Matematyka

Autorzy:Drążek Anna, Duvnjak Ewa, Kokiernak-Jurkiewicz Ewa

Wydawnictwo:WSiP

Rok wydania:2016

Oblicz wartości liczbowe wyrażeń. 4.5 gwiazdek na podstawie 8 opinii
  1. Gimnazjum
  2. 2 Klasa
  3. Matematyka

Oblicz wartości liczbowe wyrażeń.

5
 Zadanie
6
 Zadanie

7
 Zadanie

8
 Zadanie
9
 Zadanie

`a) \ \  5x^2y+1/(y^2)=5*(sqrt2)^2*(-0,5)+1/((-0,5)^2)=5*2*(-0,5)+1/(-5/10)^2=`

`=10*(-0,5)+1/(-1/2)^2=-5+1/(1/4)=-5+1*4/1=-5+4=-1`

`b) \ \  -2[x/3-y/4+z/5*(-x+y-z)]^2=-2[-6/3-8/4+10/5*(-(-6)+8-10)]^2=`

`=-2[-2-2+2*(6+8-10)]^2=-2[-4+2*4]^2=-2*(-4+8)^2=-2*4^2=-2*16=-32`

`c) \ \  y=-0,5=-5/10=-1/2`

`z=(|-sqrt5|)/5=sqrt5/5`

`sqrt(9x^4-2y^3+5z^2)=sqrt(9*(-1/3)^4-2*(-1/2)^3+5*(sqrt5/5)^2)=`

`=sqrt(strike9^1*1/strike9^1*1/9-2*1/4*(-1/2)+strike5^1*5/strike25 *5)=sqrt(1/9+1/4+5/5)=sqrt(1/9+1/4+1)=`

`=sqrt(4/36+9/36+36/36)=sqrt49/36=7/6=1 1/6`

`d) \ \ c=-|2/3|=-2/3`

`(-3ab^2c^3de^4)^3=(-3*(-sqrt2)*(3/4)^2*(-2/3)^3*sqrt8*(-1)^4)^3=`

`=(3*sqrt2*9/16*4/9*(-2/3)*sqrt8*1)^3=(3*strike9^1/strike16^4*strike4^1/strike9^1*(-2/3)*sqrt2*sqrt8)^3=`

`=(strike3^1*1/strike4^2*(-strike2^1/strike3^1)*sqrt16)^3=(-1/2*4)^3=(-2)^3=-8`

`e)  \ \ x=-1 1/3=-4/3`

`(-3(-6x^2+4))/(4(5-3x))-(6(2-3x^3))/(10-9x^2)=(-3*(-6*(-4/3)^2+4))/(4*(5-3*(-4/3)))-(6*(2-3*(-4/3)^3))/(10-9*(-4/3)^2)=`

`=(-3*(-strike6^2*16/strike9^3+4))/(4*(5+4))-(6*(2-strike3^1*16/strike9^3*(-4/3)))/(10-strike9^1*16/strike9^1)=`

`=(-strike3^1(-32/3+12/3))/(4*strike9)+(-6*(18/9+(16*4)/9))/-6=``(-(-20/3))/(4*3)+(-strike6*(18/9+64/9))/(-strike6)=`

`=(20/3)/12+18/9+64/9=20/3*1/12+82/9=5/3*1/3+82/9=5/9+82/9=87/9=29/3=9 2/3`

`f) \ \  sqrt2^2=sqrt2*sqrt2=sqrt(2*2)=2`

`6x^2-4x^4+2x^6-0,25x^8=6*(sqrt2)^2-4*(sqrt2)^4+2*(sqrt2)^6-0,25*(sqrt2)^8=`

`6*2-4*2^2+2*2^3-25/100*2^4=12-4*4+2*8-1/strike4^1*strike16^4=12-16+16-4=8`