Answer:
The given series converges and 
Step-by-step explanation:
Given is 108, -18, 3,...
It is an alternate series. An alternate series is convergent if:
1. The series is decreasing.
2. If the last term (n-th term) of series converges to 0.
<u>Since each next term is less than its preceding term, so it is decreasing.</u>
First term, a = 108
Second term = -18
Common ratio, r = -18/108 = -1/6
General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ
<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>
Hence, the given series converges.
Now limit will be: 
Hence,
Answer:
143π in³
Step-by-step explanation:
A basketball has the shape of a sphere
Volume of a basketball = 4/3πr³
Diameter = 9.5 in
Radius = diameter/2
= 9.5/2
= 4.75 in
Volume of a basketball = 4/3πr³
= 4/3 * π * 4.75³
= 4/3 * π * 107.17
= (4*π*107.17) / 3
= 428.68π / 3
= 142.89π in³
Approximately
143π in³ to the nearest whole number
Y = <span>b^x
when x = 1
y = b^1
y = b
Therefore, the value of b is the same as the value of y when x =1
From the graph,
When x = 1, y = 0.5
Therefore, b = 0.5
To confirm this
From the graph,
When x = -1, y = 2
Since </span>y = b^x<span>
2 = </span>b^-1
2 = 1/b
2b = 1
b = 0.5
When x = -2, y = 4
Since y = b^x
4 = b^-2
4 = 1/(b^2)
b^2 = 1/4
b = √(1/4)
b = 1/2
b = 0.5
Therefore, it is conformed that b = 0.5
Easy! Just substitute.
That will be 3 + 8 * 4
Remember PEMDAS? Multiplication comes before addition, so FIRT MULTIPLY.
3+ 32= 35
Final answer= 35
9514 1404 393
Answer:
4. True
5. False
Step-by-step explanation:
4. The number of x-intercepts produced by the quadratic formula may be 0, 1, or 2. It will be 0 if the two roots are complex. It will be 1 if the two roots lie in the same place (one root with multiplicity 2). It is true that there may be only one x-intercept.
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5. The value of 'b' in the quadratic formula is the coefficient of the linear term. In the given quadratic, it is -5, not 5.
