The series as represented in the task content is divergent and hence; diverges.
<h3>What convergence and divergence in series?</h3>
It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
Read more on convergence and divergence of series;
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The value of x in the linear equation 4(x + 5) = 9x + 4x − 34 is 6 after applying the property.
<h3>What is a linear equation?</h3>
It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have linear equation in one variable:
4(x + 5) = 9x + 4x − 34
4x + 20 = 9x + 4x − 34 (Distributive Property)
4x + 20 -4x + 34= 9x + 4x − 34 -4x +34
(Subtraction Property of Equality and Addition Property of Equality)
54 = 9x
x = 6 (Division Property of Equality)
Thus, the value of x in the linear equation 4(x + 5) = 9x + 4x − 34 is 6 after applying the property.
Learn more about the linear equation here:
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X² + 10x +2 = 0 .Complete the square of (x² + 10x + ??)
We know that (10x) is equal to twice the square root of the 1st (x) by ??
10x = 2.x.(??) and ?? = 5 and its square is 25. Then I have to add 25 and subtract 25 so that not to change the equation:
(x² + 10x + 25) -25 +2 =0
(x+5)² -23
Complete question :
Each state imposes its own excise tax on gasoline. Suppose, for example, that the state of Massachusetts imposes a state gasoline tax of $0.26 per gallon. Suppose further that an average of 1,022,000 gallons of gasoline per day were sold in Massachusetts in 2010. The average revenue from gasoline tax in 2010 is approximately?
Answer:
$265,720
Step-by-step explanation:
Given that:
State gasoline tax = $0.26 per gallon
Average number of gasoline sold per day = 1,022,000 gallons
. From the availabke information given :
Revenue generated = gasoline tax per gallon multiplied by the average number of gallons sold
= $0.26 * 1,022,000
= $265,720
