Answer:
Step-by-step explanation:
It’s C
Answer:
14
Step-by-step explanation:
to find the answer to this you would have to ethier convert 1 3/4 to 1.75 or multiply top heavy fractions
converted way
1.75x8= 14 - stays the same
nonconverted way
7/4 x 8/1 = 56/4 = 14
etheir way you get the same answer
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Answer: A number with the same absolute value of 23 is -23.
Explanation: The absolute value of a number is how far it is from zero, and the absolute value of a number is always positive, unless the number is 0, in which case the absolute value is neutral, and the absolute value is 0.
Examples: 6 is 6 away from zero, so the absolute value of 6 is 6.
−6 is 6 away from zero, so the absolute value of −6 is 6.
The sum of the inner angles of any triangle is always 180°, i.e. you have
In the particular case of an equilater triangle, all three angles are the same, so
and the expression becomes
which implies 
So, if you rotate the triangle with respect to its center by 60 degrees, the triangle will map into itself. In particular, if you want point A to be mapped into point B, you have to perform a counter clockwise rotation of 60 degrees with respect to the center of the triangle.
Of course, this is equivalent to a clockwise rotation of 120 degrees.
Finally, both solutions admit periodicity: a rotation of 60+k360 degrees has the same effect of a rotation of 60 degrees, and the same goes for the 120 one (actually, this is obvisly true for any rotation!)
