{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#4: Simplification"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.1, Page number 4.7"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=10+(1/2);\n",
"b=8+(1/2);\n",
"c=6;\n",
"d=7;\n",
"e=6;\n",
"f=4;\n",
"\n",
"#Calculation\n",
"result=a-(b+(c-(d-(e-f))));\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.2, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.75;\n",
"b=0.25;\n",
"\n",
"#Calculation\n",
"#given question is (a*a)+(b*b)+(2*a*b) which can be solved using (a+b)**2\n",
"result=(a+b)**2;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.3, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.87;\n",
"b=0.13;\n",
"\n",
"#Calculation\n",
"Nr=(a**3)+(b**3);\n",
"Dr=(a**2)+(b**2)-(a*b);\n",
"result=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.4, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 576.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=9840;\n",
"b=410;\n",
"\n",
"#Calculation\n",
"result=(a/b)**2;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.5, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"required number is 70.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=40;\n",
"b=30;\n",
"c=10;\n",
"\n",
"#Calculation\n",
"x=((a**2)-(b**2))/c; #required number\n",
"\n",
"#Result\n",
"print \"required number is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.6, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"required number is 3\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3;\n",
"b=4;\n",
"c=6;\n",
"d=9;\n",
"\n",
"#Calculation\n",
"p=b+c-d;\n",
"x=a**p; #required number\n",
"\n",
"#Result\n",
"print \"required number is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.7, Page number 4.8"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2;\n",
"b=math.sqrt(2);\n",
"\n",
"#Calculation\n",
"c=1/(a+b);\n",
"d=1/(b-a);\n",
"result=a+b+c+d;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.8, Page number 4.9"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 243\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"x=7;\n",
"y=5;\n",
"z=2;\n",
"\n",
"#Calculation\n",
"xstary=((x+z)**2)*(y-z);\n",
"\n",
"#Result\n",
"print \"result is\",xstary "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.9, Page number 4.9"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1000.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=121;\n",
"\n",
"#Calculation\n",
"m=math.sqrt(a);\n",
"#since we are considering square root, value of n will be 2\n",
"n=2;\n",
"result=(m-1)**(n+1); \n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.10, Page number 4.9"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"k=1;\n",
"x=3*k;\n",
"y=4*k;\n",
"\n",
"#Calculation\n",
"result=(6/7)+((y-x)/(y+x));\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.11, Page number 4.9"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 72.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"rootxminusrooty=1;\n",
"rootxplusrooty=17;\n",
"\n",
"#Calculation\n",
"#we get value of rootx and rooty by adding and subtracting the 2 equations\n",
"rootx=(rootxminusrooty+rootxplusrooty)/2;\n",
"rooty=(rootxplusrooty-rootxminusrooty)/2;\n",
"result=rootx*rooty;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.12, Page number 4.9"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 17.28\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=12;\n",
"b=0.2;\n",
"c=3.6;\n",
"d=2;\n",
"\n",
"#Calculation\n",
"x=a*b*c*d;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.13, Page number 4.9"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 3.11\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=7;\n",
"b=18;\n",
"c=84;\n",
"\n",
"#Calculation\n",
"x=((c/b)**2)/7; \n",
"\n",
"#Result\n",
"print \"result is\",round(x,2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.15, Page number 4.10"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 3.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=256;\n",
"b=2;\n",
"\n",
"#Calculation\n",
"c=math.log(a)/math.log(b);\n",
"x=math.log(c)/math.log(b);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.16, Page number 4.10"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 9.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=13;\n",
"b=2;\n",
"c=4;\n",
"\n",
"#Calculation\n",
"d=math.log(c)/math.log(b);\n",
"e=d*b;\n",
"x=(a-e); \n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.17, Page number 4.10"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 6.0 *math.sqrt(3)\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3*math.sqrt(27);\n",
"b=math.sqrt(75);\n",
"c=math.sqrt(12);\n",
"\n",
"#Calculation\n",
"x=a-b+c; \n",
"\n",
"#Result\n",
"print \"result is\",x/math.sqrt(3),\"*math.sqrt(3)\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.19, Page number 4.11"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 3 3/8\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from fractions import Fraction\n",
"\n",
"#Variable declaration\n",
"a=8+(1/4);\n",
"b=8+(1/2);\n",
"c=20+(1/8);\n",
"\n",
"#Calculation\n",
"x=c-(a+b);\n",
"y=x-int(x);\n",
"\n",
"#Result\n",
"print \"result is\",int(x),Fraction(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.20, Page number 4.11"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 9.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=math.sqrt(1296);\n",
