Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top half of the circle x² + y² 16. The mass density of the wire is described by the function p(x, y) = x⁴y. Find the total mass of the wire.
Answers
To find the total mass of the wire, we need to integrate the mass density function p(x, y) over the region of the semicircle C. Since C is the top half of the circle x² + y² = 16, we can write it as y = sqrt(16 - x²), where x ranges from -4 to 4.
Thus, the mass of an infinitesimal piece of the wire, dm, is given by dm = p(x, y) * ds, where ds is the length of the infinitesimal piece of the wire.
Since the wire is in the shape of a semicircle, we can use the formula for the length of a curve to find ds:
ds = sqrt(1 + (dy/dx)²) dx
Here, dy/dx = -x/y = -x/sqrt(16 - x²), so we have:
ds = sqrt(1 + (x² / (16 - x²))) dx
Substituting p(x, y) and ds into the expression for dm, we get:
dm = x⁴y * sqrt(1 + (x² / (16 - x²))) dx
Integrating this expression over the range of x from -4 to 4 gives us the total mass of the wire:
m = ∫₋₄ ⁴ x⁴y * sqrt(1 + (x² / (16 - x²))) dx
To simplify the integration, we can make the substitution y = sqrt(16 - x²), which gives us:
m = ∫₋₄ ⁴ x⁴ * sqrt(16 - x²) * sqrt(1 + (x² / (16 - x²))) dx
This integral can be evaluated using a trigonometric substitution, but it is quite complicated. We can instead use a numerical method, such as Simpson's rule, to approximate the integral.
Assuming we use Simpson's rule with n = 100 subintervals, we get:
m ≈ 12.905
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Related Questions
Solve for indicated side. Round to the nearest hundredth.
Z=
Answers
Answer:
145.62
Step-by-step explanation:
sin 18° = 45/z
z sin 18° = 45
z = 45/sin 18°
z = 145.62
_____ show the change in one or more variables progressively across time. a. Histograms b. Pie charts c. Line graphs d. Bar charts e. Diagrams.
Answers
The correct answer is c. Line graphs show the change in one or more variables progressively across time.
Histograms show the distribution of data, pie charts show the proportions of a whole, bar charts compare categories or groups, and diagrams show the relationships between different elements.
The correct answer is c. Line graphs show the change in one or more variables progressively across time
A histogram is a visual depiction of data distribution in statistics. The histogram is shown as a collection of neighbouring rectangles, where each bar represents a certain type of data. Numerous fields use statistics, which is a branch of mathematics. Frequency, which can be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data.
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Line graphs show the change in one or more variables progressively across time. C
A line graph is a type of chart that displays data as a series of data points connected by straight lines.
The horizontal axis of the graph typically represents time, while the vertical axis represents the value of the variable being measured.
By connecting the data points with lines, a line graph can show the trend or pattern of change in the variable over time.
Line graphs are commonly used in fields such as economics, finance, and science to visualize trends in data over time.
They can be used to identify patterns, compare different variables, or forecast future trends.
In contrast, histograms, pie charts, bar charts, and diagrams are different types of charts that are used to display data in different ways.
Histograms are used to show the distribution of data within a single variable, while pie charts and bar charts are used to compare different categories or groups of data.
Diagrams are used to represent complex systems or relationships, often using visual symbols or icons to represent different components.
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PLZ HELP!! PLZ !!!!!!!!!!!!!
Answers
Answer:
16 tons, $9108
Step-by-step explanation:
Let's set up our equation. I can already tell you that each of these are linear equations. A linear equation can be set up with y=mx+b (slope-intercept form).
This will be helpful since the problem is telling you the slope (m) and the constant (b). b is also known as the y-intercept.
The problem says the first company charges $7500 to rent trucks plus an additional fee of $100.50 for each ton of sugar.
When you see the words, for each, per, for every, etc; that will be your slope (m). The $7500 is our constant (b).
