David’s scores on the first three of four 100-point math tests were 86, 92, and 89. What score does he need on his fourth math t
2 answers:
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Well, a logarithmic expression is just an exponential expression written from the point of the exponent.
now, ln is just a shorthand for the logarithm with a base "e" or euler's constant, so-called the "natural logarithm", now, let's use the exponential version of that here, and let's say equals an constant exponent of "k",
now, look closely, what "k" value, what exponent, negative or fraction or positive, will ever make "e" to 0? none, so one can say is "undefined".
now, ln is just a shorthand for the logarithm with a base "e" or euler's constant, so-called the "natural logarithm", now, let's use the exponential version of that here, and let's say equals an constant exponent of "k",
now, look closely, what "k" value, what exponent, negative or fraction or positive, will ever make "e" to 0? none, so one can say is "undefined".
Standard form
ok, so the factored form of a polynomial with roots r1,r2,r3,r4 is
f(x)=(x-r1)(x-r2)(x-r3)(x-r4)
so
since the roots are 0,1,-2i,3+√3
I am assuming you want real coefients so ince -2i is a root, 2i is also a root
f(x)=(x-0)(x-1)(x+2i)(x-2i)(x-(3+√3))
f(x)=x⁵-(√3)x⁴-4x⁴+(√3)x³+7x³-(4√3)x²-16x²+12x
if you were allowed to have no-real coefients then exclue the 2i
f(x)=(x-0)(x-1)(x+2i)(x-(3+√3))
f(x)=
ok, so the factored form of a polynomial with roots r1,r2,r3,r4 is
f(x)=(x-r1)(x-r2)(x-r3)(x-r4)
so
since the roots are 0,1,-2i,3+√3
I am assuming you want real coefients so ince -2i is a root, 2i is also a root
f(x)=(x-0)(x-1)(x+2i)(x-2i)(x-(3+√3))
f(x)=x⁵-(√3)x⁴-4x⁴+(√3)x³+7x³-(4√3)x²-16x²+12x
if you were allowed to have no-real coefients then exclue the 2i
f(x)=(x-0)(x-1)(x+2i)(x-(3+√3))
f(x)=