consider the integral integral subscript 2 superscript 14 (2 x squared plus 4 x plus 2 )d x. (a) find the reimann sum for this integral using left endpoints and n equals 4. l subscript 4 equals (a) find the reimann sum for this integral using right endpoints and n equals 4. r subscript 4 equals
Answers
(a) the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.
(b) the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.
What is riemann sum?
A Riemann sum is a method used in calculus to approximate the area under a curve or the value of an integral. It involves dividing the region under the curve into smaller subintervals and approximating the area of each subinterval using a specific rule.
To find the Riemann sum using left endpoints and n equals 4, we need to divide the interval [2, 14] into four equal subintervals. The width of each subinterval, denoted as Δx, is calculated as (b - a) / n, where b is the upper limit (14) and a is the lower limit (2).
So, Δx = (14 - 2) / 4 = 12 / 4 = 3.
Now, we evaluate the function at the left endpoint of each subinterval and multiply it by the width (Δx).
The left endpoints for n = 4 are: x₀ = 2, x₁ = 5, x₂ = 8, x₃ = 11.
The Riemann sum using left endpoints is given by:
L₄ = f(x₀) Δx + f(x₁) Δx + f(x₂) Δx + f(x₃) Δx.
Now, let's substitute the given function f(x) = 2x² + 4x + 2 into the Riemann sum equation:
L₄ = (2x₀² + 4x₀ + 2) Δx + (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx.
L₄ = (2(2)² + 4(2) + 2) (3) + (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3).
L₄ = (8 + 8 + 2) (3) + (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3).
L₄ = (18)(3) + (72)(3) + (162)(3) + (288)(3).
L₄ = 54 + 216 + 486 + 864.
L₄ = 1620.
Therefore, the Riemann sum using left endpoints and n equals 4 is L₄ = 1620.
To find the Riemann sum using right endpoints and n equals 4, the process is similar. However, this time we evaluate the function at the right endpoint of each subinterval.
The right endpoints for n = 4 are: x₁ = 5, x₂ = 8, x₃ = 11, x₄ = 14.
The Riemann sum using right endpoints is given by:
R₄ = f(x₁) Δx + f(x₂) Δx + f(x₃) Δx + f(x₄) Δx.
Substituting the function into the Riemann sum equation:
R₄ = (2x₁² + 4x₁ + 2) Δx + (2x₂² + 4x₂ + 2) Δx + (2x₃² + 4x₃ + 2) Δx + (2x₄² + 4x₄ + 2) Δx.
R₄ = (2(5)² + 4(5) + 2) (3) + (2(8)² + 4(8) + 2) (3) + (2(11)² + 4(11) + 2) (3) + (2(14)² + 4(14) + 2) (3).
R₄ = (50 + 20 + 2) (3) + (128 + 32 + 2) (3) + (242 + 44 + 2) (3) + (392 + 56 + 2) (3).
R₄ = (72)(3) + (162)(3) + (288)(3) + (450)(3).
R₄ = 216 + 486 + 864 + 1350.
R₄ = 2916.
Therefore, the Riemann sum using right endpoints and n equals 4 is R₄ = 2916.
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Related Questions
What is the slope of 5?
Answers
A slope of 5 indicates that the corresponding y varies by 5 units for every unit change in x
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
Given:
The slope of 5.
Think of a slope of 5, which entails climbing 5 steps for each step you take. Much more quickly, you ascend to the top.
The slope is a measurement that indicates how much y shifts when x shifts.
For instance, a slope of 5 indicates that the corresponding y varies by 5 units for every unit change in x.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Therefore, think of a slope of 5, which entails climbing 5 steps for each step you take. Much more quickly, you ascend to the top.
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If:
JL = 26,
KL=3x + 7, and
JK = 8x + 8,
Find KL.
