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Willem Einthoven invented the ECG in 1903. The letters P Q R S T were assigned to the points on the ECG because it was thought that there may be more points in either direction to be found. The letters remained in use out of common practice even after it was determined there were no further points to be labelled.
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L is not as tall as P or R but is taller than S and Q Q being shorter than R S is shorter than R who is shorter than P who is taller than Q Who among P Q R and S is the shortest?
The answer is Q.
Greatest prime number that can be represented as both the sum of 2 prime numbers as well as difference of 2 prime numbers?
We will use the fact that if p prime, a divides p, then a = p or a = 1. Then if p + q = r, for primes p, q, r, then one of p,q,r is even, or all three are (consider mod 2). p = q = r = 2 clearly doesn't work, and p + q = 2 doesn't work for primes p,q >= 3. So without loss of generality p = 2, then r = q+2. r is also the difference of two primes, r = s - t. Again considering mod 2, knowing that r is odd, one of s or t is even (and so equal to 2). If s = 2 then r is negative, so t = 2, and we have q + 2 = r = t - 2, so t = q + 4. So we have q, r = q + 2 and t = q + 4 all prime. By considering q mod 3, one of them has a factor 3. If a prime has a factor 3, it is equal to 3. So q = 3, as q + 2 = 3 or q + 4 = 3 mean q is not prime. So, r = q + 2 = 5. Therefore, 5 is the only prime that can be represented as both the sum of two primes and the difference of two primes: 5 = 2 + 3 = 7 - 2. Since it is the only one, it is the greatest.
If p q and q r then p r.?
Unfortunately, the browser used for posting questions is hopelessly inadequate for mathematics: it strips away most symbols. All that we can see is "If p q and q r then p r.?". There is no operator between the variables. Some operators are transitive, others are not. In the case of the operator "is not equal to", the answer is that it depends. In the case of "is the parent of" the answer is no.
How to find the chord length of a curve with radius and 2 bearings given?
Suppose the radius is r and the bearings of the two points, P and Q are p and q respectively. Then the coordinates of P are [r*cos(p), r*sin(p)] and the coordinates of Q are [r*cos(q), r*sin(q)]. The distance between these two points can be found, using Pythagoras: d2 = (xq - xp)2 + (yq - yp)2 where xp is the x-coordinate of P, etc.
What is the Analogy for d is B as r is to p or T or q or P?
P
