how to increase the accuracy of simpson rule and maclaurin series expansion respectively?
Answers
Because it matches a parabola to the curve rather than a straight line, Simpson's rule is more precise.
The other approaches are only accurate for functions whose graphs are linear, whereas Simpson's rule yields the exact area beneath the graphs of functions of degree two or less (parabolas and straight lines).Why is trapezoidal less accurate than Simpson's rule?
When the underlying function is smooth, Simpson's Rule is more accurate than the trapezoidal rule because it employs quadratic approximations rather than linear ones. In cases where there are an odd number of evenly spaced points, the formula is typically provided.What are Simpson's rule's restrictions?
It is obviously incorrect because the actual integral will always differ from it (except in some cases, such as the area under straight lines). Integrals, unlike Simpson's technique, allow you to obtain precise results in terms of basic constants.Learn more about Simpson's Rule
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Related Questions
find the sum of the first 46 terms of the following series to the nearest integer 12,15,18
Answers
Here, we want to find the sum of the first 46 terms of the series
Here, what we have is a series with a first term of 12 and a common difference of 15-12=18-15 = 3
Before we proceed to get the sum of the first 46 terms, we can calculate the last term
The last term is given as;
\(\begin{gathered} a_n\text{ = a + (n-1)d} \\ \\ a_{46}\text{ = 12 + (46-1)3} \\ \\ a_{46}\text{ = 12 + 45(3)} \\ \\ a_{46}\text{ = 12 + 135 = 147} \end{gathered}\)Now, we can apply the formula to get the sum
The formula is given as;
\(\begin{gathered} Sn\text{ = }\frac{n}{2}\text{ (a + l)} \\ \\ S_{46}\text{ = }\frac{46}{2}(12\text{ + 147)} \\ \\ S_{46}\text{ = 23(159)} \\ \\ S_{46}\text{ = 23 }\times\text{ 159 = 3657} \\ \text{Where the last term is given as l above} \end{gathered}\)A shirt originally cost $15, but it was marked down 5%. How much does the shirt cost now? Don't forget the $ symbol.
Answers
===============================================
Explanation:
There are two approaches we can take.
The first approach is finding the amount we save, which is 5% of 15 = 0.05*15 = 0.75 dollars or 75 cents.
So the new price is 15 - 0.75 = 14.25 dollars
----------------
The second approach is to think of it like this: If you save 5%, then you still have to pay the remaining 95% (the two percentages add to 100%).
95% of 15 = 0.95*15 = 14.25
This second approach is handy if you want to chain multiple discounts together. So let's say there's a special 10% off sale on top of the 5% discount. We would multiply by 0.90 to further discount by 10% and get to 0.90*0.95*15 = 12.825 = 12.83. It also works in reverse too and we could chain percent increases along with percent decreases.
A person places $9680 in an investment account earning an annual rate of 5.3%, compounded continuously. Using the formula V = P e r t V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.
Answers
Answer:
\(\displaystyle V \approx 25129.99\)
General Formulas and Concepts:
Math
Euler's number e ≈ 2.718Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Continuously Compounded Interest Rate Formula: \(\displaystyle V = Pe^{rt}\)
V is value of accountP is principle initially investede is base of lnr is rate of interestt is time in yearsStep-by-step explanation:
Step 1: Define
P = $9680
r = 5.3% = 0.053
t = 18 years
Step 2: Solve
Substitute in variables [Continuously Compounded Interest Rate]: \(\displaystyle V = 9680e^{0.053(18)}\)Multiply exponents: \(\displaystyle V = 9680e^{0.954}\)Evaluate exponents: \(\displaystyle V = 9680(2.59607)\)Multiply: \(\displaystyle V = 25129.988684793\)Round: \(\displaystyle V \approx 25129.99\)Two side lengths of a triangle are 7 inches and 12 inches. Which choice could be the length of the third side?
Answers
Answer:
between 2 and 12.
Step-by-step explanation:
Hope this helps :)
What is 4 & 1/2+1/8? *
Answers
Answer:
4 5/8
Step-by-step explanation:
Rewriting our equation with parts separated
=4+12+18
Solving the fraction parts
12+18=?
Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.
LCD = 8
48+18=58
Combining the whole and fraction parts
4+58=458
find the present value of 2400 due in 4months at 4.5% simple interest
Answers
Answer:
Step-by-step explanation:
Interest per annum - 4.5
Interest per 1/3 of an annum - 4.5 x 1/3 = 1.5%
Use the S.I formula,
2400 x (100 + interest)/100
= 2400 x (100 + 1.5)/100
= 24 x 101.5
= 12 x 203
= 2436.
Pls mark as brainliest for no real reason. Cheers
A population of bacteria is growing at a rate of 20% per hour. If the population starts at 320, what is it an hour later?
