Find PD if coordinate P is -7 and coordinate of D is -1.

Shannon Andrews
2022-07-28
Answered

Find PD if coordinate P is -7 and coordinate of D is -1.

You can still ask an expert for help

Lillianna Mendoza

Answered 2022-07-29
Author has **16** answers

Well, if we have PD that P is -7 and D is -1, the distance will bebetween the two coordinates.

so you have to do it basically by-1+7, does that help? because you must find the distance betweenthe two coords.

so you have to do it basically by-1+7, does that help? because you must find the distance betweenthe two coords.

asked 2022-05-09

Suppose you have a pair of lines passing through origin, $a{x}^{2}+2hxy+b{y}^{2}=0$, how would you find the equation of pair of angle bisectors for this pair of lines. I can do this for 2 separate lines, but I am not able to figure it out for a pair of lines. Can someone please help.

asked 2022-05-10

Given a lattice $\mathrm{\Gamma}\subset \mathbb{C}$, a Theta function $\vartheta :\mathbb{C}\to \mathbb{C}$ is a holomorphic function with the following property:

$\vartheta (z+\gamma )={e}^{2i\pi {a}_{\gamma}z+{b}_{\gamma}}\vartheta (z)$

for every $\gamma \in \mathrm{\Gamma}$, and ${a}_{\gamma},{b}_{\gamma}\in \mathbb{C}$.

Exercise: A Theta function never vanishes iff $\vartheta (z)={e}^{p(z)}$ with $p(z)$ a polynomial of degree at most 2.

Hint: The "only if" part is trivial. The hint is: show that $\mathrm{log}(\vartheta (z))=O(1+|z{|}^{2})$. I tried to apply log on both sides, or derive one and two times, or everything I could have thought of. I don't get where the square comes from.

$\vartheta (z+\gamma )={e}^{2i\pi {a}_{\gamma}z+{b}_{\gamma}}\vartheta (z)$

for every $\gamma \in \mathrm{\Gamma}$, and ${a}_{\gamma},{b}_{\gamma}\in \mathbb{C}$.

Exercise: A Theta function never vanishes iff $\vartheta (z)={e}^{p(z)}$ with $p(z)$ a polynomial of degree at most 2.

Hint: The "only if" part is trivial. The hint is: show that $\mathrm{log}(\vartheta (z))=O(1+|z{|}^{2})$. I tried to apply log on both sides, or derive one and two times, or everything I could have thought of. I don't get where the square comes from.

asked 2022-07-02

The property I'm talking about is:

There is some partition of the plane figure P into $n$ congruent figures for any $n$.

Is it true that only discs, sectors of discs, annuli, sectors of annuli and parallelograms have this property?

There is some partition of the plane figure P into $n$ congruent figures for any $n$.

Is it true that only discs, sectors of discs, annuli, sectors of annuli and parallelograms have this property?

asked 2022-06-26

By Bertrand's postulate, we know that there exists at least one prime number between $n$ and $2n$ for any $n>1$. In other words, we have

$\pi (2n)-\pi (n)\ge 1,$

for any $n>1$. The assertion we would like to prove is that the number of primes between $n$ and $2n$ tends to $\mathrm{\infty}$, if $n\to \mathrm{\infty}$, that is,

$\underset{n\to \mathrm{\infty}}{lim}\pi (2n)-\pi (n)=\mathrm{\infty}.$

Do you see an elegant proof?

$\pi (2n)-\pi (n)\ge 1,$

for any $n>1$. The assertion we would like to prove is that the number of primes between $n$ and $2n$ tends to $\mathrm{\infty}$, if $n\to \mathrm{\infty}$, that is,

$\underset{n\to \mathrm{\infty}}{lim}\pi (2n)-\pi (n)=\mathrm{\infty}.$

Do you see an elegant proof?

asked 2022-05-14

Show that the circumscribed circle passes through the middle of the segment determined by center of the incircle and the center of an excircle.

asked 2022-06-02

Let ABC be an acute angled triangle with circumcenter O. A circle passing through A and O intersects AB, AC at P, Q respectively. Show that the orthocentre of triangle OPQ lies on the side BC.

asked 2022-07-28

In each diagram, BD bisects