The volume of the cylindrical shell will be 20 cubic unit using integration.
Indicate integrationIntegration is the process of calculating an integral. Integrals are used by mathematicians to compute a range of useful quantities, such as areas, volumes, displacement, etc. Usually, when we talk about integrals, we mean definite integrals. Indefinite integrals are used for antiderivatives. Integration is one of the two primary calculus topics in mathematics, along with differentiation (which measure the rate of change of any function with respect to its variables).
Fundamental IntegralAn integral that has both the upper and lower boundaries is said to be definite. Only a real line may be used for X to lay. A Riemann Integral is another name for the Definite Integral.
n example of an Integral is:
f(x)dx, from a to b.
Indefinite integral
∫f(x)dx = F(x) + C
Where C is any constant and the function f(x) is called the integrand.
Now,
As we can see in image
Volume = ∫x³.dx from 1 to 3 Using integration formula
=x⁴/4
=81/4-1/4
=80/4
volume =20 cubic unit
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5 T-shirts cost R120. How much will 9 cost?
A pizza place changed the size of their large pizzas from a 28-inch diameter to a 24-inch diameter. What is the percent change?
Consider the given matrix A and right-hand sides 6, and b2: [o.6 A = ~0.8 [ijp]. 6, = [o.8 [4 6= [1] 0.6 Find the pseudoinverse A+ Compute the projection matrices AtA and AA+ _ Find the ~best" solution z+ = A+b for each right-hand side. Which solutions fromn (c) arC exact? Which solutions are unique?
The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).
To find the pseudoinverse of a matrix A, the first step is to take the singular value decomposition (SVD) of A, which can be written as A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix with nonnegative singular values. The pseudoinverse of A is given by A^+ = VΣ^+U^T, where Σ^+ is the same as Σ except that the nonzero elements of Σ are replaced by their inverses.
Next, the projection matrices are given by AtA and AA+, which are used to project a vector onto the column space and the row space of A, respectively.
The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).
Whether a solution is exact or unique depends on the rank of A and the number of linearly independent columns and rows. If the rank of A is equal to the number of columns, then the solution is unique, otherwise, the solution may not be unique.
Therefore, The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).
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Find The Slope Of The Graph Of The Function At The Given Point F(T) = 5 - 3/5t (1/4, 13/5)
Answer:
The slope of a graph at a point can be found by computing the derivative of the function at that point. The derivative of the function f(t) = 5 - 3/5t is:
f'(t) = -3/5
So the slope of the graph of the function at the point (1/4, 13/5) is -3/5.
Your foot measures 10.8 inches. what proportion can you use to determine how many centimeters, x, it is? :A) 10.8in. 2.54in. xcm 1cm 2.54in. B) 10.8cm xin lcm C) 10.8in lin. хст 2.54cm D) 10.8in 2.54cm XCM lin
Your foot measure in centimeter is 4.25 centimeters and the proportion is 10.8 inches / 2.54 centimeters = x centimeters.
A proportion is an equation that states that two ratios are equal. It's often used to convert from one unit of measurement to another.
In your case, you want to convert 10.8 inches to centimeters, so you'll use a proportion to help you do that.
Here the correct proportion to use is 10.8 inches / 2.54 centimeters = x centimeters.
In this proportion, the first ratio on the left side of the equation represents 10.8 inches in terms of centimeters, and the second ratio on the right side of the equation represents x centimeters in terms of inches.
Since we know the conversion factor between inches and centimeters, 2.54 centimeters per inch, we can substitute that into the proportion.
=> 10.8 inches / 2.54 centimeters = x centimeters
=> 10.8 inches / 2.54 centimeters
=> 10.8 / 2.54 centimeters = 4.25 centimeters.
Therefore, 10.8 inches is equal to 4.25 centimeters.
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How long does it take for a deposit of $1400 to double at 5% compounded continuously?
Deposit of $1400 will be double in 14.2 years.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
Given,
Deposited Principal Amount P = $1400
Rate of interest r = 5% = 0.05
Amount A = double the deposit = 2× $1400 = $2800
Let the number of years = n
Amount A = P(1 + r)ⁿ
$2800 = $1400(1 + 0.05)ⁿ
(1 + 0.05)ⁿ = 2
Taking log on both side
n log(1.05) = log2
n = log2 / log(1.05)
n = 0.3010/0.0212
n = 14.2
Hence, It will take 14.2 years to double the deposit of $1400.