Answers
Answer:
384.
Step-by-step explanation:
The population is given by the expression;
\(Y(t) = Pr^{t}\)
Where;
Y(t) is the number of bacteria at time, t.
P is the starting amount.
r is the growth rate.
Given that, P = 320, r = 20% = 0.2, t = 1
Substituting the parameters into the equation;
\(Y(t) = Pr^{t}\)
Y(1) = 320 * 0.2¹
Y(1) = 320 * 0.2
Y(1) = 64.
Therefore, the population of bacteria increases hourly by 64.
An hour later; 320 + 64 = 384.
The map of a walking trail is drawn on a coordinate grid with three points of interest.
The trail starts at R(−3, 2) and goes to S(2, 2) and continues to T(2, −5). The total length of the walking trail is ____ units. (Input whole numbers only.)
PLEASEE HELPPPP!!!!!!!!
Answers
Answer:
12 units
Step-by-step explanation:
Given the points :
R(−3, 2) - - - > S(2, 2) - - - - > T(2, −5).
Distance between R and S
Distance between two points is obtained thus :
D = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Distance between R and S
x1 = - 3 ; y1= 2 ; x2 = 2 ; y2 = 2
D1 = sqrt((2 - (-3))^2 + (2 - 2)^2)
D1 = sqrt((5^2 + 0^2))
D1 = sqrt(25)
D1 = 5
Distance between S and T
x1 = 2 ; y1= 2 ; x2 = 2 ; y2 = - 5
D2 = sqrt((2 - 2)^2 + (-5 - 2)^2)
D2 = sqrt((0^2 + (-7)^2))
D2 = sqrt(49)
D2 = 7
Hence, total length = D1 + D2 = 5 + 7 = 12 units
Answer:
:'(
Step-by-step explanation:
Mr samuels purchased 6 bags of fertilizer for 8.70. She wants to purchase another 8 bags at this same unit price. How much will 8 bags of fertilizer cost
Answers
Answer:
The Evergreen Fertilizer Company produces fertilizer. The company's fixed monthly costis $25,000, and its variable cost per pound of fertilizer is $0.15. Evergreen sells thefertilizer for $0.40 per pound. Determine the monthly break-even volume for thecompany.Break Even Volume = Fixed cost / (Selling price per pound – Variable cost perpound)= 25000/(0.40-0.15)= 100,000 PoundsQuestion 12:If the Evergreen Fertilizer Company in problem 4 changes the price of its fertilizer from$0.40 per pound to $0.60 per pound, what effect will the change have on the break-evenvolume?Break Even Volume = Fixed cost / (Selling price per pound – Variable cost perpound)= 25000/(0.60-0.15)= 55,555.56 PoundsThe break even volume
Step-by-step explanation:
If a perpetuity pays a cash flow (C) every time period, forever, how come it is not worth an
infinite amount of money right now? Explain.
Answers
6) What is the mystery number?
The mystery number has ...
• 9 in the Ones place.
8 in the Millions place.
4 in the Hundred Thousands place.
3 in the Hundreds place.
3 in the Thousands place.
3 in the Tens place.
O in the Ten Thousands place.
Answers
is what I believe the mystery number would be
Answer:
8,403,339
Step-by-step explanation:
........................................
Answers
Answer:
a) x = 2 and x = 4
Step-by-step explanation:
A quadratic function is a mathematical function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x represents the independent variable.
The solutions of a graphed quadratic function are the x-values of the points where the parabola crosses the x-axis.
These solutions are also known as the x-intercepts, roots, or zeros of the quadratic function.
From inspection of the given graph, the function crosses the x-axis at x = 2 and x = 4.
Therefore, the solutions of g(x) = -x² + 6x - 8 are:
x = 2 and x = 4Answer:
x=2 and x=4.
Step-by-step explanation:
The solution of g(x)=-x^2+6x-8 is the point where the graph of the function intersects the x-axis. This point is (4,0) and (2,0).
Therefore, the solution of g(x)=-x^2+6x-8 is x=4 and x=2.
Another method:
Similarly, we can find the value of x by factorization method too.
g(x)=x^2+6x-8
let g(x)=0
0=x^2+6x-8
x^2-6x+8=0
doing middle-term factorization:
x^2-(4+2)x+8=0
x^2-4x-2x+8=0
x(x-4)-2(x-4)=0
(x-4)(x-2)=0
either
x=4
0r
x=2
Therefore x=4 and x=2.
You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per
minute. The second plan charges a monthly fee of $39.95 plus 11 cents per minute. How many minutes
would you have to use in a month in order for the second plan to be preferable? Round up to the nearest
whole minute.
minutes
Check Answer
Answers
HELP!!!
Rounded to the nearest tenth, approximately how many kilometers is 4,170,000 inches?
A.
10.6 kilometers
B.
