To approximate the sum of the series [infinity] (−1)n−1n^2/(8n), we can use a numerical method such as the partial sum method.
Let's calculate the partial sums of the series and add up terms until the sum converges to a desired level of accuracy. We will stop adding terms once the absolute difference between two consecutive partial sums is less than the desired accuracy.
Let's start by calculating the partial sums:
S_1 = (-1)^1-1(1^2)/(81) = 1/8
S_2 = (-1)^2-1(1^2)/(82) + (-1)^1-1(2^2)/(82) = 1/8 - 1/16 = 1/16
S_3 = (-1)^3-1(1^2)/(83) + (-1)^2-1(2^2)/(83) + (-1)^1-1(3^2)/(83) = 1/8 - 1/16 - 1/24 = -1/24
We can observe that the partial sums alternate between positive and negative values. This indicates that the series does not converge to a specific value but oscillates between two values.
To approximate the sum, we will calculate partial sums until the difference between two consecutive partial sums is less than the desired accuracy. Let's say we want the accuracy to be 0.0001.
Let's continue calculating partial sums:
S_4 = (-1)^4-1(1^2)/(84) + (-1)^3-1(2^2)/(84) + (-1)^2-1(3^2)/(84) + (-1)^1-1(4^2)/(84) = 1/8 - 1/16 - 1/24 + 1/32 = -1/48
S_5 = (-1)^5-1(1^2)/(85) + (-1)^4-1(2^2)/(85) + (-1)^3-1(3^2)/(85) + (-1)^2-1(4^2)/(85) + (-1)^1-1(5^2)/(8*5) = 1/8 - 1/16 - 1/24 + 1/32 + 1/40 = 1/120
The difference between S_4 and S_5 is 1/120 - (-1/48) = 1/120 + 1/48 = 1/80, which is greater than 0.0001.
Therefore, we can approximate the sum of the series as -1/48, correct to four decimal places.
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please help.I don’t understand
Answer:
y=13 degrees
Step-by-step explanation:
This is an isosceles triangle, we know this because NO and NM are equal.
In an isosceles triangle, the base angles are congruent. In this case, they are angle NOM and angle NMO.
We also know that the sum of the interior angles of a triangle are equal to 180.
With this information, we can make an equation by gathering all the interior angles:
8y+2(3y-1)=180
Solve for y.
8y+6y-2=180
14y-2=180
14y=182
y=13
A shelf is designed so it will fit in a 90º corner between two walls. The shelf has dimensions, rounded to the nearest tenth, as shown. A triangle has side lengths 11 centimeters, 11 centimeters, and hypotenuse of StartRoot 242 EndRoot centimeters. [Not drawn to scale] Will the shelf fit snugly in a 90º corner?
Answer:
Yes, it will fit snugly in a 90º corner
Step-by-step explanation:
To do this, we simply need to check if the given sides of the shelf is right-angled.
So, we have:
[tex]Hypotenuse = \sqrt{242[/tex]
[tex]Side\ 1 = Side\ 2 = 11[/tex]
To check for right-angle triangle, we make use of:
[tex]Side\ 1^2 + Side\ 2^2 = Hypotenuse^2[/tex]
This gives:
[tex]11^2 + 11^2 = \sqrt{242}^2[/tex]
[tex]121 + 121 = \sqrt{242}^2[/tex]
[tex]242 = \sqrt{242}^2[/tex]
[tex]242 = 242[/tex]
This shows that the given sides of the shelf is a right-angled triangle.
Hence, it will fit the wall
Answer:
A
Step-by-step explanation:
Find the inverse of one-sided Laplace transform of following signal. Then Find its poles and ROC. X(s) = (x+1)(22+4 48+4)
The inverse Laplace transform of [tex]X(s) = (s+1)/(s^2 + 4s + 4)[/tex] is [tex]x(t) = e^-^t * (t + 1)[/tex]. The poles are located at s = -2, and the region of convergence (ROC) includes all values of s to the right of -2 on the real axis. This means that the Laplace transform is valid for all values of s greater than -2.
