find the 6th term of the expansion of (2p - 3q)11. a. -7,185,024p4q7 c. -7,185p4q7 b. -7,185,024p6q5 d. -7,185p6q5 select the best answer from the choices provided a b c d
the first thing to do is to subtract 16 from both side of the equation:
16 - 16 - b = 7 - 16
the 16s on the left cancel out resulting in:
-b = -9
think of the -b as -1(9). this is multiplication. by doing the inverse operation (division) we can get rid of the negative on the b. we will divide both sides by -1.
this leaves a positive b. since both parts of the right side of the equation are negative it becomes positive ( a negative divided by a negative is a positive).
the final answer is b= 9.
check our work by plugging in the b value (9) into the original equation:
16 - 9 = 7
7 = 7 is true so we now we have the right answer.
the given series converges and
given is 108, -18,
it is an alternate series. an alternate series is convergent if:
1. the series is decreasing.
2. if the last term (n-th term) of series converges to 0.
since each next term is less than its preceding term, so it is decreasing.
first term, a = 108
second term = -18
common ratio, r = -18/108 = -1/6
general term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
when n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.
hence, the given series converges.
now limit will be:
the answer is 16 inches
40.64 centimeters divided by 2.54 is equal to 16