2019年6月3日 · Or, use a little calculus: set y = x2 − 8x + 17; then y ′ = 2x − 8 = 0 x = 4, y ″ = 2 x = 4is a minimum; since y ′ has precisely one zero, it follows that x = 4 is a global minimum; also, y(4) = 42 − 8 ⋅ 4 + 17 = 16 − 32 + 17 = 1; we conclude that ∀x ∈ R, x2 − 8x + 17 ≥ 1> 0.

Notice furthermore ζ−1 is the complex conjugated of ζ, thus η8:= ζ +ζ−1 = 2 cos(2π 17). Therefore, I will express η8 using radicals. Let's look at the tower of fields: Q ⊂Q(η2) ⊂Q(η4) ⊂Q(η8) ⊂Q(ζ). Note that Q(η8) corresponds to the unique subgroup H8:= −1 ⊂F∗17 of index 8. Where Q(η4) resp. Q(η2) correspond to the unique subgroups H4:= 4 resp. H2:= −8 of ...

In this example, the modular inverse of 7 with respect to 31 is 9. How can we find out that 9? What are the steps that I need to do? Update If I have a general modulo equation: 5x + 1 ≡ 2 (mod 6)

2020年10月5日 · Prove that some member of the sequence $7, 77, 777, 7777, \\dots$ is divisible by $2019$. So far I have figured that as $2019$ is divisible by $3$, then if one of the terms of the sequence $$ a_{n}...

2022年6月2日 · Here it is. Just click on the “functions” tab on the right hand side of the panel and scroll down. EDIT FOR CLARITY: Look at the text box closely. First up, the cursor is positioned in the region where you want the base to be. So after clicking the loga l o g a button, immediately type 5 (if the cursor moves, click in the lower region between “log” and “ (“.) Then click inside …

2011年11月10日 · Note that this is the same as adding all the vectors using vector addition and then multiplying by 1 n 1 n where n n is the number of vectors. In other words, just the same formula as an average of real numbers: 1 n(v1 +v2 + ⋯ +vn) 1 n (v 1 + v 2 + ⋯ + v n).

Finding the kernel of a matrix A is finding the set of vectors that, when multiplied by A, result in the vector 0. (It is easy to verify that this set of vectors is a vector space) Mathematically speaking, you must solve the equation: Ax = 0, where x is an vector. Note that this equation might have one solution or infinite solutions. In the second case, you'll find, while solving the system, a ...

2018年1月16日 · I'm looking to convert it to the parametric form of straight line like this:

(Note: I did not check your F′ F ′.) Because of the way the De Morgan laws work, the complement of a product of sums is always a sum of products, and the complement of a sum of products is always a product of sums.

2014年12月5日 · I know how to find the Taylor expansion of both $\\sinh x$ and $\\cosh x$, but how would you find the Taylor expansion of $\\tanh x$. It seems you can't just divide both the Taylor series of $\\sinh x$...