How do you calculate that?
We had math homework today and yes folks, what can I say…
It wasn't good because there were a few calculations, but instead of working them out, they just raised question marks. The topic is the midnight formula, meaning there's always an A, B, and C point. If there's a zero at the end, that's clear to me anyway, but of course there are special cases, and those are exactly the ones she gave up.
For example, with the first one, I don't know what I should have done because there was a similar example.
For the second one I would only know one point, namely the whole thing times 8
At the bottom everything times 2, so that then it says 2k to the power of 2 – 3k = 0 and then it says k(2k-3k) =0
w1=0 and w2= 2k-3k=0
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For i), k(2k-3) would have been correct. But multiplying by 2 doesn't really do anything.
k(k – 3/2) immediately yields the two solutions 0 and 3/2.
For e) you can divide by 10 and finally have v(v – 15) = 0.
For f) we get x(x – 1/8) = 0.
v² = 150 v | : v (nur zulässig für v ungleich 0)
v = 150
oder v = 0, denn dann stimmt die Gleichung auch!
x² = x/8 (wie oben)
x = 1/8 oder x = 0
k² -3/2k = 0
k(k-3/2) = 0
Ein Produkt ist null, wenn einer der Faktoren 0 ist…
10v^2 = 150v ⎜-150v
10v^2 – 150v = 0 ⎜:10
v^2 – 15v = 0 ⎜ausklammern
v(v-15) = 0
Satz vom Nullprodukt:
v1 = 0
v2 = 15
Man könnte es aber auch über die Mitternachtsformel lösen:
f)
x^2 = X/8 ⎜ *8
8x^2 = x ⎜-x
8x^2 – x = 0 ⎜ausklammern
x(8x -1) = 0
Satz vom Nullprodukt:
x1 = 0
8×2 – 1 = 0
x2 = 1/8
Aber auch die Mitternachtsformel würde gehen.
i)
k^2 – 3/2k = 0 ⎜*2
2k^2 – 3k = 0 ⎜ausklammern:
k(2k – 3) = 0
k1 = 0
k2 = 1,5
The following must always be kept in mind as long as you are dealing with mathematics (if not, you will not be dealing with mathematics for long)
1) Equivalence transformations of equations
2) Exclude
3) Zero product theorem
Task e)

The other two marked tasks are also only possible if you consider 1) to 3) sufficiently.