To find the inverse Laplace transform, we can use partial fraction decomposition. The denominator of X(s) factors as [tex](s + 2)^2[/tex], indicating a repeated pole at s = -2. The numerator is (s + 1), which is a first-order polynomial.
Applying partial fraction decomposition, we can express X(s) as [tex](A/(s + 2)) + (B/(s + 2)^2)[/tex]. Solving for A and B, we find A = 1 and B = -1.
Now, we can take the inverse Laplace transform of each term. The inverse Laplace transform of A/(s + 2) is [tex]e^-^2^t[/tex], and the inverse Laplace transform of [tex]B/(s + 2)^2[/tex] is [tex]t * e^-^2^t[/tex].
Thus, the inverse Laplace transform of X(s) is [tex]x(t) = e^-^t * (t + 1)[/tex].
The poles of X(s) are located at s = -2. The region of convergence (ROC) can be determined by examining the values of s for which X(s) converges. In this case, since the poles are at s = -2, the ROC includes all values of s to the right of -2 on the real axis.
In summary, the inverse Laplace transform of X(s) = [tex](s+1)/(s^2 + 4s + 4)[/tex] is [tex]x(t) = e^-^t * (t + 1)[/tex]. The poles are located at s = -2, and the ROC includes all values of s to the right of -2 on the real axis.
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Find all the missing sides and angles of this triangle,
А
7
B
70°
The measurement of angle A
A A=
The length of side BC
The length of side AC-
Answer:
See solutions below
Step-by-step explanation:
From the given diagram;
AC = opposite
AB = 7 = hypotenuse
Angle of elevation = 70 degrees
Using SOH CAH TOA
Sin theta = opp/hyp
Sin theta = AC/AB
Sin 70 = AC/7
AC = 7sin70
AC = 7(0.9397)
AC = 6.58
Similarly
tan 70 = AC/BC
tan 70 = 6.58/BC
BC = 6.58/tan70
BC = 6.58/2.7475
BC = 2.39
tan m<A = BC/AC
tanm<A = 2.39/6.58
tan m<A = 0.3632
m<A = 19.96degrees
Two functions are defined by the equations f(x)=5−0.2x and g(x)=0.2(x+5). all statements that are true about the functions.
Answer:
The true statements are -: A f(3)>0 , C g(-1)=0.8 and D g(-1)< f(-1)
Step-by-step explanation:
Given f(x)= 5- 0.2x and g(x)= 0.2(x+5)
(A) f(3) > 0
Putting this value in the given equation -
f(3) =5 -0.2(3)
f(3)=5 - 0.6
f(3) =4.4
Therefore , f(3) > 0 . This is a true statement .
(B) f(3) > 5
We got the value of f(3) from the above equation,
Therefore , f(3) = 4.4 , hence f(3) > 5 option is False.
(C) g(-1) = 0.8
Taking the second given equation ,
g(-1) = 0.2 ( -1+ 5)
g(-1) = 0.2 (-4)
Therefore, g(-1) = -0.8 . Hence , this statement is true.
(D) g(-1) < f(-1)
g(-1) = -0.8
f(-1) =5 - 0.2(-1)
f(-1) = 5 +0.2
f(-1) = 5.2
Therefore , g(-1) < f(-1) , Hence this option is true.
(E) f(0) =g(0)
f(0) = 5 + 0.2(0)
f(0) = 5
g(0) = 0.2(0+5)
g(0) = 0.2 +5
g(0) = 1
Therefore , f(0)[tex]\neq[/tex] g(0) , Hence , the option is false .
Hence , true statements about the functions are - A , C , D .
which undefined geometric term is described as a location on a coordinate plane that is designated by an ordered pair?
I've calculated the area inside the circle r=3acos(θ)
and outside the cardioid r=a(1+cos(θ))
The integral for the area becomes:
A = ∫₀ᵃʳᶜᶜᵒˢ(ᵃ/₂) ∫ₐ(₁+ᶜᵒˢ(θ))³ᵃᶜᵒˢ(θ) r dr dθ
To find the area inside the circle r = 3acos(θ) and outside the cardioid r = a(1 + cos(θ)), we can set up a double integral in polar coordinates.
