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The difference of two squares can also be illustrated geometrically as the difference of two square areas in a plane. In the diagram, the shaded part represents the difference between the areas of the two squares, i.e. a 2 − b 2 {\displaystyle a^{2}-b^{2}} .
For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with a common difference of 2. If the initial term of an arithmetic progression is a 1 {\displaystyle a_{1}} and the common difference of successive members is d {\displaystyle d} , then the n {\displaystyle n} -th term of the sequence ( a n {\displaystyle a_{n ...
By convention, if the most significant digit can be either 0 or 1, it is termed a half-digit; if it can take higher values without reaching 9 (often 3 or 5), it may be called three-quarters of a digit. A 5 + 1 ⁄ 2-digit multimeter would display one "half digit" that could only display 0 or 1, followed by five digits taking all values from 0 ...
[8] [9] Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet ("The galvanic circuit investigated mathematically"). [10] He drew considerable inspiration from Joseph Fourier's work on heat conduction in the theoretical explanation of his work.
The final digit of a triangular number is 0, 1, 3, 5, 6, or 8, and thus such numbers never end in 2, 4, 7, or 9. A final 3 must be preceded by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every triangular number is either divisible by three or has a ...
The resistivity can be expressed using the SI unit ohm metre (Ω⋅m) — i.e. ohms multiplied by square metres (for the cross-sectional area) then divided by metres (for the length). Both resistance and resistivity describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an ...
if p ≡ 3 (mod 8), then p is not a congruent number, but 2 p is a congruent number. if p ≡ 5 (mod 8), then p is a congruent number. if p ≡ 7 (mod 8), then p and 2 p are congruent numbers. It is also known that in each of the congruence classes 5, 6, 7 (mod 8), for any given k there are infinitely many square-free congruent numbers with k ...
Also called chordal or DC resistance This corresponds to the usual definition of resistance; the voltage divided by the current R s t a t i c = V I. {\displaystyle R_{\mathrm {static} }={V \over I}.} It is the slope of the line (chord) from the origin through the point on the curve. Static resistance determines the power dissipation in an electrical component. Points on the current–voltage ...