Now to construct our equation for the first company it will be this:
y=100.50x+7500
Apply the same thing for the second company, $6296 to rent trucks plus $175.75 for each ton of sugar:
y = 175.75x+6296
Now that you have the equations of both companies, the problem is asking you for two things:
When will the companies have the same cost (x)What the cost will be when the cost is the same (y)But to this, we need some formula right? You could do this via looking on a graph but it may be hard if you don't have the appropriate technology. However, we just so happen to remember that we can set these equations together to find what value of x will both equations be the same.
Set the equations equal to each other:
\(175.75x+6296=100.5x+7500\)
And solve for x
\(175.75x+6296=100.5x+7500\\175.75x+6296-6296=100.5x+7500-6296\\175.75x=100.5x+1204\\175.75x-100.5x=100.5x-100.5x+1204\\\\75.25x=1204\\75.25x/75.25=1204/75.25\\x=16\)
When using this equation, this means that when x is 16, both equations will equal each other. We have solved the first question.
Now to solve for y, we replace x with the number we found, 16. You can choose any equation since they both will be the same at x = 16.
y=175.75(16) + 6296 = 9108
The cost will be $9108 when both companies cost the same amount.
Consider the initial value problem y'=ty(4-y)/(1+t), y(0)=ysubnot. (a) Determine how the solution behaves as t goes to infinity. (b) If y subnot equals 2, find the time T at which the solution first reaches the value 3.99. (c) Find the range of initial values for which the solution lies in the interval 3.99
Answers
Thus, the range of initial values for which the solution lies in the interval [3.99, 4] is ysubnot in (0, 4).
(a) As t goes to infinity, the denominator of the right-hand side approaches infinity while the numerator approaches 4ty. Thus, the solution approaches the equilibrium solution y=4.
(b) Using separation of variables and partial fractions, we can obtain the solution: y = 4 / (1 + 3e^(2t^2/2 + C)). Setting y = 3.99 and solving for t, we obtain t = sqrt[ln(3.99/0.01) / 2].
(c) We can rearrange the differential equation to obtain y'/(y(4-y)) = t/(1+t) and then integrate both sides. This gives ln|y/(4-y)| = C + ln(1+t) - t, where C is the constant of integration. To find the range of initial values for which the solution lies in the interval [3.99, 4], we need to solve the inequality 3.99 <= y <= 4 for y in terms of t. This gives the condition -∞ < t <= ln(999/1).
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Can someone plz help me with the answer
Answers
Step-by-step explanation:
\( \frac{12 \times 8}{2} + {( \frac{8}{2}) }^{2} \pi = \\ = 48 + 16\pi\)
98.24
Use the method of Frobenius and the larger indicial root to find the first four nonzero terms in the series expansion about x=0 for a solution to the given equation for x>0. 3xy''+(1-x)y'-2y=0 (Type an expression in terms of a0, up to the first four terms for the series.)
Answers
Thus, the first four nonzero terms in the series expansion are: y(x) = (5/81)x^(2/3) - (35/1944)x^(8/3) + O(x^(14/3)).
We begin by assuming a power series solution of the form:
y(x) = ∑(n=0 to ∞) c_n x^(n+r)
where r is the larger indicial root, and c_n are constants to be determined.
Differentiating y(x) with respect to x, we get:
y'(x) = ∑(n=0 to ∞) c_n (n+r) x^(n+r-1)
y''(x) = ∑(n=0 to ∞) c_n (n+r)(n+r-1) x^(n+r-2)
Substituting these expressions into the differential equation, we get:
3x∑(n=0 to ∞) c_n (n+r)(n+r-1) x^(n+r-2) + (1-x)∑(n=0 to ∞) c_n (n+r) x^(n+r-1) - 2∑(n=0 to ∞) c_n x^(n+r) = 0
Simplifying and grouping terms by powers of x, we get:
∑(n=0 to ∞) [3(n+r)(n+r-1)c_n + (n+r-2)c_(n-2) - 2c_n] x^(n+r) = 0
Since the power series is assumed to be nonzero, the coefficients of each power of x must be zero. Thus, we have the recurrence relation:
3(n+r)(n+r-1)c_n + (n+r-2)c_(n-2) - 2c_n = 0
To find the first few coefficients, we can use the larger indicial root r=2/3, which we can obtain from the indicial equation:
3r(r-1) = 0
Solving for r, we get r=0 or r=2/3. Since r=0 is the smaller root, we use r=2/3 for our power series solution.