J
K
L
Answers
Answer:
KL = 10
Step-by-step explanation:
Given:
\(JL=26\)
\(KL=3x+7\)
\(JK=8x+8\)
From inspection of the given diagram:
\(JK+KL=JL\)
Substitute the given values into the found equation and solve for x:
\(\implies 8x+8+3x+7=26\)
\(\implies 11x+15=26\)
\(\implies 11x+15-15=26-15\)
\(\implies 11x=11\)
\(\implies \dfrac{11x}{11}=\dfrac{11}{11}\)
\(\implies x=1\)
Substitute the found value of x into the expression for KL:
\(\implies KL=3(1)+7\)
\(\implies KL=3+7\)
\(\implies KL=10\)
Formula we use,
→ JK + KL = JL
Now the value of x will be,
→ (8x + 8) + (3x + 7) = 26
→ 11x + 15 = 26
→ 11x = 26 - 15
→ x = 11/11
→ [ x = 1 ]
Then the value of KL will be,
→ 3x + 7
→ (3 × 1) + 7
→ 3 + 7 = 10
Hence, the value of KL is 10.
The length of one side, s, of a shipping box is s(x) = ^3√2x, where x is the volume of the box in cubic inches. A manufacturer needs the volume of the box to be between 108 in^3 and 256 in^3. What are the minimum and maximum possible lengths of s?
please help
Answers
Answer:
Hey
Step-by-step explanation:
Can u say me the chapter name of this question belonging to....!?
Answer:
min: 5
max:8
Step-by-step explanation:
f(x)=5sinx+cosx then f ′
(x)=−5cosx−sinx Select one: True False
Answers
False. The derivative of the function f(x) = 5sin(x) + cos(x) is not equal to -5cos(x) - sin(x). The correct derivative of f(x) can be obtained by applying the rules of differentiation.
To find the derivative, we differentiate each term separately. The derivative of 5sin(x) is obtained using the chain rule, which states that the derivative of sin(u) is cos(u) multiplied by the derivative of u. In this case, u = x, so the derivative of 5sin(x) is 5cos(x).
Similarly, the derivative of cos(x) is obtained as -sin(x) using the chain rule.
Therefore, the derivative of f(x) = 5sin(x) + cos(x) is:
f'(x) = 5cos(x) - sin(x).
This result shows that the derivative of f(x) is not equal to -5cos(x) - sin(x).
In summary, the statement that f'(x) = -5cos(x) - sin(x) is false. The correct derivative of f(x) = 5sin(x) + cos(x) is f'(x) = 5cos(x) - sin(x).
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The standard form of a circle is (x-5)^2+(y-5)^2=16. Convert the standard form into general form.
Answers
Therefore, the general form of the circle is:
\(x^2 + y^2 - 10x-10y+34=0\).
What is circle?A circle is a geometric shape that is defined as the set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). The distance from the center to any point on the circle is always the same. Circles are often represented using the symbol "O" or "⚪" and are important in mathematics, geometry, and physics. They have many properties, such as circumference (the distance around the circle), area (the space inside the circle), and diameter (the distance across the circle through the center). Circles are used in various fields, including architecture, engineering, and art.
To convert the standard form of a circle to the general form, we expand and simplify the equation as follows:
\((x - 5)^2 + (y - 5)^2 = 16\)
\(x^2 - 10x + 25 + y^2 - 10y + 25 = 16\) (using the identity \((a - b)^2 = a^2 - 2ab + b^2)\)
\(x^2 + y^2 - 10x-10y+34=0\)
Therefore, the general form of the circle is:
\(x^2 + y^2 - 10x-10y+34=0\)
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Solve for c.
c= -9 - 8c
Answers
c=-9-8c
+8c
9c=-9
c=-1
Hope this helps:D!!
The letter C is equal to negative one.
c = -1
Hope this helps!
An angle measures 112 What is the measure of its supplement?
Answers
The supplement of the angle that measures 112 degrees is 68 degrees.
