Odpowiedzi

Najlepsza Odpowiedź!
2010-04-11T23:20:33+02:00
ZAD1.
a) S = (0,-1), r = √4 = 2
b) x²+y²-2x+2y+2=0
x²-2x+1+y²+2y+1 = 0
(x-1)²+(y+1)² = 0
S = (1,-1), r = √0 = 0
c) S = (2,-2), r = √9 = 3

ZAD2.
-1+a = -2 ---->a=-1
-2+b = 0 ----->b=2

-2+a=-2-1=-3
0+b=0+2=2

K=(-3,2)

ZAD3.
x²+y²-2x-3=0
x²-2x+1+y²=4
(x-1)²+y²=4

S=(1,0)

odległość:
d=√((1-0)²+(0-0)²) = √1 = 1

ZAD5.
a) = 1/3³=1/27
b) = (2^3+1/2^3)/(4^3+1)=(8+1/8)/65 = (65/8)/65 = 1/8
c) = 8 + 3 - 1/4 *4 +(4/(1/2))*8 = 8+3-1+64 = 74
d) = 5^5 * 2^2 * (5^2)^(-5) = 5^5 * 2^2 * (5^(-5))^2 = 2^2 * 5^(-5) = 4 * 1/3125 = 4/3125

ZAD6.
a) = 11^(1/2)
b) = 2^(-1/3)
c) = 4^(2/3) = 2^(4/3)

ZAD7.
a) dziedzina:
x∈R

b)dziedzina:
x∈R

ZAD8.
a)2^(x-1)=2^2
x-1 = 2
x=3

b)5^(x-2) = 5^2
x-2=2
x=4

c)2^(x-5) * 2^(2x+6) = 2^2
2^(3x+1) = 2^2
3x+1 = 2
3x=1
x=1/3

d) x^2+2 = 3x
x^2 - 3x +2 = 0
delta=9-8=1
pierwiastek(delta) = 1
x1=(3-1)/2 = 1
x2=(3+1)/2 = 2

e)x-1 = -1
x=0

ZAD9.
a) 3^x = 9
3^x = 3^2
x=2

b) (1/2)^x = (1/2)^(-3)
x=-3

ZAD10.
a) (1/3)^(-4) = x
x=3^4=81

b) (1/10)^(-2)=x
x=10^2=100

c) x^2 = 100 = 10^2
x=10

d) x^3=1/27 = (1/3)^3
x = 1/3