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Julie

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Submitted By juliemb
Words 337
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Mat 5
Opgave 4 ) løs andengradsligningen 3x2 -5x+2 = 0 d = b -4ac
2

d = (-5)2 -4*3*2 = 1 x= x= x= -b- + d 2*a -(-5)+ 1 =1 2*3 -(-5)- 1 2 = 2*3 3

opgave 6) Figuren viser graferne for tre funktioner af type y = b*ax F(o) = 8, det er funktion c Halveringskonstanten er funktion c fordi den er aftagende. og den skære i 8. Opgave 7) Udviklingen i størrelsen af den indfødte kystbefolkning i Aztekerriget. f(x) = 5,5*0,932x f(x) er kystbefokningenstørrlsen som er målt i mio x er antal år efter 1531 a) 1550-1531 b)

5,5*0,93219 = 1,443 mio 5,5 fortæller hvor mange mennesker der boede ved kysten, 1531 er begyndelsenværdien, 0,932 er aftagende, den aftager med 0,932-1 = -0,068 c)

solve(2,75 = 5,5*0,932x,x) = 9,8427

År efter 1531. Ca 10 år dvs i løbet f 1540 kommer befolkingen ned på 2,75 mio i følge modellen .

opgave 8) figuren viser en trekant ABC. a) vinkel a er

b2 +c2 - a2 cosA = 2bc cosA =

652 +442 -622 2*65*44

cos-1(0,40507) A = 66,11 Vinkel A er 66,11 grader b)

1 *bc*sinA 2 1 T= *65*44*sin(66) = 1307 2 T= c) sin(c) =

sin(66,11) *44 højden er 40 Dvs trekantens højde er 44 cm Opgave 9) pusle spil, a) a = 1,43 b) b = 1,56 man kan lægge 194 prikker på 3000 sek. c) Fxa = Fy Fy = 21,43 = 2,69

mod hyp

Hvis puslespillet er dobbelt så stort så tager det 2,70 gange s meget tid at lægge det. Opgave 10 )

f(x) = 2x-ex +3 a) f'(x) = 2-ex

funktionfrkskriften for f indtastes f' finder f' = f'(x) c) bestem monotoniforholden for f x x < 0.693 voksende x = 0.693 lok. maksimum

0.693 > x f aftagende

I]- ∞ ;0,693] vokser i]0,693; ∞ ] aftager maksimum 2,39

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