First, let's find the points of intersection between the two curves. The circle r = 3acos(θ) and the cardioid r = a(1 + cos(θ)) intersect when:
3acos(θ) = a(1 + cos(θ))
Simplifying, we get:
3acos(θ) - a(1 + cos(θ)) = 0
2acos(θ) - a = 0
acos(θ) = a/2
θ = arccos(a/2)
Now, let's set up the integral. We want to find the area inside the circle and outside the cardioid, so the region of integration is defined by:
0 ≤ θ ≤ arccos(a/2)
a(1 + cos(θ)) ≤ r ≤ 3acos(θ)
Evaluating this double integral will give us the desired area inside the circle and outside the cardioid.
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Five students participated in an Easter egg hunt. Ally snatched up one
quarter of all of the eggs. Brett only managed to get half of what Ally
found. Lee snagged six more than Brett. Jen ended up with half of Lee's
take, while Lisa snagged three times that. How many eggs were there in
total?
Answer:
There were a total of 72 Easter eggs.
Step-by-step explanation:
Since five students participated in an Easter egg hunt, where Ally snatched up one quarter of all of the eggs, Brett only managed to get half of what Ally found, Lee snagged six more than Brett, Jen ended up with half of Lee's take, While Lisa snagged three times that, to determine how many eggs were there in total, the following calculation must be performed:
Ally: 0.25X
Brett: 0.125X
Read: 0.125X + 6
Jen: 0.0625X + 3
Smooth: 0.1875X + 9
X - 0.25X - 0.125X - 0.125X - 0.0625X - 0.1875X = 0.25
0.25X = 6 + 3 + 9
0.25X = 18
Ally: 18
Brett: 9
Read: 15
Jen: 7.5
Smooth: 22.5
18 + 9 + 15 + 7.5 + 22.5 = X
72 = X
Thus, there were a total of 72 Easter eggs.
Help please I’ll give brainlest
Answer:
1m²
Step-by-step explanation:
Answer:
A = 157.3 units²
Step-by-step explanation:
A = 1/2(6.9)(8 x 5.7) = 157.3 units²
identify the pattern then write the next three terms in each sequence 2,8,32,128
Step-by-step explanation:
the difference is the previous term multiplied by 4 to get the next term
2,8,32,128,512,2048,8192
Hope that helps :)
Mr. Brown gave a test the day after a big football game and gave a different test the day after a half day for students.
The distribution with the larger median is ???
A. Test scores after football
B. Test scores after half day
The distribution with the larger mean is ???
A. Test scores after football
B. Test scores after half day
Answer:
The distribution with the larger median is test scores after football.
The distribution with larger mean is test scores after half day.
Step-by-step explanation:
Witch 3 ingredients will add up to $14.40? (Only one bowl can be chosen, bowls are required)
Solve the initial value problem below using the method of Laplace transforms
y" + 5y' + 6y-24 e t, y(0) -5, y'(0)-19 Click here to view the table of Laplace transforms Click here to view the table of properties of Laplace transforms y(t)= __
(Type an exact answer in terms of e.)
To solve the given initial value problem using the method of Laplace transforms, we'll take the Laplace transform of both sides of the differential equation. Let's denote the Laplace transform of the function y(t) as Y(s).
The Laplace transform of the second derivative y" is s²Y(s) - sy(0) - y'(0), where y(0) and y'(0) are the initial conditions given.
The Laplace transform of the first derivative y' is sY(s) - y(0).
The Laplace transform of the term 6y is 6Y(s).
The Laplace transform of the term -24e^t can be found using the table of Laplace transforms.
Applying the Laplace transform to the entire differential equation, we get:
s²Y(s) - sy(0) - y'(0) + 5(sY(s) - y(0)) + 6Y(s) - 24/(s-1) = 0
Substituting the initial conditions y(0) = -5 and y'(0) = -19, we have:
s²Y(s) + 5sY(s) + 6Y(s) - 5s + 19 - 24/(s-1) = 0
Now, we can solve this equation for Y(s). Once we find Y(s), we can take the inverse Laplace transform to obtain y(t), the solution to the initial value problem.