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Find the distance between the points (–5,5) and (9.6,5).
The distance between the two points is 14.6 units. The distance is always positive.
What is a point?
A point is a basic concept in classical Euclidean geometry that represents an exact location in space and has no length, width, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.
Given points are (–5,5) and (9.6,5).
The y-coordinate of both points is the same. The distance between two points is the absolute value of the difference of x-coordinates.
The x-coordinate of (–5,5) is -5.
The x-coordinate of (9.6,5) is 9.6.
The distance between points is
|-5 - 9.6| units
=|-14.6| units
= 14.6 units
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Simplify. Assume all variables are positive.
Answer:[tex]\sqrt[9^4]{10x}[/tex] there that should be ur answer ad ur hot
Step-by-step explanation:
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Which of the following tables represents a linear relationship that is also proportional?
x −1 2 5
y −1 0 1
x −2 −1 0
y −1 0 1
x −2 −1 0
y −4 −2 0
x −4 −2 1
y −2 0 3
Answer:
x −2 −1 0
y −1 0 1
Step-by-step explanation:
Condition:
A linear relationship is proportional if the ratio of the change in the dependent variable to the change in the independent variable is constant. This constant is known as the proportionality constant and can be represented by "k" in the equation y = kx. When a linear relationship is proportional, there is a direct relationship between the variables and as one increases, the other increases and vice versa.
The second table (x = -2, -1, 0 and y = -1, 0, 1) represents a linear relationship that is also proportional. A proportional relationship means that the ratio of y to x remains constant, or in other words, y is a constant multiple of x. In this table, for every 1 unit increase in x, y increases by 1 unit, making it proportional.
The third table represents a linear relationship that is also proportional.
find the z-score for which the area under the standard normal curve to its left is 0.96. round to two decimal places
The z-score for which the area under the standard normal curve to its left is 0.96 is approximately 1.75.
The z-score for which the area under the standard normal curve to its left is 0.96 can be found using a standard normal table or a calculator with a standard normal cumulative distribution function (CDF).
Using a standard normal table, we find that the z-score that corresponds to an area of 0.96 to its left is approximately 1.75.
Alternatively, using a calculator with a standard normal CDF, we can calculate the inverse CDF of 0.96:
z = invNorm(0.96)
This gives us a z-score of approximately 1.75.
Therefore, the z-score for which the area under the standard normal curve to its left is 0.96 is approximately 1.75, rounded to two decimal places.
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Find a power series representation for the function.
f(x) = x (1 + 8x)2
f(x) =[infinity] n = 0
Determine the radius of convergence, R.
R =
As a result, the radius of convergence, R, is equal to one. As a result, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 +...) = x + 16x^2 + 64x^3 +... This is the function f's power series representation (x).
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example.
Here,
The power series representation for f(x) = x(1 + 8x)^2 can be found by expanding the function (1 + 8x)^2 as a Taylor series centered at x = 0:
(1 + 8x)^2 = 1 + 16x + 64x^2 + ...
So, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 + ...) = x + 16x^2 + 64x^3 + ...
This is the power series representation for the function f(x).
To determine the radius of convergence, R, we use the formula:
R = 1 / limsup |a_n|^(1/n)
where a_n is the nth coefficient in the power series and limsup refers to the limit superior of the sequence {|a_n|^(1/n)}.
In this case, a_n = 16n x^n, so |a_n|^(1/n) = |16n|^(1/n) * |x|^(1/n). Since |16n|^(1/n) is a constant, the limit superior is just equal to |x|^(1/n). Therefore,
R = 1 / limsup |a_n|^(1/n) = 1 / |x|^(1/n) = 1
So, the radius of convergence, R, is equal to 1. So, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 + ...) = x + 16x^2 + 64x^3 + ... This is the power series representation for the function f(x).
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For George’s party, his dad bought an ice cream cake. After the party,
1/3 of the cake was left. The next day, George ate half of what was left. Choose the model that shows what fraction of cake George ate.
Answer: 4 aka the one on the bottom
Step-by-step explanation: There is 3 sections, only one filled in to make 1/3, then you split that in half
Answer:
1/6
Step-by-step explanation:
If we know that only 1/3 of the ice cream cake was left, and George ate 1/2 of that, we can use the equation:
1/3 ÷ 2 = 1/6
If we were to divide a fraction, we would take the denominator, in this case its 3, and multiply that by the amount being divided, which is 2.