How to find supplementary angles?Supplementary angles are those angles that sum up to 180 degrees.
In other words, two angles are supplementary when they add up to 180 degrees.
Therefore,
let the other supplement = x
Hence,
x + 112 = 180
x + 112 = 180
subtract 112 from both sides of the equation
x + 112 - 112 = 180 - 112
x = 68 degrees
x = 68 degrees
Therefore, the supplement of the angle that measures 112 degrees is 68 degrees.
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Graph a variety of functions, including piecewise functions, and evaluate limits graphically, numerically and analytically, including limits at infinity and infinite limits." 3cos(fix), x S-1 For the function f(x) = {-2x), – 1 1 = a) Sketch the graph of the function. b) Evaluate limx--1f(x) numerically. Confirm the value of this limit graphically, i.e. just look at your graph and see if the graph supports your limit answer. c) Evaluate limx-1f(x) algebraically. Confirm the value of this limit graphically. In parts b&c, be sure to make a clear conclusion about the value of each limit. Note: part b is approaching -1 and part c is approaching 1.
Answers
a) To sketch the graph of the function f(x) = {-2x), – 1 < x ≤ 1, we first observe that the function is defined piecewise.
For x values less than or equal to -1, the function is -2x. For x values greater than -1 and less than or equal to 1, the function is -1. b) To evaluate limx→-1 f(x) numerically, we substitute x values approaching -1 into the function. As x approaches -1 from the left side, we have f(x) = -2x, so limx→-1- f(x) = -2(-1) = 2. From the right side, as x approaches -1, f(x) = -1, so limx→-1+ f(x) = -1. Therefore, limx→-1 f(x) does not exist since the left-hand and right-hand limits do not match.
c) To evaluate limx→-1 f(x) algebraically, we refer to the piecewise definition of the function. As x approaches -1, we consider the values from the left and right sides. From the left side, as x approaches -1, f(x) = -2x, so limx→-1- f(x) = -2(-1) = 2. From the right side, as x approaches -1, f(x) = -1, so limx→-1+ f(x) = -1. Since the left-hand and right-hand limits are different, limx→-1 f(x) does not exist.
In conclusion, the graph of the function f(x) = {-2x), – 1 < x ≤ 1 consists of a downward-sloping line for x values less than or equal to -1 and a horizontal line at -1 for x values greater than -1 and less than or equal to 1. Numerically, limx→-1 f(x) does not exist as the left-hand and right-hand limits differ. Algebraically, the limit also does not exist due to the discrepancy between the left-hand and right-hand limits. This conclusion is supported by the graphical analysis of the function.
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Check
Consider the expression.
1. Express each exponent in expanded form:
6.6.6.6.6.6.6
6.6.6.6
6.6.6.6.6.6.6
6.6.6.6
2. Divide common factors:
What is the exponent of the simplified power?
Done
Answers
Answer:
\((a)\ \frac{6^7}{6^4} = \frac{6*6*6*6*6*6*6}{6*6*6*6}\) --- expanded form
\((b)\ \frac{6^7}{6^4} = 6*6*6\) --- Divide common factor
(c) The exponent of the simplified power is 3
Step-by-step explanation:
The original question is:
\(\frac{6^7}{6^4}\)
Required
- Express the exponents in expanded form
- Divide common factors
We have:
\(\frac{6^7}{6^4}\)
In indices:
\(x^2 = x * x\)
So, the above expression becomes:
\(\frac{6^7}{6^4} = \frac{6*6*6*6*6*6*6}{6*6*6*6}\)
Divide the common factors, to give:
\(\frac{6^7}{6^4} = 6*6*6\)
Express as an exponent
In indices;
\(x * x * x = x^3\)
So, we have:
\(\frac{6^7}{6^4} = 6^3\)
The simplified power is \(6^3\) and 3 is the exponent
PLEASE HELP ME!! IM ABOUT TO FAIL MY MATH CLASS
Laura and Brent paddled a canoe 6 miles upstream in four hours. The return trip took 3 hours. What is the rate at which they paddled the canoe?
