Answer:
6 terms
Step-by-step explanation:
2 − 2/4 + 2/9 − 2/16 + ...
∑ (-1)ⁿ⁺¹ 2 / n²
Applying alternating series test:
lim(n→∞) 2/n² = 0
2/(n+1)² < 2/n², so the series is decreasing.
Therefore, the series converges.
2/(n+1)² < 0.05
(n+1)²/2 > 20
(n+1)² > 40
n+1 > 6.32
n > 5.32
n = 6
This equation uses two properties of logarithms:


So you could take the ln from left and right hand side in the equation, and get:
(2-x)ln 3 = x ln 5
then
2 ln 3 - x ln 3 - x ln 5 = 0 =>
x(ln 3 + ln 5) = 2 ln 3
so x = 2 ln 3 / (ln3 + ln5)
Now using the 1st property you can say 2 ln 3 is ln 3² = ln9
and using the 2nd property you can say ln3 + ln5 = ln15
so x= ln9 / ln15
Answer:
D. 251.2 feet
Step-by-step explanation:
On carefully observing the diagram,it can be seen that 80 feet is the diameter of the circular ride, i.e.,the circle,in this case.
The radius of the circle will be half the diameter,r=(80/2) feet=40 feet
The distance of one complete loop of this circular path will be the circumference of the circle.
So, Circumference
=2*π*r
=2*3.14*40 feet
=251.2 feet [ANS]
altogether there are 7 marbles in the bag.
put the marbles in fractions, so blue would be 3/7
and red would be 4/7. but becuase you need 2 of the same, you do
3/7 x 3/7 = 9/49
4/7 x 4/7 = 16/49
then add them togther
25/49
if you need it as a percentage, it is
51.020408163265%
D- 2x-1
plug in a number for x and you'll see