Since the given question doesn't specify a particular form for Y(s), I'm unable to provide the exact solution y(t) in terms of e.
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your velocity is given by v(t)=1t2 8 in m/sec, with t in seconds. estimate the distance, s, traveled between t=0 and t=8. use the average of the left and right sums with 4 subdivisions
To estimate the distance traveled between t=0 and t=8 using the average of the left and right sums with 4 subdivisions, we can approximate the area under the velocity curve.
The average of the left and right sums is a numerical integration technique used to estimate the area under a curve. In this case, we want to estimate the distance traveled, which corresponds to the area under the velocity curve.
Given that the velocity function is v(t) = t^2 - 8, we can divide the interval [0, 8] into 4 equal subdivisions. Using the left and right sums, we evaluate the velocity at the left and right endpoints of each subdivision and multiply it by the width of each subdivision.
Calculating the estimates for each subdivision and summing them will give us an approximation of the total distance traveled between t=0 and t=8.
To perform the calculation, we evaluate the velocity at the left endpoints of each subdivision (0, 2, 4, 6) and the right endpoints (2, 4, 6, 8). Then, we multiply each velocity value by the width of the subdivision (2 units). Finally, we sum these estimated distances to obtain the approximation of the total distance traveled.
The detailed calculations would involve substituting the values into the velocity function, multiplying by the width, and summing the results.
Therefore, by using the average of the left and right sums with 4 subdivisions, we can estimate the distance traveled between t=0 and t=8 for the given velocity function.
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Solve 7 sin(2x) = 6 for the two smallest positive solutions A and B, with A
To solve the equation 7 sin(2x) = 6 for the two smallest positive solutions A and B, we can use algebraic techniques and trigonometric properties.
The solutions A and B are approximately equal to A ≈ 0.287 and B ≈ 1.569, respectively.
To explain the solution, let's begin by rearranging the equation: sin(2x) = 6/7. Since the range of the sine function is between -1 and 1, the equation has solutions only if 6/7 is within this range. We can find the corresponding angles by taking the inverse sine (arcsin) of 6/7. Using a calculator, we find that the arcsin(6/7) is approximately 0.942.
However, this gives us only one of the solutions. To find the other solution, we can use the periodicity of the sine function. We know that sin(θ) = sin(π - θ), where θ is the angle in radians. Therefore, the second solution is π - 0.942, which is approximately 2.199. However, since we're looking for the smallest positive solutions, we need to consider only the values between 0 and 2π. Thus, the two smallest positive solutions are A ≈ 0.287 and B ≈ 1.569.
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In quadratic functions/equations; roots/solutions/x-intercepts/zeros all represent the same values/points.
True
False
Answer:
True
Step-by-step explanation:
Solutions to quadratic equations are often called
roots / zeros / x- intercepts
Which of the following shows the polynomial below written in descending
order?
Answer:
A. 4x¹² + 9x⁷ + 3x³ -x
Step-by-step explanation:
Hi!
==================================================================
To write a polynomial in descending order, we write the terms with higher degrees, or exponents, first.
3x³ + 9x⁷ -x + 4x¹²
4x¹² has the highest degree, so it is written as the first term.
⇒4x¹²
9x⁷ has the next highest degree, so it is written next.
⇒4x¹² + 9x⁷
3x³ has the next highest degree, so it is written next.
⇒4x¹² + 9x⁷ + 3x³
-x has the lowest degree, so it is written last.
⇒4x¹² + 9x⁷ + 3x³ -x
4x¹² + 9x⁷ + 3x³ -x
==================================================================
Hope I Helped, Feel free to ask any questions to clarify :)
Have a great day!
-Aadi x
A flywheel (I = 185.0 kg m2) rotating counterclockwise at 350.0 rev/min is brought to rest by friction in 5.0 min. What is the frictional torque on the flywheel (in N m)? (Indicate the direction with the sign of your answer
The frictional torque on the flywheel is `22.58 N.m` in the clockwise direction.