This is supposed to be a system of equations question, but all the answers I’m seeing are solving them differently. PLEASE HELP!!
Answers
5(5-5)=4(5-5) why cant you cancel the 5-5
Answers
Answer:
you cannot cancel (5-5) because it is multiplied to 5 and 4 if the question was 5+(5-5)=4+(5-5) you can cancel 5-5
The reason that we can't cancel out the (5 - 5) is because it is attached to different numbers and as such they must be multiplied first with distributive property.
How to use properties of algebra?According to the distributive property of algebra, multiplying the sum of two or more addends by a number will give us the same result as when each addend is multiplied individually by the number and the products are added together.
This also applies to addition as well.
We are given;
5(5 - 5) = 4(5 - 5)
Now, according to the distributive property, we will have to first multiply out the bracket to get a solution. Thus, we can't cancel out the (5 - 5) because it is attached to different numbers and as such they must be multiplied first with distributive property in mind.
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rohan wants a field in the shape of trapezium . its side along the pond is parallel to and double the side along the road .Area of the field is 10200sqm.What is the length of the side along the river?
plss answer, will mark u the brainlliast
Answers
Answer:
The length of side along the river is 68 m
Step-by-step explanation:
Area of trapezium = 10200 m²
Length of side along the road (a) = x
Length of side along the river (b) = 2x
Height = 200 m
We need to find Length of side along the river.
The formula used is: \(Area\: of\: trapezium=\frac{a+b}{2}\times h\)
Putting values and finding length:
\(Area\: of\: trapezium=\frac{a+b}{2}\times h\\10200=\frac{2x+x}{2}\times 200\\10200=2x+2\times 100\\\frac{10200}{100} =2x+2\\102=3x\\x=\frac{102}{3}\\x=34\)
So, Value of x = 34
Length of side along the road (a) = x = 34
Length of side along the river (b) = 2x = 2(34) = 68
So, the length of side along the river is 68 m
How do I find the slope between (8,12) (10,20)
Answers
Answer: m = 4
hope thats right .
Step-by-step explanation:
Answer:
Let
Step-by-step explanation:
Let, (8,12) be (x1 and y1)
(10,20) be (x2 and y2)
We know that,
Slope = y2-y1
-----------.
x2-x1
= 20-12
-----------
10-8
= 8
-------
2
= 4 ans
so, the slope between twoo points is 4
Could someone help me please if you don’t mind thank you so much!
Answers
Answer:
m = 11
Step-by-step explanation:
Given
\(\frac{2}{5}\) (m + 4) = 6 ← multiply both sides by 5 to clear the fraction
2(m + 4) = 30 ( divide both sides by 2 )
m + 4 = 15 ( subtract 4 from both sides )
m = 11
This method avoids having to deal with awkward fractions
What is another way to express this problem
Answers
Answer:
It would be 16(3+2)
Step-by-step explanation:
Because, 16 times 3 is 48, Then 16 times 2 is 32. You add them then you get 80, which is the same answer as the original problem
Decide whether the triangles can be proven congruent by the given postulate or theorem. If not, state what information is needed. 11. AFLWAYLW by SAS
Answers
On this problem we have two triangles FLW and YLW. We know that the sides FL and LY are congruent and the side LW is shared between the two triangles. Therefore we know that two sides are congruent, we don't know however if the angles F and Y are congruents, there is no indication of that, so we can't prove that it is congruent, because we need to know if the angles are congruents.
Find the value of x in the triangle shown below
Answers
The answer is C, the square root of 65 (8.062).
The graph of a function is shown below. What is its range?
O (1, 2, 4)
O (1, 2, 3, 5)
O All real numbers.
O (1, 2, 3, 4)
Answers
(1,2,4)
Step-by-step explanation:Range describes the y-values of a graph.
