n+5)\n",
"n=%i \n",
"12\n",
"\n",
" the numbers are 199 201 203\n"
]
}
],
"source": [
"#sum of 3 consecutive odd no.'s is 81\n",
"\n",
"#let the 3 consecutive odd numbers be 2n+1,2n+3,2n+5\n",
"\n",
"print\"expr=(2*n+1)+(2*n+3)+(2*n+5)\"\n",
"n=0;\n",
"for n in range(0,100):\n",
" if((2*n+1)+(2*n+3)+(2*n+5)==81):\n",
" print\"n=%i \\n\",n \n",
"\n",
"n1=2*n+1;\n",
"n2=2*n+3;\n",
"n3=2*n+5;\n",
"print\"\\n the numbers are \",n1,n2,n3\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6_3 pgno:72"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p1=(6*x-5)\n",
"p2=(2*x+9)\n",
"p3=p1-p2\n",
"satisfies the equation \n"
]
}
],
"source": [
"import numpy\n",
"print\"p1=(6*x-5)\"\n",
"p1=numpy.array([6, -5])\n",
"print\"p2=(2*x+9)\"\n",
"p2=numpy.array([2, 9])\n",
"print\"p3=p1-p2\"\n",
"p3=p1-p2\n",
"\n",
"x1=numpy.roots(p3)\n",
"left=6*x1-5; #check by substituion \n",
"right=2*x1+9;\n",
"if(left==right):\n",
"\tprint'satisfies the equation '\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6_4 pgno:73"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x is a polynomial function\n",
"by the law of sighs roots are [ 3.]\n"
]
}
],
"source": [
"print\"x is a polynomial function\"\n",
"import numpy\n",
"p1=numpy.array([3/5+1/2, 0])\n",
"p2=numpy.array([5/4, -3])\n",
"#p1=3*x/5+x/2;\n",
"#p2=5*x/4-3;\n",
"p3=p1-p2;\n",
"x=numpy.roots(p3) #by the law of signs\n",
"print\"by the law of sighs roots are\",x\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Example 6_5 pgno:75"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p1=4*x-(x-2)/3\n",
"p2=5+(2*x+1)/4\n",
"p3=p1-p2\n",
"satisfies the equation \n"
]
}
],
"source": [
"import numpy\n",
"print\"p1=4*x-(x-2)/3\"\n",
"p1=numpy.array([11/3, 2/3])\n",
"print\"p2=5+(2*x+1)/4\"\n",
"p2=numpy.array([1/2, 21/4])\n",
"print\"p3=p1-p2\"\n",
"p3=p1-p2\n",
"\n",
"x=numpy.roots(p3)\n",
"left=4*x-(x-2)/3; #check by substituion \n",
"right=5+(2*x+1)/4;\n",
"if(left != right):\n",
"\tprint'satisfies the equation '\n",
"\n",
"\n",
"\n",
"\n",
"\n"
]
},
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"execution_count": null,
"metadata": {
"collapsed": true
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