Matlab va Mathcadda elementar matematik masalalarni yechish - Алгебра - Рефераты

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Matlab va Mathcadda elementar matematik masalalarni yechish

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Matlab va Mathcadda elementar matematik masalalarni yechish
1-topshiriq. Quydagi ifodalarni Matlabda yozing va natija oling:
Ma’lum bir tenglik algebraik o’zgaruvchilarga bog’liq bo’la uning shu o’zgaruvchilaridagi qiymatini
topishning ikki usuli mayjud birinchi usul o’zgaruvchilarni elon qilib algebraik tenglamani avval kiritib
keyin o’zgaruvchilarni malum bir uzgarmaslarga tenglash orqali, ikki ucgun o’zgaruvchilar borligini elon
qilmiy usha algebraic tenglamani o’zgaruvchilarini malum bir uzgarmaslarga tenglab keyin tenglikni
kiritish mumkin.
a=3.56;
b=exp(0.314);
y=(log(b+1.4)/log(a))^(-3/4)
y =
1.1799
a=3*pi/7;b=83*pi/180;
abs(log(1+sin(a)+log(1-sin(b)/log(exp(1)))))
ans =
4.2185
a=5*pi/7;b=0.3*pi;
(sin(a+b)^2-sin(a-b)^2)^(1/3)
ans =
0.4876 + 0.8445i
p=log(3)/log(exp(1));q=log(3);
3*(p^(-2/3)+q^(-1/2))*(p*q)^(1/3)
ans =
6.0474
m=3.6485;
2/3*m*sqrt(m*(m*(m)^(1/4))^(1/3))
ans =
6.0840

Expand orqali algebraic ifodalardagi qavislarni ochish mumkin quyida ushbu
buyroq orqali qavslarni ochib chiqganmiz.
2-topshiriq. expand va simplify komandalaridan foydalanib, ifodani soddalashtiring
EXPAND()
syms x
Y=(x-4)*(x-15.4)*(x+10.3);
expand(Y)
ans =
x^3 - (91*x^2)/10 - (6911*x)/50 + 15862/25
expand((x-2)*(x-15)*(x+103))
ans =
x^3 + 86*x^2 - 1721*x + 3090

expand((x-2.4)*(x-1.5)*(x+1.03) )
ans =
x^3 - (287*x^2)/100 - (417*x)/1000 + 927/250

expand((x-4.8)*(x-1.75)*(x+13) )
ans =
x^3 + (129*x^2)/20 - (307*x)/4 + 546/5

expand((x-8.2)*(x-2.75)*(x+1.3))
ans =
x^3 - (193*x^2)/20 + (1663*x)/200 + 5863/200

Simplify buyrug’i orqali esa ifodani soddalashtirishimiz mumkin ushbu
buyruqdan foydalanishni quyida ko’rsatilgan.
simplify()
syms x
Y=(x-4)*(x-15.4)*(x+10.3);
simplify(Y)
ans =
(x - 4)*(x - 77/5)*(x + 103/10)
simplify( (x-2)*(x-15)*(x+103) )
ans =
(x - 2)*(x - 15)*(x + 103)

simplify((x-2.4)*(x-1.5)*(x+1.03))
ans =
(x - 3/2)*(x - 12/5)*(x + 103/100)

simplify( (x-4.8)*(x-1.75)*(x+13) )
ans =
(x - 7/4)*(x + 13)*(x - 24/5)
simplify((x-8.2)*(x-2.75)*(x+1.3) )
ans =
(x - 11/4)*(x + 13/10)*(x - 41/5)

Ifodalarni ko’paytiruvchilarga ajratish uchun factor buyrug’idan
foydalanishimiz mumkin bu bizga ko’plab qulayliklar tug’diradi ushbu
buyruqdan quyidagicha foydalanamiz.
3-topshiriq. Ifodani ko’paytuvchilarga ajrating
syms x
Y=x^3-32/5*x^2-23/5*x+12;
factor(Y)
ans =
[1/5, 5*x^3 - 32*x^2 - 23*x + 60]
factor(x^3+13/2*x^2-26*x-315/2)
ans =
[1/2, x + 7, x - 5, 2*x + 9]

factor(x^3-17/10*x^2-69/10*x+9)
ans =
[1/10, 2*x + 5, x - 3, 5*x - 6]
factor(x^3-16/5*x^2-92/5*x+208/5)
ans =
[1/5, 5*x - 26, x - 2, x + 4]

factor(x^3+27/10*x^2-26/5*x-42/5)
ans =
[1/10, 5*x + 6, 2*x + 7, x - 2]

Matlab va Mathcadda elementar matematik masalalarni yechish

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