The formula for angular velocity is given by;`ω = (2π / T)`.Where;ω = angular velocity of the object. T = time period (in seconds).`I = 185.0 kg m2` represents the moment of inertia of the flywheel.`ω = 350.0 rev/min = (350.0 * 2π) / 60 = 36.61 rad/s` represents the initial angular velocity of the flywheel.
The flywheel is brought to rest by friction in `5.0 min = 5.0 * 60 = 300 seconds`.
The formula for the angular acceleration is given by;`α = (ωf - ωi) / t`. Where;`α` = angular acceleration of the object.`ωi` = initial angular velocity.`ωf` = final angular velocity of the object.`t` = time taken (in seconds).
At rest, the final angular velocity of the flywheel is zero.
Therefore;`α = (- ωi) / t`.The formula for torque is given by;`τ = I * α`.Where;τ = torque exerted on the object.I = moment of inertia of the object.α = angular acceleration of the object.
Substituting the values;`τ = I * α = 185.0 * (-36.61) / 300 = -22.58 N.m`.
Therefore, the frictional torque on the flywheel is `22.58 N.m` in the clockwise direction.
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3.
Convert the recurring decimal to fraction
A) 1.45°
Answer:
A
Step-by-step explanation:
Using the given values, create a confidence interval with a significance level of 0.1:
2, 4, 5, 7, 9, 6, 3, 1, 1, 2, 2, 6, 3, 10, 13
If the sample size decreased but alpha remained the same, what would happen to the length of the confidence interval?
If the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.
If the sample size decreases but the significance level (alpha) remains the same, the length of the confidence interval will typically increase.
In general, the length of a confidence interval is influenced by two main factors: the variability of the data (measured by the standard deviation or standard error) and the sample size. A larger sample size provides more information and reduces the variability, resulting in a shorter confidence interval.
When the sample size decreases, the amount of information available to estimate the population parameter decreases as well. This can lead to increased variability and uncertainty in the estimation process. As a result, the confidence interval tends to widen to account for the increased uncertainty and potential sampling error.
Therefore, if the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.
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7) Find the perimeter of triangle ABC. Round all answers to the nearest tenth.[6 points)
A
Please help!!! I’ll mark brain list too!
Answer: 14.6
Step-by-step explanation:
I made a square around the triangle which I then counted the squares, found the Pythagorean theorem, and then added the missing sides together
Find the 82nd term of the following sequence.
-32, -27, -22, ....
!!!!NEED HELP ASAP DUE SOON!!!!!This table of values represents a linear function. Enter an equation that represents the function defined by this table of values.
Answer:
y=3x+6
Step-by-step explanation:
Just test this on like a graph or something and you will see it works. Let me know if there is a fault in my answer. Thanks! Have a good day.
Glen is driving to the mega
mall that is 30 miles away from his
mom's house. On Glen's map app, his mom's house and the mega
mall are 5 inches apart. What is the scale on Glen's map?
A. 1 inch = 150 miles
B. - 1 inch = 35 miles
C. 1 inch = 25 miles
D. 1 inch = 6 miles
Answer:
D
Step-by-step explanation:
The probability of flu symptoms for a person not receiving any treatment is 0.021. In a clinical trial of a common drug used to lower cholesterol. 26 of 1133 people treated experienced flu symptoms. Assuming the drug has no effect on the likelihood of flu symptoms, estimate the probability that at least 26 people experience fiu symptoms. What do these results suggest about flu symptoms as an adverse reaction to the drug? (a) P(X226)
Using binomial probability, the probability that at least 26 people experience flu symptoms is 0.8788 and It indicates a potential adverse reaction to the drug, and further investigation or monitoring may be required to assess the relationship between the drug and flu symptoms.
What is the probability that at least 26 people experience flu symptoms?To estimate the probability that at least 26 people experience flu symptoms, we can use the binomial distribution. The probability of flu symptoms for a person not receiving any treatment is given as 0.021.
