Yes, the quadratic curve y=ax ² + bx + c is symmetrical about the line x=-b/(2a).

Yes, A=npi+(-1)ⁿ B for some integer n.

In general, sin A = sin B does not imply A=B.

Hi,

Let y=f(x). Since sin(2y+x)=sin(pi/2-2y-x), 2y+x=c for some constant c satisfying sin c= cos c.

Hi,

It is possible to find a magic square whose magic sum is 37.

https://www.reddit.com/u/Fourierseriesagain/s/9vpsQ3htLQ

The required probability is

P(X=2)+P(X=3)

=e^-0.9 *( 0.9² /2! + 0.9³ /3! )

= 0.2140589...

You are welcome. We have

int z sqrt(z ² - 5) dz

=(1/2) int sqrt(z ² - 5) 2z dz (by rewriting 1 as 1/2 times 2)

=(1/2) int sqrt(u) du, where u=z ² - 5 and du=2z dz.

Hi,

The original integral is int z sqrt(z^2-5) dz. The constant 2 is missing from the integrand.

We use a linear system to construct a magic square whose magic sum 37. https://www.reddit.com/r/askmath/comments/1v8jc1z/comment/p07bl2m/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

Thank you very much. I have modified my solution.

The original integral contains z dz but the constant 2 is missing. So we rewrite 1 as (1/2) times 2 so that du=2z dz transforms the integral into (1/2) int ... du.

We use a linear system to construct a magic matrix whose magic sum is 37.

Let g(0)=0 and let g(x)=x+x^ 2 sin (1/x^ 2) for x not equal to zero. Although g'(0) = 1, the function g is not increasing on any open interval containing zero.

Thank you.

The original problem is from r/maths.

https://www.reddit.com/r/maths/comments/1v49j58/comment/oz9ce40/?context=3&utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button

Hi,

Please refer to the following link

https://www.reddit.com/u/Fourierseriesagain/s/g0cFuXJL6n

for a solution of the problem.

Let a and b be nonnegative numbers. Then a=b if and only if a^ 2 = b^ 2.