For n=0, we have:
3(2/3)(2/3-1)c_0 - 2c_0 = 0
c_0 = 0
For n=1, we have:
3(5/3)(5/3-1)c_1 + (1/3)c_-1 - 2c_1 = 0
c_1 = 0
For n=2, we have:
3(8/3)(8/3-1)c_2 + (5/3)c_0 - 2c_2 = 0
c_2 = 5/81
For n=3, we have:
3(11/3)(11/3-1)c_3 + (7/3)c_1 - 2c_3 = 0
c_3 = -35/1944
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if rooms revenue is $75,884 and the total number of rooms sold is 662, then the average daily rate is: group of answer choices $114.63 $125.00 $118.75 $136.50
Answers
The average daily rate is calculated by dividing the total rooms revenue by the total number of rooms sold. In this case, the average daily rate is (option) $114.63.
The average daily rate is a measure of the average amount of money that a hotel is able to generate per room per day. It is calculated by dividing the total rooms revenue by the total number of rooms sold. In this case, the total rooms' revenue was $75,884 and the total number of rooms sold was 662, which gives us an average daily rate of $114.63. This is a useful measure for hotels to gauge the performance of their business and to set pricing accordingly. It also helps hotels identify opportunities for increasing revenue, such as offering discounts or promotions to attract more customers.
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Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=8.4 and x=7.3 and passes through the point (0,8.2).
Answers
Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)
What is parabola?The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.
According to given data:We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)
As we parabola is quadratic function,
f(x) = a(x-8.4)(x-7.3)
It is passing through the point (0, 8.2)
8.2 = a(-8.4)(-7.3)
a = 8.2/61.32 =7.5 (approx)
Now, equation of parabola is
F(x) = 7.5(x-8.4)(x-7.3)
f(x) = 7.5(x^2-7.3x-8.4x+61.32)
F(x) = 7.5(x^2-15.7x+61.32)
Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).
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what is a=1/4 b if b is the subject?
Answers
Answer:
b = 4a
Step-by-step explanation:
Given
a = \(\frac{1}{4}\) b
Multiply both sides by 4 to clear the fraction
4a = b
pls help meeeeeeeeeeee
Answers
Answer:
b=22/15 or 1.46 repeating
Step-by-step explanation:
Define carefully the following terms
I. Simultaneous equations system
II. Exogenous variables
III. Endogenous variables
IV. Structural form model
V. Reduced form model
Answers
In conclusion, a simultaneous equations system involves solving multiple equations together, exogenous variables are independent, endogenous variables are dependent, a structural form model represents causal relationships, and a reduced form model simplifies the relationships between variables.
I. Simultaneous equations system refers to a set of equations where multiple unknown variables are solved simultaneously. These equations are interdependent and must be solved together.
II. Exogenous variables are independent variables in a statistical or economic model. They are not influenced by other variables in the model and are often determined outside the system being analyzed.
III. Endogenous variables, on the other hand, are dependent variables in a statistical or economic model. They are influenced by other variables in the model and are determined within the system being analyzed.
IV. Structural form model is a representation of a system that shows the relationships between endogenous and exogenous variables. It describes the underlying theory or causal relationships between variables.
V. Reduced form model is a simplified version of the structural form model, where all variables are expressed as functions of exogenous variables. It focuses on the relationships between endogenous variables without considering the underlying theory or causality.
In conclusion, a simultaneous equations system involves solving multiple equations together, exogenous variables are independent, endogenous variables are dependent, a structural form model represents causal relationships, and a reduced form model simplifies the relationships between variables.
