we have been asked to find the sum of the series
As we know that a geometric series has a constant ratio "r" and it is defined as
The first term of the series is
Geometric series sum formula is
Plugin the values we get
On simplification we get
Hence the sum of the given series is
See the attached figure
we know that
[<span>the area of the trapezoid]=[area rectangle]+2*[area triangle]
</span>[the area of the trapezoid]=[14*12]+2*[12*2/2]=192 in²
the answer is 192 in²
Multiply 44580 by .47
that gives you 20952.6 which equals 47% of the water
take the 44580, and subtract the 20952.6
giving you the remainder as your answer
23627.4
He was meant to divide by 3 when the equation was 3x=15, not multiply, so he would get the answer x=5
Sure, provided that the coefficients of the polynomial are complex, and not strictly real.
If you require that the coefficients of the polynomial be real, then the answer would be no. For such a polynomial, any complex roots occur in conjugate pairs, so if
is a root, then so must be
.
A degree-4 polynomial can have up to four distinct roots, so if the coefficients are all real, then the remaining fourth root must be real.