"b=2.25;\n",
"\n",
"#Calculation\n",
"c=a*b;\n",
"x=math.sqrt(c);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.21, Page number 4.11"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 95.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=124.9;\n",
"b=63.15;\n",
"c=65/100;\n",
"\n",
"#Calculation\n",
"d=a-b;\n",
"x=d/c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.22, Page number 4.11"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.09090909091\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=17;\n",
"aplusb=23;\n",
"\n",
"#Calculation\n",
"b=aplusb-a;\n",
"result=aplusb/(a-b);\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.23, Page number 4.12"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=math.sqrt(24);\n",
"b=math.sqrt(216);\n",
"c=math.sqrt(96);\n",
"\n",
"#Calculation\n",
"x=(a+b)/c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.25, Page number 4.12"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.333333333333\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"x=5;\n",
"y=-2;\n",
"\n",
"#Calculation\n",
"result=(x-(2*y))**(1/y);\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.26, Page number 4.12"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 20.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2+(2/3);\n",
"b=4/5;\n",
"c=1/6;\n",
"\n",
"#Calculation\n",
"result=a/(b*c); \n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.27, Page number 4.12"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"value of 5/6 of 1/20 of 24 rupees is 1.0 rupee\n",
"value of 4/7 of 14 of 2 1/4 kg is 18.0 kg\n",
"answer given in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=5/6;\n",
"b=1/20;\n",
"c=24;\n",
"d=4/7;\n",
"e=14;\n",
"f=2+(1/4);\n",
"\n",
"#Calculation\n",
"r1=a*b*c; #value of 5/6 of 1/20 of 24 rupees(rupee)\n",
"r2=d*e*f; #value of 4/7 of 14 of 2 1/4 kg(kg)\n",
"\n",
"#Result\n",
"print \"value of 5/6 of 1/20 of 24 rupees is\",r1,\"rupee\"\n",
"print \"value of 4/7 of 14 of 2 1/4 kg is\",r2,\"kg\"\n",
"print \"answer given in the book is wrong\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.28, Page number 4.12"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 3.68181818182\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=11;\n",
"b=2+(1/5);\n",
"c=11/5;\n",
"d=2+(1/2);\n",
"e=2;\n",
"\n",
"#Calculation\n",
"r1=a/b;\n",
"r2=r1/c;\n",
"result=(r2*d)-e;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.29, Page number 4.13"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.27777777778\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2/3;\n",
"b=1/5;\n",
"c=1/10;\n",
"d=4/5;\n",
"e=1/8;\n",
"f=1/2;\n",
"\n",
"#Calculation\n",
"Nr=a+b-c;\n",
"Dr=(d*e)+f;\n",
"result=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.30, Page number 4.13"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 54.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=18;\n",
"b=162;\n",
"c=1;\n",
"\n",
"#Calculation\n",
"x2=a*b*c;\n",
"x=math.sqrt(x2);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.31, Page number 4.13"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 100.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.55;\n",
"b=0.07;\n",
"c=0.027;\n",
"d=0.01;\n",
"\n",
"#Calculation\n",
"Nr=(a**2)+(b**2)+(c**2);\n",
"Dr=d*Nr;\n",
"result=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.32, Page number 4.13"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 270.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=137;\n",
"b=133;\n",
"\n",
"#Calculation\n",
"Nr=(a**3)+(b**3);\n",
"Dr=(a**2)-(a*b)+(b**2);\n",
"result=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.33, Page number 4.14"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=20.25;\n",
"b=2.8;\n",
"c=28.35;\n",
"\n",
"#Calculation\n",
"result=a*b/c;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.34, Page number 4.14"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.0247933884298\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=54;\n",
"b=66;\n",
"c=33;\n",
"\n",
"#Calculation\n",
"r=a/b;\n",
"result=r/c;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.35, Page number 4.14"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 229.0\n",
"hence middle digit is 2\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=916;\n",
"b=16;\n",
"c=4;\n",
"\n",
"#Calculation\n",
"r=a*c/b;\n",
"\n",
"#Result\n",
"print \"result is\",r\n",
"print \"hence middle digit is 2\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.36, Page number 4.14"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.00121\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.011;\n",
"b=10;\n",
"\n",
"#Calculation\n",
"x=b*(a**2);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.37, Page number 4.14"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1000.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=67.6;\n",
"b=0.26;\n",
"\n",
"#Calculation\n",
"x=a/(b**2); \n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.38, Page number 4.15"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.18\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.324;\n",
"b=10;\n",
"\n",
"#Calculation\n",
"x=math.sqrt(a/b);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.39, Page number 4.15"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=63;\n",
"b=36;\n",
"\n",
"#Calculation\n",