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Rewrite 40 − 8x^3 using a common factor.
Answers
Answer:
4(10-2x³)
Step-by-step explanation:
4×10=40
4×-2x³ = -8x³
final answer = 40 - 8x³
I NEED HELP PLEASE HELP IF YOU CAN ASAP
Answers
Answer:
C. None of these
Step-by-step explanation:
three identical circular coins are lined up in a row as shown. the distance between the centers of the first and third coins is 3.2 centimeters. what is the radius of one of these coins?
Answers
Since the coins are identical and lined up in a row, the distance between the centers of adjacent coins must be equal to the sum of their radii. Let r be the radius of one of these circular coins. Then, the distance between the centers of adjacent coins is 2r.
According to the problem, the distance between the centers of the first and third coins is 3.2 centimeters. This can be expressed as the sum of the distance between the first and second coins and the distance between the second and third coins:
3.2 = 2r + 2r
Simplifying:
3.2 = 4r
Dividing both sides by 4:
r = 0.8 centimeters
Therefore, the radius of one of these circular coins is 0.8 centimeters.
Let's call the radius of one of these circular coins "r". Since the coins are identical and lined up in a row, the distance between the centers of the first and third coins is equal to the sum of the diameters of the first two coins.
Step 1: Write the equation representing the relationship between the radius and the distance between the centers of the first and third coins:
2r (diameter of the first coin) + 2r (diameter of the second coin) = 3.2 cm
Step 2: Combine the terms on the left side of the equation:
4r = 3.2 cm
Step 3: Solve for the radius "r":
r = 3.2 cm / 4
r = 0.8 cm
The radius of one of these circular coins is 0.8 centimeters.
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I need help with the part that says “match the graph”!
Don’t bots or I’ll report them :)
Answers
7: Graph A
8: Graph B
9: Graph C
therefore: Graph A has infinitely MANY solutions; Graph B has ONE solution; Graph C has NO solution
also!! khan academy has a lesson that talks about this and is super helpful: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:systems-of-equations/x2f8bb11595b61c86:number-of-solutions-to-systems-of-equations/a/number-of-solutions-to-system-of-equations-review
funny they were already in order :) also could you please give me brainliest? all my brainliest answers disappeared :/
I need the correct answer
(Give the correct answer and an explanation on how you got it for brainlyist)
Answers
Answer:
1) 27/2 2) 8pi 3) 48 4) 16+2pi
Step-by-step explanation:
1) The length of the triangle is 9 (found by finding the distance between (-5,-3) and (4,-3)) and the height is 3 (found by finding the distance between (1,0) and (1,-3)). The area of a triangle is 1/2 (length times height) which in this case is 27/2.
2) The shape is a semicircle, so the area is 1/2 pi*r^2.
1/2 * pi * r^2=8pi
3) B*H=8*6=48
4) The figure is a semicircle and a square.
The area of the semicircle is 1/2 * pi * r^2=2pi
The area of the square is b*h=4*4=16
The area is 16+2pi.
8 x 9/9_ 8
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=
pls help my teacher will yell at me:(
Answers
Answer:
=
Hope that helps!
Step-by-step explanation:
How many solutions does the equation below have?
5
(
�
−
2
)
=
8
+
5
�
5(x−2)=8+5x
no solution
one solution
two solutions
infinitely many solutions
Answers
Answer:
It has no solution.
Step-by-step explanation:
5(x - 2) = 8 + 5x
5x - 10 = 8 + 5x
5x = 18 + 5x
0 = 18
The variable cancels out, so there is no solution to substitute it for.
as we wrap this up for stat 3113, recall that in class, we talked about how the statistics and could be calculated from a sample of data but that the parameters and could not be calculated. why is this?
Answers
Parameters are values that describe the entire population, while statistics are values that describe only a sample of the population. Since there is no way to know the exact values of the parameters, they cannot be calculated from a sample of data.
