The letters "9 r p s s" can represent the phrase "9 Red Plastic Spoons." This fits well as it describes a specific quantity and type of object. Alternatively, it could be a code or puzzle where the letters and number signify something else depending on the context.
The answer is Q.
Suppose you have the points with coordinates (p, q) and (r, s) then, provided p is different from r, the slope of the line is (q - s)/(p - r) = m, say. Then, if (x, y) is any point on the line, (x - s)/(y - r) = m That, after simplification, is the linear equation of the line. This will be a lot simpler when you have numerical values for p, q, r and s rather than work algebraically throughout. If p is not different from r, then the equation is x = p (or r), a vertical line.
Yes. If one matrix is p*q and another is r*s then they can be multiplied if and only if q = r and, in that case, the result is a p*s matrix.
9 P. in the S. S. equals 9 planets in the solar system EDIT: Which is no longer the case, as Pluto has now been classified as a dwarf planet.
Two ratios, p/q and r/s (q and s non-zero) are equal if p/q - r/s = 0.
Prove: [ P -> Q AND R -> S AND (P OR R) ] -> (Q OR S) -> NOT, --- 1. P -> Q ___ hypothesis 2. R -> S ___ hypothesis 3. P OR R ___ hypothesis 4. ~P OR Q ___ implication from hyp 1. 5. ~R OR S ___ implication from hyp 2 6. ~P OR Q OR S ___ addition to 4. 7. ~R OR Q OR S ___ addition to 5. 8. Let T == (Q OR S) ___ substitution 9. (~P OR T) AND (~R OR T) ___ Conjunction 6,7 10. T OR (~P AND ~R) ___ Distribution from 9 11. T OR ~(P OR R) ___ De Morgan's theorem 12. Let M == (P OR R) ___ substitution 13. (T OR ~M) AND M ___ conjunction 11, hyp 3 From there, you can use distribution to get (T AND M) OR (~M AND M). The contradiction goes away leaving you with T AND M, which can simplify to T.
P=s r t , so, s= P/(st)
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p/q * r/s = (p*r)/(q*s)
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A rational number is a number of the form p/q where p and q are integers and q > 0.If p/q and r/s are two rational numbers thenp/q + r/s = (p*s + q*r) / (q*r)andp/q - r/s = (p*s - q*r) / (q*r)The answers may need simplification.
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It is 3*(q + p)/(r + s)
If a is rational then there exist integers p and q such that a = p/q where q>0. Similarly, b = r/s for some integers r and s (s>0) Then a*b = p/q * r/s = (p*r)/(q*s) Now, since p, q r and s are integers, p*r and q*s are integers. Also, q and s > 0 means that q*s > 0 Thus a*b can be expressed as x/y where p and r are integers implies that x = p*r is an integer q and s are positive integers implies that y = q*s is a positive integer. That is, a*b is rational.
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yea and its spelled sprouse not sprose s-p-r-o-u-s-e not s-p-r-o-s
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