Range
Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.
Finding Range
In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).
8 divided by 1766? please help me out
Answers
Answer:
220.75
Step-by-step explanation:
hope this helped
Answer:
1766/8=220.75
8/1766=0.00453001132
Step-by-step explanation:
Please help asap :(((
Answers
Answer:
The option you chose is correct (second option)
Step-by-step explanation:
This is because since -4x is only greater than and not equal to 20, the circle should be open. Then the larges the number, the better because a negative times negative is a positive. The product of -4x has to result in something larger than 20.
Hope this helps!
The average of the squared distanced of the data values from the mean.
Answers
The average of the squared distances of the data values from the mean is known as the variance.
Variance is a statistical measure that quantifies the spread or dispersion of a dataset. It is calculated by taking the mean of the squared differences between each data point and the mean of the dataset. By squaring the differences, the negative values are eliminated, and the distances from the mean are emphasized. The resulting variance value provides insights into how closely the data points are clustered around the mean. A larger variance indicates a wider spread of data points, while a smaller variance suggests a more concentrated distribution. Variance is commonly used in various fields, including finance, physics, and social sciences, to analyze and compare datasets.
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I WILL GIVE YOU BRAINLIEST ,5 STARS⭐, AND THANKS❤️. (P.S. AT LEAST TWO PEOPLE GIVE ANSWER SO I CAN GIVE BRAINLIEST)
Answers
Answer:
0.002
Step-by-step explanation:
cuz
Tekan-Tekan Sdn. Bhd. has order for 200 Model AS-120 calculator for delivery on day 200. The calculator consists of three parts. Components 2 and 3 form subassembly 1 . Sub-assembly 1 and component 4 form the final assembly. Following are the work centers and times of each operation. Table Q3(a) shows routine file of the operation. Assuming: - Only one machine is assigned to each operation - The factory works on 8-hour shift, 5 days a week - All parts move in one lot of 200. (a) Illustrate the backward schedule based on the information given above. (12 marks) (b) Identify when component 3 must be started to meet the delivery date. (2 marks)
Answers
Component 3 must be started on day 197 to meet the delivery date of day 200.
To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.
(a) Backward schedule:
Operation | Work Center | Time (hours) | Start Day
--------------------------------------------------------
Final Assembly | Work Center 1 | 1 | 200
Sub-assembly 1 | Work Center 2 | 2 | 199
Component 4 | Work Center 3 | 3 | 197
Component 2 | Work Center 4 | 4 | 196
Component 3 | Work Center 5 | 3 | ????
(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.
From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.
Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.
Hence, component 3 must be started on day 197 to meet the delivery date of day 200.
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3RD TIME ASKING PLS HELP
Answers
The angles surrounding the point p are 90 degrees
Then using the angle given, find the missing angles.
JPH = 90
HJP = 49
90+49 = 139
180 - 139 = 41
Therefore JHP = 41
HLP = HJP = 49
HLP = 49
KLP = 72
KLP + HLP = 72 + 49 = 121
Therefore, HLK = 121
LP = JP = 16
JP = 16
HL = HJ = 13
HL = 13
Hope this helps! =)
A city has 14,200 people. In a random sample
Answers
Answer:
43/80 * 14,200
Step-by-step explanation:
Since 80 random people were sampled its will become our denominator and out of 80 people there were 43 people and that 43 will become our numerator the next step is to mulitply 14,200 (im really bad at explaining stuff hope it helps!)
Answer:
43/80 * 14,200
Step-by-step explanation:
It was right when I answered it.
Rewrite the equation below so that it does not have fractions.
3/4x-5=3/8
Do not use decimals in your answer
Answers
Calculate costs given specific criteria
Compare costs given specific criteria
Create a moving and living plan given specific criteria
Directions: Complete the task below.