Parameters are values that describe the characteristics of the entire population. They are used to make inferences about the population and provide a basis for making decisions. On the other hand, statistics are values that describe only a sample of the population. They are used to estimate the parameters of the population. Since it is not possible to know the exact values of the parameters, they cannot be calculated from a sample of data. Instead, we use statistics to estimate the parameters. This is why it is important to use a representative sample when collecting data, as it provides a better estimate for the population parameters
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Tell whether the angles are adjacent or vertical. Then find the value of x.
The angles are angles
The value of x is
Answers
Answer:
If two angles have common side and they shares common vertex, they are called adjacent angles.
When two lines crosses each other, the opposite angles are called vertical angles as they share same vertex.
Two angles shown in diagram are adjacent as they are on common side.
Both the angles are on a straight line, hence
Subtracting 109 from both sides
Both angles shown in diagram are opposite to each other, hence vertical angles.
As they are opposite to each other, they both are equal.
Subtracting x from both sides
Subtracting 1 from both sides
Both angles are having a common side means they are adjacent angles.
As they are on straight line, both angles will add up to 180 °.
Subtracting 96 from both sides
Dividing from 6 in both sides
Hope it will help :)
Could these triangles be congruent?
B
E
O yes,
O yes, if AB - DE
s, if BC = 7
O yes, if AB EF
O no, because the hypotenuses must have different
lengths
A
7
С
D
7
F
Answers
Answer:
yes, if AB ≅ DE
Step-by-step explanation:
Triangles are said to be congruent if they have the same sides and the same angles.
The following measures are used to determine if triangles are congruent:
1) Angle-side-angle: If two angles and a side of a triangle is equal to two angles and corresponding side of another triangle, then they are congruent.
2) Side-side-side: If all three sides of a triangle is equal to three sides of another triangle, then the two triangles are congruent.
3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are congruent.
4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are congruent.
From the triangles DEF and ABC, already, they already have one equal triangle that is ∠F = ∠B and an equal side i.e DF = AC.
To satisfy congruence, two sides and an angle have to be equal, therefore if AB = DE then the two triangles would be congruent
Answer:
D). no, because the hypotenuses must have different lengths
Step-by-step explanation:
I just did the assignment on Edge and it's 100% correct.
Hope this helps!! Also heart and rate if you found this answer helpful!! :)
(1) A pizza restaurant had 3/5 of a gallon of pizza sauce left at the end of the evening and
divided it equally among 6 pizzas. How much sauce did they put on each pizza?
Answers
Answer:
The pizza restaurant put 1/10 of the sauce on each pizza.
Step-by-step explanation:
Take the 3/5, and on a calculator divide the 3 by the 5:
0.6
Then, take the 0.6 and divide it by the 6 pizzas:
0.1, converted into a fraction equals 1/10.
The pizza restaurant put 1/10 of the sauce on each pizza.
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
PLEASE HELP MEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
c
Step-by-step explanation:
Answer:
he would have 175
Step-by-step explanation: because if u have saved up 125 and multiplied it by 140 then it would be 175.
52 divided by 5424
198 div by 8549 but need to see how to get the correct answer . Don’t want to use a calculator
Answers
Answer:
52 / 5424 = 0.00958..
198 / 8549 = 0.0231 ..
Step-by-step explanation:
52 / 5424
First of all, you need to add 0 plus a coma → 0.
52 becomes 520, but this value is smaller than 5424, so we need to add another 0
5200 → another 0 → 52000
So now, we have 52000 / 5424.
We start, 5424 . 10 = 54240, we are higher than 52000, so let's try 9
5424 . 9 = 48816, great!
52000 - 48816 = 3184
This is smaller than 5424, so we need a zero, again. But we do not add 0 to the result, because we are in the decimal side
31840 → 31840 / 5424. We would try 6,
5424 . 6 = 32544. It's bigger!, We use 5
5424 . 5 = 27120!
31840 - 27120 = 4720. We get another 0
47200, and we try 8.
5424 . 8 = 43392
47200 - 43392 = 3808.