16.4 kilometers
C.
106 kilometers
D.
164.2 kilometers
Answers
Solve the following system of equations.
6x -5y=13 & 9y-15+2x=0
Answers
x = 3
y = 1
Step-by-step explanation:Hi !
6x - 5y = 13
9y - 15 + 2x = 0
6x - 5y = 13
2x + 9y = 15 | ×(-3)
6x - 5y = 13
- 6x - 27y = - 45
add
6x - 6x - 5y - 27y = 13 - 45
- 32y = - 32 | ×(-)
32y = 32
y = 1
replace y = 1
6x - 5(1) = 13
6x - 5 = 13
6x = 13 + 5
6x = 18
x = 3
Good luck !
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, what would the same 30 second commercial have cost during the first Super Bowl in 1967, when the CPI was 33.4? Round your answer to the nearest hundred dollars.
Answers
In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.
To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).
The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.
Given data:
Cost of a 30-second commercial in 2021 = $5.6 million
CPI in 2021 = 271.4
CPI in 1967 = 33.4
To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:
Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)
Cost in 1967 = ($5.6 million) * (33.4 / 271.4)
Cost in 1967 ≈ $0.689 million
To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:
Cost in 1967 ≈ $68,900
For more such information on: CPI
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I need help in this pls:)
Answers
The value of angle x as shown in the diagram is 137°.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
To calculate the value of the angle x, we use the formula below
Formula:
x+93+86+44=360 (Sum of the angle in a quadrilateral)Solve for the value of x
x+223 = 360x = 360-223x = 137°Hence, the value of x is 137°.
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Match the vocabulary to the correct operation
Answers
Sum= Addition
Difference=Subtraction
Quotient=Division
Quantity=Parenthesis
Answer:
Step-by-step explanation:
Product—Multiplication
Sum— Addition
Difference—Subtraction
Quotient—Division
Quantity— Parenthesis
The support beams of truss bridges are triangles. James made a model of a truss bridge with a scale of 1 inch = 4 feet. If the height of the tallest triangle on the model is 9 inches, what is the height of the tallest triangle on the actual bridge?
Answers
The height of the tallest triangle on the actual bridge is 12 feet.
If James made a model of a truss bridge with a scale of 1 inch = 4 feet, we can use this information to find the height of the tallest triangle on the actual bridge.
Let x be the height of the tallest triangle on the actual bridge. Since the scale of the model is 1 inch = 4 feet, the height of the tallest triangle on the model can be converted to feet by multiplying by 4. Therefore, the height of the tallest triangle on the model is:
9 inches * (1 foot / 12 inches) * 4 = 3 feet
We can use the similarity of triangles to set up a proportion to find x. The corresponding sides of similar triangles are proportional. In this case, the height of the triangle on the model corresponds to the height of the triangle on the actual bridge, and the scale factor from the model to the actual bridge is 1/4 (since 1 inch on the model represents 4 feet on the actual bridge). Therefore, we have:
height of triangle on model / height of triangle on actual bridge = scale factor
3 feet / x = 1/4
Multiplying both sides by x, we have:
3 feet = (1/4) x
Multiplying both sides by 4, we have:
12 feet = x
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7. Kelly developed a formula for using a computer to find for a specific quote within a large set of articles.
The following function gives the length of the search, in seconds, over a set of n articles.
S(n) = 1.6 In (0.8n). What is the instantaneous rate of change of the search length for a set of 12 article:
Use correct units to explain the meaning of the answer.
Answers
instantaneous rate of change of the search length 0.1667 seconds per
How to find the instantaneous rate of change?We need to take the derivative of the function S(n) with respect to n and evaluate it at n=12 in order to determine the instantaneous rate of change of the search length for a set of 12 articles.
Taking the derivative of S(n) with respect to n using the chain rule, we get:
S'(n) = 1.6 * (1/(0.8n)) * 0.8 = 2/n
Evaluating this expression at n=12, we get:
S'(12) = 2/12 = 0.1667 seconds per article
This indicates that the search time will increase by approximately 0.1667 seconds per article if the set contains 12 articles by one unit. Alternately, the search time per article will decrease by approximately 0.1667 seconds if the set's number of articles decreases by one unit from 12.
Therefore, the units for the instantaneous rate of change are "seconds per article", indicating the change in search time for each additional or fewer article in the set.
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anyone knows how to solve this
Answers
Answer:
x = 4
Step-by-step explanation:
the angle immediately to the left of 20x must be 25x. that's because the two lines with double arrows at the top are parallel lines.
the angle to the left of 20x and the 25x are called alternate angles. they are equal.
also, 20x and the angle to the left of it are on a straight line. angles on a straight line add up to 180°.
so, we now have 20x + 25x = 180.
45x = 180
divide both sides by 45:
x = 180/45
= 4.
x = 4.