"r1=(a+b)**2;\n",
"r2=(a-b)**2;\n",
"Nr=r1+r2;\n",
"Dr=(a**2)+(b**2)\n",
"x=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.40, Page number 4.15"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 111.5\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=44.6;\n",
"b=2.5;\n",
"\n",
"#Calculation\n",
"x=a*b;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.41, Page number 4.15"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 3.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=14;\n",
"b=46;\n",
"c=11;\n",
"d=6;\n",
"e=4;\n",
"\n",
"#Calculation\n",
"Nr=(a**2)-b;\n",
"Dr=(c*d)-(e**2);\n",
"x=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.42, Page number 4.15"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1803\n",
"answer given in the book varies due to rounding off errors\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2002;\n",
"b=10.10;\n",
"\n",
"#Calculation\n",
"x=a-(a/b);\n",
"\n",
"#Result\n",
"print \"result is\",int(x)\n",
"print \"answer given in the book varies due to rounding off errors\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.43, Page number 4.16"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.333333333333\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=8;\n",
"b=3;\n",
"c=4;\n",
"d=2;\n",
"e=6;\n",
"f=5;\n",
"g=8;\n",
"\n",
"#Calculation\n",
"Nr=a-(b*c)+d;\n",
"Dr=-(e*f)+(b*g);\n",
"x=Nr/Dr;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.45, Page number 4.16"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 4096 or 4 ** 6\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=4;\n",
"b=3;\n",
"c=2;\n",
"d=5;\n",
"e=0;\n",
"\n",
"#Calculation\n",
"p=(a*b)-(b*c)+(d*e); #power is calculated using indices\n",
"x=a**p;\n",
"y=math.log(x)/math.log(a);\n",
"\n",
"#Result\n",
"print \"result is\",x,\"or\",a,\"**\",int(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.46, Page number 4.16"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=1;\n",
"b=25/144;\n",
"c=12;\n",
"\n",
"#Calculation\n",
"r=math.sqrt(a+b);\n",
"x=(r-a)*c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.47, Page number 4.16"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"b=1;\n",
"a=2;\n",
"\n",
"#Calculation\n",
"x1=a-b;\n",
"x2=a+b;\n",
"result=(x1/x2)+(2/3);\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.48, Page number 4.17"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 28.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=18;\n",
"b=14;\n",
"c=84;\n",
"\n",
"#Calculation\n",
"x=(c**2)/(a*b);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.49, Page number 4.17"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 9.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=243;\n",
"b=0.8;\n",
"c=0.4;\n",
"\n",
"#Calculation\n",
"p=b-c;\n",
"x=a**p;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.50, Page number 4.17"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 4.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=1.2;\n",
"b=0.8;\n",
"\n",
"#Calculation\n",
"x=(a**2)+(b**2)+(2*a*b);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.51, Page number 4.17"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.352272727273\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=64/121;\n",
"b=9/64;\n",
"c=8/11;\n",
"d=3/8;\n",
"\n",
"#Calculation\n",
"x=(a-b)/(c+d);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.52, Page number 4.17"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=0.1;\n",
"b=0.75;\n",
"c=2.5;\n",
"d=0.05;\n",
"e=0.125;\n",
"f=1/4.8;\n",
"\n",
"#Calculation\n",
"r1=(a+b)/(c+d);\n",
"x=r1/(e+f);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.53, Page number 4.18"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 8731552810114645/18014398509481984\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=1/246;\n",
"b=2/3;\n",
"c=1/27;\n",
"d=4/3;\n",
"\n",
"#Calculation\n",
"r1=a**(-b);\n",
"r2=c**(-d);\n",
"x=r1/r2;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.54, Page number 4.18"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 800.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=8;\n",
"b=5/3;\n",
"c=125;\n",
"d=2/3;\n",
"\n",
"#Calculation\n",
"r1=a**b;\n",
"r2=c**(-d);\n",
"x=r1/r2;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.55, Page number 4.18"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.33333333333\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=6;\n",
"b=-2;\n",
"c=81;\n",
"d=-3/4;\n",
"\n",
"#Calculation\n",
"r1=1/(a**b);\n",
"r2=c**d;\n",
"x=r1*r2;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.56, Page number 4.18"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 10.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=math.sqrt(147);\n",
"b=math.sqrt(27);\n",
"c=math.sqrt(3);\n",
"\n",
"#Calculation\n",
"x=(a+b)/c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.57, Page number 4.19"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=math.sqrt(98);\n",
"b=math.sqrt(50);\n",
"c=math.sqrt(2);\n",
"\n",
"#Calculation\n",
"x=(a-b)/c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.58, Page number 4.19"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.35\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=math.sqrt(9/25);\n",
"b=3+(1/16);\n",
"c=math.sqrt(b);\n",
"\n",
"#Calculation\n",
