asinus

How many candies must Peter give to Xayden so that they will have the same number of candies?

Hello Guest!

\(x-\frac{2}{5}x+156=p\\ x-\frac{3}{4}x+240=p\\ x-\frac{2}{5}x+156=x-\frac{3}{4}x+240\\ \frac{3}{4}x-\frac{2}{5}x=240-156\\ \frac{7}{20}x=84\)

\(x=240\)

\(p=x-\frac{3}{4}x+240\\ p=240-\frac{3\cdot 240}{4}+240\)

\(p=300\)

\(\frac{300-240}{2}=\color{blue}30\)

30 candies must Peter give to Xayden so that they will have the same number of candies.

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x=x^2/(10x+1)(20x+1) name all possibilities for x.

Hello Guest!

\(x=\dfrac{x^2}{(10x+1)}\cdot(20x+1)\\ x=\dfrac{20x^3}{10x+1}+\dfrac{x^2}{10x+1}\\ \color{blue} x_1=0\\ \color{blue}x_{2,3}=\dfrac{9\pm \sqrt{161}}{40}\)

\(x\in \{0.544221,\ 0,\ -0.09221\}\)

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Also

"gegenteilige Rechnung" :

\((7+15)/11\times 100-107=\color{blue}93\)

oder den Vers als Gleichung rechnen:

\((x +107) /100 \cdot 11 -15 = 7\)

\(\dfrac{x+107}{100}\cdot11-15=7\\ \dfrac{11x+107\cdot 11-1500}{100}=7\\ 11x=700+1500-1177\\ 11x=1023\)

\(x=93\)

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How many values of satisfy both of the following conditions?
(a) x is a multiple of 7, not necessarily positive.
(b) x^2 is less than 5000.

Hello Guest!

If \(x\in \mathbb Z\ then\)

\(x^2<5000\\ x<\sqrt{5000}\\ x<70.71\)

\(x\in \{-70,-63,-56,\ …\ 0,\ ...\ 56,\ 63,70\}\)

\(21\ values\ meet\ the\ two\ given\ conditions.\)

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how much power does a water pump expend when it lifts 40.0 liters of water per minute to a height of 10.0 meters?

Hello Guest!

\(N=\dfrac{F\cdot s}{t}=\dfrac{40kg\cdot9.81\frac{m}{s^2}\cdot 10m}{60s}\cdot \dfrac{N\cdot s^2}{kg\cdot m}=65.4\cdot \dfrac{Nm}{s}=\color{blue}65.4\ W\)

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(a)   What was the capacity of the bucket?

(b)   How much water in the tank was filled up using the hose?

HelloRobtlukas!

\(2V_{bucket}=8dm\cdot3dm\cdot0.15dm\cdot\frac{l}{dm^3}=3.6l\)

\(V_{bucket}=1.8l\)

(a) the capacity of the bucket was 1.8l.

\(4\cdot1.8l+x=(8\cdot 3\cdot1.2)l\\ x=21.6l\)

(b) 21.6l water in the tank was filled up using the hose.

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Hello RunningMan!

(a)    Find the number of toy planes in Box A in the end.

(b)    In the end, how many more toy cars were there in Box B than Box A?

Hello RunningMan!

     A                                             B

12c+20p                                 28c+40p                     beginning

12c+20p+xc -yp                     28c+40p-xc+yp          

(12+x)c+(20-y)p                     (28-x)c+(40+y)p

(12+x):(20-y)=4:3                   (28-x):(40+y)=1:2        end

36+3x=80-4y                          56-2x=40+y               

\(y=-9-0.75x+20\\ y=16-2x\\ 16-2x=11-0.75x\\ -1.25x=-5\)

\(x=4\\ y=8\)                                         \(x=4\\ y=8\)

\((12+x)c+(20-y)p\\ (12+4)c+(20-8)p\\ \color{blue}16\ cars+12\ planes\)           \((28-x)c+(40+y)p\\ (28-4)c+(40+8)p\\ \color{blue}24\ cars+48\ planes\)

\(24\ cars-16\ cars=8\ cars\)

\((a)\ The\ number\ of\ {\color{blue}toy\ planes\ in\ Box\ A}\ in\ the\ end\ is\color{blue}\ 12. \)

\((b)\ {\color{blue}8\ cars\ more}\ toy\ cars\ were\ there\ \color{blue}in\ Box\ B\ than\ Box\ A.\)

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In how many seconds will the projectile first reach 120 feet in height?

Hello Guest!

\(f(t)=-6t^2+51t\\ \frac{df(t)}{dt}=-12t+51=0\\ t=4.25\)

\(h_{max}=-6\cdot 4.25^2+51\cdot 4.25\)

\(h_{max}=\color{blue}108.375\ feet\)

The projectile cannot reach a height of 120 feet.

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2. Bei vollständiger restloser Umsetzung von Eisen und Schwefel werden 5,385g Schwefel für 15g Eisensulfid benötigt

Zeige durch  den vollständigen Rechenweg mit Begründung für jeden Schritt wie die Massenantteile für Eisen und Schwefel sind.

Hallo Gast!

Wieviel Schwefel und wieviel Eisen gehört zur restlosen Synthese von 15g Eisensulfid?

\(Fe+S\ -->FeS\)

Ein Atom Eisen verbindet sich mit einem Atom Schwefel zu einem Molekül Eisenoxid.

Die relativen Atommassen sind:

Fe  55,85

S    32,06

Die relative Atommasse von Eisensulfid ist:

FeS 87,91

Wieviel Schwefel wird gebraucht?

Wir setzen die relativen Massen ins Verhältnis zu den realen Massen.

\(FeS_{rel}:S_{rel}=m_{FeS}:x\\ 87,91:32,06=15g:x\\ 87,91x=32,06\cdot 15g\\ x=\dfrac{32,06\cdot 15g}{87,91}\)

\(x=5,470g\)

Zur restlosen Synthese von 15g Eisensulfid gehören

5,470g Schwefel und 9,530g Eisen.

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