9514 1404 393
Answer:
64 -16π square units
Step-by-step explanation:
The area of the square is ...
A = (8 units)^2 = 64 units^2
The area of the circle is ...
A = πr^2 = π(4 units)^2 = 16π units^2
The shaded area is the difference:
shaded area = (64 -16π) units^2.
Answer:
a) -8/9
b) The series is a convergent series
c) 1/17
Step-by-step explanation:
The series a+ar+ar²+ar³⋯ =∑ar^(n−1) is called a geometric series, and r is called the common ratio.
If −1<r<1, the geometric series is convergent and its sum is expressed as ∑ar^(n−1) = a/1-r
a is the first tern of the series.
a) Rewriting the series ∑(-8)^(n−1)/9^n given in the form ∑ar^(n−1) we have;
∑(-8)^(n−1)/9^n
= ∑(-8)^(n−1)/9•(9)^n-1
= ∑1/9 • (-8/9)^(n−1)
From the series gotten, it can be seen in comparison that a = 1/9 and r = -8/9
The common ratio r = -8/9
b) Remember that for the series to be convergent, -1<r<1 i.e r must be less than 1 and since our common ratio which is -8/9 is less than 1, this implies that the series is convergent.
c) Since the sun of the series tends to infinity, we will use the formula for finding the sum to infinity of a geometric series.
S∞ = a/1-r
Given a = 1/9 and r = -8/9
S∞ = (1/9)/1-(-8/9)
S∞ = (1/9)/1+8/9
S∞ = (1/9)/17/9
S∞ = 1/9×9/17
S∞ = 1/17
The sum of the geometric series is 1/17
Answer:
Step-by-step explanation:
<u>Use Pythagorean to identify if the triangle is right:</u>
We see the triangle is <u>not </u>right and the difference of the squares tells us the angle opposite to side with measure of 9 is greater than 90°.
It means the triangle is <u>obtuse</u>.
Correct choice is B
12 x 2 x 1
4 x 3 x 2
6 x 2 x 2
1 x 24 x 1
-6 x 2 x -2
- 4 x 3 x -2
- 12 x 2 x =1
=1 x 24 x -1
