(a)
Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :
(b) The series
converges by comparison to the convergent <em>p</em>-series,
(c) The series
converges absolutely, since
That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.
Answer:
11.1803398875
Step-by-step explanation:
Refer to the graph shown below. It confirms that points A, B and P are
collinear.
Calculate the length of AP (as a).
a = √[(6 - 2)² + (11 - 3)²]
= 8.9443
Calculate the length of BP (as b).
b = √[(8 - 6)² + (15 - 11)²]
= 4.4721
Calculate ratio a/b.
a/b = 8.9443/4.4721 = 2
Therefore P partitions AB in a 2:1 ratio so that AP = 2*BP.
Answer: 2:1 ratio.
Answer:
x ≤ 4
Step-by-step explanation:
6x + 3 ≤ 27 subtract 3 both sides
6x ≤ 24 divide 6 both sides
x ≤ 4 There's your answer
<span>There is a decrease of 20% from ÂŁ800 to ÂŁ640.
A change from 800 to 640 represents a negative change (decrease) of -20% Using the formula :
Percent change = [(800 - 640) / 800] x 100 = -20 % (decrease)
800 is the old value and 640 is the new value. In this case we have a negative change (decrease) of -20 percent because the new value is smaller than the old value.</span>