"x=a+c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.59, Page number 4.19"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.18\n",
"answer given in the book is wrong\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=math.sqrt(0.01);\n",
"b=math.sqrt(0.0064);\n",
"\n",
"#Calculation\n",
"x=a+b;\n",
"\n",
"#Result\n",
"print \"result is\",x\n",
"print \"answer given in the book is wrong\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.60, Page number 4.19"
]
},
{
"cell_type": "code",
"execution_count": 81,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 0.688995215311\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=25.6;\n",
"b=36.1;\n",
"c=12.1;\n",
"d=81;\n",
"e=0.1;\n",
"\n",
"#Calculation\n",
"r1=math.sqrt(a/b);\n",
"r2=math.sqrt(c/(d*e));\n",
"x=r1/r2;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.61, Page number 4.19"
]
},
{
"cell_type": "code",
"execution_count": 83,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"51 can be expressed as 26 **2 - 25 **2\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"N=51;\n",
"\n",
"#Calculation\n",
"#to express a number as the difference of squares of 2 numbers, we use the formula N=((N+1)/2)**2-((N-1)/2)**2\n",
"a=(N+1)/2;\n",
"b=(N-1)/2;\n",
"#N can be expressed as (a**2)-(b**2)\n",
"\n",
"#Result\n",
"print \"51 can be expressed as\",int(a),\"**2 - \",int(b),\"**2\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.62, Page number 4.19"
]
},
{
"cell_type": "code",
"execution_count": 84,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 308.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=7;\n",
"b=11;\n",
"c=1232;\n",
"\n",
"#Calculation\n",
"x2=a*b*c;\n",
"x=math.sqrt(x2);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.63, Page number 4.20"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 5.41666666667\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=3+(1/4);\n",
"b=4+(1/3);\n",
"\n",
"#Calculation\n",
"Nr=(a**4)-(b**4);\n",
"Dr=(a**2)-(b**2);\n",
"result=math.sqrt(Nr/Dr);\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.64, Page number 4.20"
]
},
{
"cell_type": "code",
"execution_count": 86,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"total score in innings is 162.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2/9;\n",
"b=8;\n",
"\n",
"#Calculation\n",
"x=b/(a**2); #total score in innings\n",
"\n",
"#Result\n",
"print \"total score in innings is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.65, Page number 4.20"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 17.125\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=64;\n",
"b=32;\n",
"c=-1/2;\n",
"d=4/5;\n",
"\n",
"#Calculation\n",
"r1=(1/a)**0;\n",
"r2=a**c;\n",
"r3=b**d;\n",
"result=r1+r2+r3;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.66, Page number 4.21"
]
},
{
"cell_type": "code",
"execution_count": 91,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 3.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=243;\n",
"b=0.12;\n",
"c=0.08;\n",
"\n",
"#Calculation\n",
"p=b+c;\n",
"result=a**p;\n",
"\n",
"#Result\n",
"print \"result is\",result"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.67, Page number 4.21"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 12.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=2;\n",
"b=64;\n",
"\n",
"#Calculation\n",
"c=math.log(b)/math.log(a);\n",
"n=c*a;\n",
"\n",
"#Result\n",
"print \"result is\",n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.68, Page number 4.21"
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 36.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=1/216;\n",
"b=2/3;\n",
"\n",
"#Calculation\n",
"x=1/(a**b);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.69, Page number 4.21"
]
},
{
"cell_type": "code",
"execution_count": 97,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 16.0\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=-2;\n",
"\n",
"#Calculation\n",
"b=a**a;\n",
"x=b**a;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.70, Page number 4.21"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 2.4\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=11+(1/3);\n",
"b=4+(8/10);\n",
"c=22+(2/3);\n",
"\n",
"#Calculation\n",
"x=a*b/c;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.71, Page number 4.22"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 1.0404\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"a=1.06;\n",
"b=0.04;\n",
"c=4;\n",
"\n",
"#Calculation\n",
"r1=(a+b)**2;\n",
"x=r1-(4*a*b);\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.72, Page number 4.22"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is +/- 1/2\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"from fractions import Fraction\n",
"\n",
"#Variable declaration\n",
"a2plusb2=45;\n",
"ab=18;\n",
"\n",
"#Calculation\n",
"Nr=math.sqrt(a2plusb2+(2*ab));\n",
"result=Nr/ab;\n",
"\n",
"#Result\n",
"print \"result is +/-\",Fraction(result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Example number 4.75, Page number 4.23"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"result is 4\n"
]
}
],
"source": [
"#importing modules\n",
"import math\n",
"from __future__ import division\n",
"\n",
"#Variable declaration\n",
"#by comparing the equations we get\n",
"rootx=2;\n",
"\n",
"#Calculation\n",
"x=rootx**2;\n",
"\n",
"#Result\n",
"print \"result is\",x"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}