Answer: 156.25
Step-by-step explanation:
(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: Distance between O and the line 1 is 3 inches.
Explanation:
Since we have given that
Distance between point A and the line 1 = 10 inches
Distance between point B and the line 1 = 4 inches
Total length of segment AB is given by

Since O is midpoint of the line segment AB.
so, AO is given by

Now, Distance between O and the line 1 is given by

Hence, Distance between O and the line 1 is 3 inches.
Answer:
It should be "one solution"
Step-by-step explanation:
After graphing the equations, the two lines only intersect at one point which makes it "one solution." Hope this helps.
Answer:
Every week, the mass of the sample is multiplied by a factor of 0.81
Step-by-step explanation:
Let's rewrite the base and find the expression whose exponent is just ttt.
(0.97)7t+5=(0.97)7t⋅(0.97)5=(0.977)t⋅(0.97)5
Therefore, we can rewrite the modeling function as follows.
M(t)=(0.97)5⋅(0.977)t
According to this model, the mass of the sample is multiplied by 0.977 every week. Rounding this to two decimal places, we get 0.977≈0.81.