2 × 3 = 6
Now that we have 6, simply add it back to the fraction denominator with the same numerator which is 1. This would make it 1/6.
Therefore, the picture that best matches this is the last one.
draw a curve through these points that illustrates the relationship between balloon rides and price when the temperature is constant at 50 degrees.
The curve for the relationship between balloon rides and price when the temperature is constant at 50 degrees is illustrated below.
The term constant in math is defined as a value or number that never changes in expression it's constantly the same.
When the temperature is constant, it means that one of the variables that can affect the demand for balloon rides is eliminated. This allows us to focus on the relationship between balloon rides and price. The relationship between these two variables can be represented by a curve. The curve can show us how the price of a balloon ride changes as the number of rides changes.
Then table for the relationship between balloon rides and price when the temperature is constant at 50 degrees is attached below.
when the temperature is constant, the relationship between balloon rides and price can be shown by a curve. The shape of the curve will depend on the relationship between the two variables, which can be upward-sloping, downward-sloping, or remain constant. The constant temperature allows us to focus on the relationship between balloon rides and price without the interference of other factors that can affect the demand for rides.
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Please help i got stuck!!!!
Divide using polynomial long division.
[tex](6x^2-5x+9) / (2x-1)[/tex]
Please help!!!!!!
Answer: 36=2547^3
Step-by-step explanation: calulat0r your welcome
The variables x
and y
vary directly. Use the values to find the constant of proportionality, k
. Then write an equation that relates x
and y
.
y=72; x=3
Answer: k = 24, y = 24x
Step-by-step explanation:
y = kx (the variables x and y varies directly)
when x = 3, y = 72
k = y/x = 72/3 = 24
y = 24x
Determine the intervals on which the following function is continuous. f(x) = x + 6/x^2 - 36 The function is continuous on the interval(s) (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.)
Function is continuous everywhere expect x = 6 and x = -6
What does a math interval mean?
In mathematics, an interval is quantified in terms of numbers. The range of numbers between any two specific numbers is known as the interval.
Every real number between those two values is included in this range. All kinds of numbers, including imaginary ones, are real numbers.
The function will not be continuous if the denominator becomes zero .
f(x) = x+6/(x² - 36 )
to become denominator zero -
x² - 36 = 0
(x + 6) ( x - 6 ) =0
x = 6 or x = -6
so at x = 6 and x = -6 the function is not continuous .
the interval for continuity is -
= ( -∞ , - 6), ( -6 , 6) , ( 6, ∞ )
In other words function is continuous everywhere expect x = 6 and
x = -6
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a student in a statistics class decided to analyze the number of candies per package for a project. a dot plot of the counts of candies in one package is shown below. what was the most common number of candies in a package?
To determine the most common number of candies in a package, the student would need to examine the dot plot and identify the value(s) with the highest frequency.
A dot plot is a type of graph that can be used to display the distribution of data by plotting individual observations as dots on a number line. To determine the most common number of candies in a package, the student would need to look at the dot plot and identify which value appears most frequently.
Typically, the most common number of candies in a package, also known as the mode, would be the value that has the highest number of dots plotted on the number line. If there are multiple values that have the highest frequency, then the data set is considered to have multiple modes. If all values in the data set appear with equal frequency, then the data set is considered to have no mode.
Thus, In conclusion, to determine the most common number of candies in a package, the student would need to examine the dot plot and identify the value(s) with the highest frequency.
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The most common number of candies in a package is 60
To analyze the number of candies per package for the project
60 candidates make up the majority of packages.
For a project in statistics class, a student chose to examine how many candies are contained in each container.
The maximum number of dots in a dot plot of the candy counts in one package is 60.
60 are the maximum limit of candies that can be placed in each and every package so these are the maximum number of candies that can be placed
The average candidate package has 60
So the most number of candies in each package are 60
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Need help ASAP PLEASE!
Using the fact that the sum of the interior angles must be 180°, we will get:
∠B = 101°
XYZ = 76°
How to find the measure of angle B?Let's solve the problem for the first triangle.
Ok, remember that the sum of the interior angles of any triangle is always equal to 180°, then we can write:
∠B + ∠C + ∠A = 180°
Replacing the values that we know we will get:
∠B + 44° + 35° = 180°
Now we can solve that equation to get:
∠B = 180° - 44° - 35° = 101°
So the answer is 101°.
