Recent content by earboth

Good afternoon, have a look here: https://en.wikipedia.org/wiki/Regular_icosahedron If I understand you correctly you are looking for the dihedral angle between two faces. You'll find the value of this angle in the table of properties of the icosahedron.

Good afternoon, I don't know if this could be a step into the right direction, but you can factor the denominator into a lot of factors: $$1-x^{512} = (x + 1)(1 - x)(x^2 + 1)(x^4 + 1)(x^8 + 1)(x^{16} + 1)(x^{32} + 1)(x^{64} + 1)(x^{128} + 1)(x^{256} + 1)$$ Now cancel as much factors as possible.

Good evening, with p = 75 cm (I assume that this is the distance of the object from the lens?) and i = 55,26 cm (I assume that this is the distance of the image from the lens?) and $$f = \tfrac{350}{11} \ cm$$ you should get a real image which is inverted (if you mean by inverted that the...

Hello again, I'll show you how I've learned to use a log table. (I visited school without calculators or computers. The most advanced piece of technology was a slide-ruler!) You want to calculate $$|x| = \frac{1.84194}{0.46}$$ with a log table. "op" means operation of the logarithms, N is...

Good morning, I've marked in red the calculations where you made a mistake: $$-2 + 0.15806 \approx -1.84194$$ and $$\log(1.84194) = 0.26528$$ This error occurs in your following calculations again. The best would be if you keep mantissae and prefixes separated.

Hello, I've marked the line where you made a tiny (but fatal) mistake. After facvtorization you should come out with $$x^2-5x-6 = (x+1)(x-6)=0$$

Good evening, use the unit circle:

Good morning, Google is your friend: https://www.google.de/search?q=geometrische+Figuren+in+der+Natur&biw=1126&bih=864&tbm=isch&tbo=u&source=univ&sa=X&ved=0CC0QsARqFQoTCK3P4JyGkcYCFYQ6FAodXdsAtw

Good evening, If $$h_B=0.9 \cdot p^{0.6}$$ then you only have to replace p by the weight of A relative to B. Afterwards simplify a little bit. If you mean: $$\left(\frac{x^{4-n} \cdot y^{n+4}}{x \cdot y^{n-4}}\right)^2$$ and you want to use the power rules then you should come out with...

Hello, now everything is OK. (Yes)

Hello, there are no mistakes except in the very last line: Why do you change $$(3-c)$$ into $$(c-3)$$ ? The correct answer is: $$b = \frac{6(a-2c)}{3-c}$$ In fact you changed the sign of the term because: $$(3-c)=(-1) \cdot (c-3)$$

Hallo, all your calculations are OK. Nevertheless you can factor out (-3) in the numerator and the denominator and afterwards cancel.

Good morning, replace a by $$\frac12$$ in $$k(a)\leq \frac{(a+1)(a-2)}{a(a-1)}$$ and you'll get $$k\left(\frac12 \right) \leq \frac{\left(\frac12 +1 \right)\left(\frac12 - 2 \right)}{\frac12 \left(\frac12 - 1 \right)} = \frac{-\frac94}{-\frac14}=9$$ That is the maximum value for k.

And I did: Substitute b = 1-a and you'll get $$k(a)\leq \frac{(a+1)(a-2)}{a(a-1)}$$ Calculate the extremum by using the 1st derivation: $$\frac{dk}{da}\leq \frac{2(2a-1)}{a^2(a^2-1)}$$ which is zero if $$a = \frac12$$. Determine b.

Hello, take Pascal's triangle of binomial coefficient and look (for n > 4) for those neighbouring coefficients which are in the relation 3 to 4. The first hit is for n = 6. Expanding $$(4x+3)^6$$ you'll find that the coefficients in question are 34560.