The defining characteristic of all geometric sequences is a common ratio which is a constant when dividing any term by the term preceding it.
In this case the common ratio is: -6/9=4/-6=r=-2/3
An infinite series will have a sum when r^2<1, so in this case the sum will converge to an actual value because (-2/3)^(+oo) approaches zero.
The sum of any geometric sequence is:
s(n)=a(1-r^n)/(1-r), since we have a common ratio of -2/3 and we want to calculate an infinite series, ie, n approaches infinity, the sum becomes simply:
s(n)=a/(1-r) (because (1-r^+oo) approaches 1 as n approaches +oo)
So our infinite sum is:
s(+oo)=9/(1--2/3)
s(+oo)=9/(1+2/3)
s(+oo)=9/(5/3)
s(+oo)=27/5
s(+oo)=54/10
s(+oo)=5.4
Since the volume of a cylinder is hπr^2 and the volume of a cone is (hπr^2)/3, the volume of the cone will just be 1/3 the volume of the cylinder with the same radius and height. In this case:
V=32.25/3=10.75 in^3
Answer:
20,000 cm³
Step-by-step explanation:
The shape is a triangular prism
Base area × height
½ × 20 × 25 × 80
20,000 cm³
Answer:
See below ~
Step-by-step explanation:
<u>Question 18</u>
- Diameter = Difference in y-coordinates
- Diameter = 12 - 2 = 10
- We know : Radius = Diameter/2
- Radius = 10/2
- Radius = 5 cm
- <u>(1) 5 cm</u>
<u></u>
<u>Question 19</u>
- 3x² - 34x - 24 = 0
- (3x + 2)(x - 12) = 0
- Solution set = {-2/3, 12}
- <u>(3) {-2/3, 12}</u>
Answer:
8,000
Step-by-step explanation:
You can simplify it to (-4+24)^3a