For the second triangle, the interior angles are:
(5x + 1)
(3x + 11)
And, the one at the right is:
180° - 12x + 20
Then the sum gives:
(5x + 1) + (3x+ 11) + 180° - 12x + 20 = 180
5x + 1 + 3x + 11 - 12x + 20 = 0
-4x + 32 = 0
-4x = -32
x = 32/4 = 8
And XYZ = 12x - 20 = 12*8 - 20 = 76
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which process occurs between steps (iii) and (iv) in the diagram shown below?
Answer: Diploid cells divide to form four haploid daughter cells during mitosis.
Step-by-step explanation:
The answer is: Sister chromatids separate to form haploid daughter cells during meiosis.
What is chromatids?One of a chromosome's two identical halves that has undergone replication in order to facilitate cell division is referred to as a chromatid. A chromosomal region known as the centromere is where the two "sister" chromatids are fused.
One of the two identical copies of a duplicated chromosome is called a chromatid. At the centromere, a portion of the chromosome, the twin copies of the DNA join together during cell division. Sister chromatids are those that are joined. A chromosome is a protein and DNA-based structure that resembles a thread. It contains an organism's whole genetic makeup. Parents pass this on to their children. One of a chromosome's halves is called a chromatid. There is just one chromatid per chromosome.
The chromatids in each thread-like structure in the chromosome are the result of the chromosome's DNA replicating itself. Haploid cells are produced as a result of the segregation of the chromatids during meiosis II.
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The complete question is as follows:
Riggoletto's Portraits specializes in making circular portraits of people. A large portrait is 18 in. In diameter. A medium portrait is 6 in. In diameter. Estimate the difference between the areas of the two sizes of portraits. Use 3. 14 for T. Round your answer to the nearest whole number.
The estimated difference between the areas of the two sizes of portraits is 226.
First, find the area of the large portrait:
A = πr^2 = π(9)^2 = 3.14 * 81 = 253.94
Next, find the area of the medium portrait:
A = πr^2 = π(3)^2 = 3.14 * 9 = 28.26
Finally, subtract the area of the medium portrait from the area of the large portrait to find the difference:
253.94 - 28.26 = 225.68
Rounding to the nearest whole number, the difference is 226.
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A political scientist was interested in studying america's voting habits. So, he decided to make a least squares regression equation to predict the percentage of people in a state that would vote for obama in 2012 based on the percentage of people in a state that voted for obama in 2008. The least squares equation is y-hat = -4. 599 +1. 04x. In the state of wyoming, 32. 54% voted for obama in 2008; whereas, 27. 82% voted for him in 2012. What is the value of the residual?.
The residual in this case is 4.72%, which is calculated by taking the difference between the predicted value (32.54%) and the actual value (27.82%).
The political scientist's least squares regression equation predicted that 32.54% of people in Wyoming would vote for Obama in 2012. However, the actual percentage of people who voted for Obama in Wyoming in 2012 was 27.82%, which was lower than the predicted value. This difference between the predicted and actual value is the residual, which in this case is 4.72%. This suggests that the least squares equation was not very accurate in predicting the voting habits in Wyoming for the 2012 election.
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Maria is planting a row of flowers in a bed 37 feet long. The instructions say to space the plants 1 foot apart. The flowers come in flats containing 6 plants per flat
Maria has 6.33 flower plants remaining.
A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.
Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.
Given that the length of the bed is = 37 feet long
The space between plants is = 1 foot
Finding the number of plant flowers to be planted along this bed = 37/1 + 1 = 38 flower plants
Given that
6 flower plants= 1 flat
38*1/6= 6.33
The remaining flower plants are 6.33.
Complete question:
Maria is planting a row of flowers in a bed 27 feet long. The instructions say to space the plants 1 foot apart. The flowers come in flats containing 6 plants per flat.
How many flats will she need?
How many plants will she have left over?
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5. Parallelogram AB'C' D' was obtained by dilating parallelogram ABCD using A as
the center of dilation.
B
В'
A
D
a. What was the scale factor of the dilation?
b. How many congruent copies of ABCD have we fit inside AB'C' D'?
c. How does the area of parallelogram AB'C' D' compare to parallelogram
ABCD?
D'
d. If parallelogram ABCD has area 12 square units, what is the area of
parallelogram AB'C' D'?
A parallelogram is a two-dimensional shape with four straight sides that are parallel to one another and with opposite sides that are of equal length. The parallel and equal lengths of the opposing sides give the shape its name.