What is the circumference of the circle? Use 3.14 for Pi. A circle with radius 6.4 centimeters.
Answers
Answer:
C≈40.21cm
Step-by-step explanation:
Answer:
40.192
Step-by-step explanation:
the radius is half of the diameter so the diameter is 12.8 now 12.8 times pi / 3.14
please help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
second is 24
Third is 12
Answer:
1 is 12
2 is 106
3 is 42
Step-by-step explanation:
1: PEMDAS. 5x2=10 4 to the power of 2 is 16 so 18-16=2 2+10=12
2: 9 to the power of 2 is 81. 4x7=28 28-3=25 81+25=106
3: 5 to the power of 2 is 25 7x3=21 25-4=21 21+21=42
what is the product of 2/1 and (-2/3)?
Answers
Answer: -4/3 or - 1 1/3
Step-by-step explanation: 2 times -2 = -4 and 3 times 1 is 3.
Max points I need these answered quick
Answers
Answer:
3/5...
Step-by-step explanation:
Just trust me
Answer:
3/5
Step-by-step explanation:
The angle of elevation to the top of a Building in New York is found to be 10 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths. Hint: 1 mile = 5280 feet
Answers
Answer:
931.00
Step-by-step explanation:
First, we need to draw out a right triangle.
The building will be the opposite, the ground will be the adjacent, and the angle of elevation will be the hypotenuse.
Angle B is 10 degrees, and the adjacent is 5280 feet.
We can find the opposite using trigonometric ratios
tan 0 = opposite/adjacent
Now we solve this equation.
Substitute 5280 for the adjacent
tan 0 = x/5280
0 is the degree, so it would be 10. Substitute this in
tan 10 =x/5280
solve for tan 10
0.1763 =x/5280
Solve for x
0.1763 Times 5280 = x
x= 931.0065
rounded to the nearest tenth, our answer is 931.00
so, the opposite side, or the height of the building, is 931.00
Hope this helps! Have a great rest of your day!
PLEASE HELP ME
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the expressions with their simplified forms.
Answers
(a) √2 · √8. The simplified surd expression is 4.
(b) √80. The simplified surd expression is 4√5.
(c) √5/√20. The simplified surd expression is 1/2.
(d) √20. The simplified surd expression is 2√5.
What is the simplification of the surd expression?The given surd expression is simplified as follows;
(a) √2 · √8
we can simplify it as;
√2 · √8 = √(2 x 8) = √16 = 4
(b) √80
we can simplify it as;
√80 = √ (16 x 5) = √16 x √5 = 4√5
(c) √5/√20
we can simplify it as;
√5/√20 x √20 / √20
= (√5 x √20 ) /(20)
= √100 / 20
= 10/20
= 1/2
(d) √20
we can simplify it as;
√20 = √4 x √5 = 2√5
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Bill paid $45in tax on a laptop that cost $500. What percent sales tax did Bill pay?
Answers
Answer:
9%
Step-by-step explanation:
9% of 500 is 45
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
Answers
Answer:
1. >
2. <
3. =
4. <
Step-by-step explanation:
23.197 > 23.179
3 2/10 which is the same as,
3.2 < 3.243
30.423 = 30 423/1000
18.546 < 18 56/100
The dot plot shows the prices (in dollars) of jeans. What are the most appropriate measures to describe the center and the variation? Find the measures you chose.
Answers
To describe the center of the data, we can use either the mean or the median.
To describe the variation of the data, we can use either the range or the interquartile range (IQR).
Looking at the dot plot, it seems that the data is somewhat skewed to the right, with a few high-priced outliers. In this case, the median and the IQR may be more appropriate measures of the center and variation, respectively, as they are less sensitive to outliers.
To find the median and IQR:
Arrange the data in order from smallest to largest.
Find the median, which is the middle value. If there are an even number of values, take the average of the two middle values.
Find the first quartile, which is the median of the lower half of the data.
Find the third quartile, which is the median of the upper half of the data.
Calculate the IQR as the difference between the third quartile and the first quartile.
Here are the steps applied to the dot plot:
We can see that the smallest value is about 20 and the largest value is about 120, giving a range of 100 dollars.
The median is approximately 60 dollars, as it is the middle value between the 11th and 12th data points when the data is arranged in order.
The first quartile is approximately 40 dollars, as it isthe median of the lower half of the data points, which are found below the median.
The third quartile is approximately 80 dollars, as it is the median of the upper half of the data points, which are found above the median.
The IQR can be calculated as the difference between the third quartile and the first quartile, which is approximately 40 dollars.
Therefore, the most appropriate measures to describe the center and the variation for this data set are the median and the interquartile range (IQR), respectively. The median is approximately 60 dollars, and the IQR is approximately 40 dollars.