The sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
<h3>How to determine the sum of the notation?</h3>
The sum notation is given as:
∞Σn=1 2(1/5)^n-1
The above notation is a geometric sequence with the following parameters
- Initial value, a = 2
- Common ratio, r = 1/5
The sum is then calculated as
S = a/(1 - r)
The equation becomes
S = 2/(1 - 1/5)
Evaluate the difference
S = 2/(4/5)
Express the equation as products
S = 2 * 5/4
Solve the expression
S= 5/2
Hence, the sum of the sum notation ∞Σn=1 2(1/5)^n-1 is S= 5/2
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Answer:
I cant see the whole question...
Answer:
C. 16√3π in.
Step-by-step explanation:
Circumference of a circle = 2πr where
r is the radius of the circle.
Given the area of one of the smaller circle to be 48π in², we can get the radius of one of the smaller circle.
If A = πr²
48π = πr²
r² = 48
r = √48 in
The radius of one of the smaller circle is √48.
To get the circumference of the larger circle, we need the radius of the larger circle. The radius R of the larger circle will be equivalent to the diameter (2r) of one of the smaller circle.
R = 2r
R = 2√48 inches
Since C = 2πR
C = 2π(2√48)
C = 4√48π in
C = 4(√16×3)π in
C = 4(4√3)π in
C = 16√3π in
Thw circumference of the larger circle is 16√3π in.
Answer:
dV = - 5.73*10⁹ m³/s
Step-by-step explanation:
Question: What is the rate of change of the volume of the prism at that instant (in cubic meters per second) ?
A function can be dependent on one or more variables. The change in the function due to a change in one o its variables is given by the functions derivative with respect to that variable. For functions that are composed of products of its variables, we may use the product rule to determine its derivative.
The volume of a square prism with base a and height h is given by
V = a²h
When the base and height are changing, we have
dV = 2ah(da/dt) + a²(dh/dt)
Given
a = 4 Km
h = 9 Km
da/dt = - 7 Km/min
dh/dt = 10 Km/min
we have
dV = 2(4 Km)(9 Km)(- 7 Km/min) + (4 Km)²(10 Km/min)
⇒ dV = - 504 Km³/min + 160 Km³/min = - 344 Km³/min
⇒ dV = - 5.73*10⁹ m³/s
Answer:
x+4y is not change because it's parallel what changes is the result 8 + 4 × 2 = 16 so the equation is x + 4y = 16