Task: You have been hired for a new job in another city. Your project is to create a moving and living plan that is within your budget. Your project must include the following:
1. The job description (The job description and salary must be reasonable and align with national averages.)
2. The location of your new job (must be at least 500 miles from your current residence)
3. The yearly gross and net income
4. Moving costs (You must compare two methods of moving to the new city)
Housing costs
Fixed and flexible expense amounts
Local newspapers or online advertisements to justify your decisions
The website address or name of sources you used in the project
Realistic pricing in this project
Use the information in the course to develop your plan.
Answers
Answer:
please mark me the brainliest
Step-by-step explanation:
Job Description: You have been hired as a software developer for a tech company in Austin, Texas. Your starting salary is $80,000 per year, which is in line with national averages for software developers with similar experience.
Location: Your new job is located in Austin, Texas, which is approximately 1,200 miles from your current residence in Chicago, Illinois.
Yearly Gross and Net Income: Your yearly gross income is $80,000. After taxes, your net income is approximately $62,400.
Moving Costs: To move to Austin, you have two options: renting a moving truck or hiring a professional moving company. After researching both options, you have decided to rent a moving truck for $1,500. This is more affordable than hiring a professional moving company, which would cost approximately $4,000.
Housing Costs: You have decided to rent an apartment in Austin. After researching local newspapers and online advertisements, you have found a one-bedroom apartment for $1,200 per month. This is within your budget and includes basic utilities such as water and trash.
Fixed and Flexible Expenses: Your fixed expenses include rent, car insurance, and student loan payments, which total approximately $2,000 per month. Your flexible expenses include groceries, entertainment, and other miscellaneous expenses, which you plan to keep under $800 per month.
Sources: To research housing costs and moving options in Austin, you used the following sources:
- Apartments.com
- Zillow.com
- U-Haul.com
- Budgettruck.com
- Austin American-Statesman (local newspaper)
Realistic Pricing: The pricing used in this project is based on current national and local averages, and is meant to be realistic and representative of actual costs.
Overall Moving and Living Plan:
- Rent a moving truck for $1,500
- Rent a one-bedroom apartment in Austin for $1,200 per month
- Keep fixed expenses at approximately $2,000 per month
- Limit flexible expenses to $800 per month
- Use local newspapers and online advertisements to find affordable housing and compare moving options
- Adjust budget as needed based on actual costs and expenses in Austin
By following this plan, you should be able to move to Austin and begin your new job within your budget. It is important to continue to monitor your expenses and adjust your budget as needed to ensure that you are able to live comfortably and save for the future.
I need the answer to this as well
find the measure of angle 6
Answers
Answer:
∠6 = 125°
Step-by-step explanation:
__________________________________________________________
FACTS TO KNOW :-
When any 2 lines intersect each other at any point , the vertical angles are always equal to each other .
__________________________________________________________
According to the figure ,
∠6 is present vertically opposite to the angle whose measure is 125°.
∴ Hence ∠6 = 125°.
When 8 spherical meatballs are dropped into a container of pasta sauce, the sauce level rises 3 inches. The container is a cylinder with a diameter of 20 inches. What is the volume of one meatball? Round answer to the tenth place
Answers
Answer:
117.8 cubic inches
Step-by-step explanation:
You want the volume of a meatball if 8 of them in a 20-inch diameter container raise the level of sauce by 3 inches.
VolumeIf 8 meatballs raise the level by 3 inches, the volume of one meatball is equivalent to the volume of a cylinder 20 inches in diameter and 3/8 inches high.
V = π/4·d²·h
V = (π/4)(20 in)²(3/8 in) = 300π/8 in³ ≈ 117.8 in³
The volume of one meatball is about 117.8 cubic inches.
__
Additional comment
That is the volume of a sphere about 6.08 inches in diameter. That's a pretty large meatball.
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What would you multiply by to decrease
an amount by 95%?
Answers
Answer:
-0.95
Step-by-step explanation:
Divide the percent by 100 and since you are decreasing it would be a negative.