What is the dilating parallelogram?A rectangle that has been extended or contracted in one direction, or two congruent adjacent rectangles combined, can be used to describe a parallelogram.
a. The scale factor, when a dilation is carried out with centre of dilation A, is the ratio of the lengths of the corresponding sides of the pre-image and image. If the parallelograms ABCD and AB'C'D' have equivalent sides with lengths of AB and AB', respectively, the scaling factor is AB'/AB.
b. Set n equal to the total number of parallelograms ABCD that can fit inside parallelogram AB'C'D'.
Then, by multiplying the area of the parallelogram AB'C'D' by the area of the parallelogram ABCD, the area of the parallelogram AB'C'D' is equal to n times the area of the parallelogram ABCD.
c. The area of the parallelogram AB'C'D' is exactly proportional to the area of the parallelogram ABCD; as a result, if the scale factor of the dilation is k, the area of the parallelogram AB'C'D' is equal to k2 times the area of the parallelogram ABCD.
d. If the area of parallelogram ABCD is 12 square units, then the area of parallelogram AB'C'D' is equal to k2, or k2 times, the area of parallelogram ABCD.
Therefore, A parallelogram's adjacent sides and opposite sides combine to form a pair of neighbouring angles and two parallel lines, respectively.
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some of our farm fields are being left unused. does this have any implications for the economy's ppf diagram (with agricultural products on one axis and all other products on the other axis)?
Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.
The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.
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what is the resultant image of point B (9,-2) after a scale factor of 4, then a transition up 4 units?
Answer:
(36, -4).
Step-by-step explanation:
The scaled point B (9,-2) would be (36,-8) and after the translation up 4 units, the final image of B would be (36, -4).
Please help im begging!
Answer:(3*7)
Step-by-step explanation:
Which question can be represented by the equation 4 2/7 =
What is 4 groups of 2/7 s?
How many 2/7 s are in 4?
What is 2/7 of 4?
How many 4s are in 2/7?
The equation 4 2/7 = can be represented by the question: "What is 2/7 of 4?"
What is the arithmetic expressions?
An arithmetic expression is a mathematical phrase that can contain numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division.
The equation 4 2/7 = is asking for the value of 2/7 times 4. The right side of the equation is a mathematical expression that represents the product of 2/7 and 4. The value of this expression can be found by performing the calculation and replacing the expression with the resulting numerical value. In this case, 2/7 of 4 can be found by dividing 2 by 7 and then multiplying that result by 4. The answer to this question would give the value of 2/7 times 4.
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A company plans to build houses. The company will use 23
acres of land to build the houses. Each home will be built on acres. How many houses will the company build?
The number of houses that can be built are 94.
What is division?A division is a process of splitting a specific amount into equal parts.
Given that, a construction company plans to build houses. The company will use [tex]23\frac{1}{2}[/tex] acres of land to build houses. Each house will be built on a 1/4 acre lot.
We need to find the number of houses that can be built,
To find the number of houses, we will divide total area by area of one house.
Therefore,
Number of house = [tex]23\frac{1}{2}[/tex] ÷ 1/4
= 47/2 ÷ 1/4
= 47 x 2
= 94
Hence, the number of houses that can be built are 94.
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-3 = -2(h-1) + 5
h =
Answer:
h = 5
Step-by-step explanation:
-3 = -2(h-1) + 5
-3 = -2h + 2 + 5
-3 = -2h + 7
-10 = -2h
h = 5
Let's check
-3 = -2(5-1) + 5
-3 = -2(4) + 5
-3 = -8 + 5
-3 = -3
So, h = 5 is the correct answer.
how to determine how many rectangles we should use in order for our estimate to be accurate within some range.
To determine the number of rectangles needed to achieve a desired accuracy, one could start with a small number of rectangles, calculate the approximation error, and then increase the number of rectangles until the error is within the desired range.
How determine the number of rectangles?The number of rectangles to use in a rectangle approximation of a definite integral depends on several factors:
The desired accuracy: The smaller the desired accuracy, the more rectangles will be required.
The shape of the function: If the function is highly curved, more rectangles will be required to capture the shape of the function than if the function is more linear.
The range of integration: The larger the range of integration, the more rectangles will be required.
In general, to determine the number of rectangles needed to achieve a desired accuracy, one could start with a small number of rectangles, calculate the approximation error, and then increase the number of rectangles until the error is within the desired range. Alternatively, one can use mathematical techniques such as adaptive quadrature methods that automatically adjust the number of rectangles to achieve a desired accuracy.
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