Let's denote the number of people treated who experience flu symptoms as X, which follows a binomial distribution with parameters n (number of trials) and p (probability of success).
In this case, n = 1133 (number of people treated) and p = 0.021 (probability of flu symptoms for a person not receiving treatment).
We want to find P(X ≥ 26), which is the probability that at least 26 people experience flu symptoms. To calculate this probability, we need to sum the probabilities of the complementary event (X < 26), which is the probability that fewer than 26 people experience flu symptoms.
Using statistical software or a binomial distribution table, we can calculate the probability as follows:
P(X ≥ 26) = 1 - P(X < 26)
Using the binomial distribution, we can calculate the probability of X < 26 as:
P(X < 26) = Σ[P(X = k)] for k = 0 to 25
Now, let's calculate the probability:
P(X < 26) = Σ[C(n, k) * p^k * (1 - p)^(n - k)] for k = 0 to 25
However, calculating this probability manually for each value of k can be cumbersome. Therefore, I'll use statistical software to estimate the probability.
Using the binomial distribution with parameters n = 1133 and p = 0.021, we find:
P(X < 26) ≈ 0.1212
Therefore, the estimated probability that at least 26 people experience flu symptoms is:
P(X ≥ 26) ≈ 1 - 0.1212 ≈ 0.8788
This suggests that the observed number of people experiencing flu symptoms (26) is higher than what would be expected if the drug had no effect on the likelihood of flu symptoms.
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help now please!!!!!! ^click picture
Answer:
A- lll
B- l
C- lV
D- V
E- ll
Step-by-step explanation:
I think that is the answer.
f(x) = x2. What is g(x)?
A. g(x) = -2-3
B. (X) = -x2
C. g(x) = x2-3
D. g(x) = -3/2
Answer: B
Step-by-step explanation:
The value g(x) if f(x) = x2 is g(x) = x2-3, the correct option is C.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
The function f(x)=x2
Now,
In the graph of g(x)
Coordinate x=0
Coordinate y=-3
Plugging in the values
g(x) = x2-y
y=3
g(x)=x2-3
Therefore, by the given function the answer will be g(x)=x2-3.
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PLEASE HELP!!! ILL GIVE BRAINLIEST
A map of a highway has a scale of 2 inches=33 miles. The length of the highway on the map is 6 inches. There are 11 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch=30 miles . How far apart are the rest stops on the new map?
How many inches apart are the rest stops?
Answer:
.305
Step-by-step explanation:
Step-by-step explanation:
2/33=6/x
x=99
since there are 11 rest stops and you are trying to find the space in the middle of the two rest stops.
99/11 rest stops
9 miles in between rest stops
9/y=30/1
9/30=y
3/10=y
.3 inches=y
Hope that helps :)
For her birthday, Gale received $200. She would like to spend all or some of the money to take
guitar lessons. After an initial $50 fee to cover rental equipment, each guitar lesson will cost $25.
Write an inequality to determine how many lessons Gale could take using her birthday money.
Highlight your inequality in green. Then, solve the inequality.
Answer:
The inequality that can be used to determine the number of guitar lessons Gale could take using her birthday money is:
[tex]25x + 50 \leqslant 200[/tex]
The solution to the inequality is:
[tex]x \leqslant 6[/tex]
She can take at most, 6 guitar lessons
Step-by-step explanation:
Total amount Gale received is $200
For rental equipment, she paid $50
Each guitar lesson will cost $25
Let x represent the number of lessons she could take, then the total amount she will spend must bot exceed $200
The guitar lesson will cost a total of 25x
So, her total spending will be:
[tex]25x + 50[/tex]
This must be at most $200
[tex]25x + 50 \leqslant 20[/tex]
Solving the above inequality:
[tex]25x \leqslant 200 - 50 = 150[/tex]
[tex]x \leqslant \frac{150}{25} = 6[/tex]
Why is it important to know the background of a poet.
Answer:
To understand their poems better
Step-by-step explanation:
First you have a general knowledge on why the author made the poem
Second you now have more info to use in order to understand the poems
Third is the same reason why there are people in history books.