So we are going to add 0, until we have four digits that can be divided by 5424 and decimals are infinte.
52 / 5424 = 0.00958..
198 / 8549 → Need to add, the first 0 to convert 198 to 1980
1980 = 0. → Another zero
19800 = 0.0 → 19800 / 8549
We try 2 → 8549 . 2 = 17098
19800 - 17098 = 2702 → we add 0
27020 / 8549 → We try 3
8549 . 3 = 25647 → 27020 - 25647 = 1373 → we add 0
13730 / 8549 → We use 1 → 13730 - 8549 = 5181
As decimal are infinite, we can express the result as:
198 / 8549 = 0.0231 ..
A triangle has a base of 4 units and a height of 3 units. Mark draws the triangle again but
doubles the height. How does the area of the triangle change?
The area increases by 3 square units.
The area increases by 6 square units.
The area increases by 12 square units.
The area does not change.
Answers
Answer:
The area increases by 6 square units.
Step-by-step explanation:
The original area of triangle
A = 1/2 bh
a = 1/2 (4)*3
6 square units
Now we double the height
A = 1/2 (4) *6
A = 12 square units
The difference is 12-6 = 6 square units
Answer:
Second option: The area increases by 6 square units.
Step-by-step explanation:
A1 = ½ × 4 × 3 = 6 units²
A2 = ½ × 4 × 2(3) = 12 units²
Increase: 12 - 6 = 6 units²
Chooe the tatement that decribe an advantage of paying a bill through the mail without check
Answers
Paying a bill amount through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.
1. Paying a bill amount through the mail without check is a convenient and secure way of making payments.
2. It allows for payment to be made without having to visit a physical location to do so.
3. It also allows for payment to be made without having to use a credit or debit card.
4. Therefore, an advantage of paying a bill through the mail without check is that it is convenient and secure.
Paying a bill through the mail without check is convenient and secure, as it allows for payment without having to visit a physical location or use a credit or debit card.
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For f(x) =2x, find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. Simplify the sum and take the limit as n--> infinity to calculate the area under the curve over [2,5]
please show all of your work as be as descriptive as you can I appreciate your help thank you!
Answers
The area under the curve over [2,5] is 24.
Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.
Let us consider n subintervals. Therefore, width of each subinterval would be:
$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty }{ R } \\&= \lim _{ n\rightarrow \infty }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$
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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.
Therefore, the area under the curve over [2,5] is 21.
From the given data, we can see that the width of the interval is:
Δx = (5 - 2) / n
= 3/n
The endpoints of the subintervals are:
[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]
Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5
The formula for the Riemann sum is:
S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx
Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:
Δx = (5 - 2) / n
= 3/n
Therefore,
Δx = 3/3
= 1
So, the subintervals are: [2, 3], [3, 4], [4, 5]
The right endpoints are:3, 4, 5. The formula for the Riemann sum is:
S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx
Here, Δx is 1, f(x) is 2x
∴ f(c1) = 2(3)
= 6,
f(c2) = 2(4)
= 8, and
f(c3) = 2(5)
= 10
∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx
= 6(1) + 8(1) + 10(1)
= 6 + 8 + 10
= 24
Therefore, the Riemann sum is 24.
To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.
∴ Area = ∫2^5f(x)dx
= ∫2^52xdx
= [x^2]2^5
= 25 - 4
= 21
Therefore, the area under the curve over [2,5] is 21.
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(Aye, aye, captain)
I can't hear you
(Aye, aye, captain)
Oh Who lives in a pinneapple under the sea?
(Spongebob Squarepants)
Absorbent and yellow and porous is he?
(Spongebob Squarepants)
If nautical nonsense be something you wish?
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Then drop on the deck and flop like a fish
(Spongebob Squarepants)
Ready?
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Answers
Mr.david gave ross a number and asked him to divide it by 15. The quotient and remainder obtained by ross are 341 and 12 respectively. Find the number that teacher gave ross.
Answers
The number the teacher gave Ross is 5127
Word problems on linear equationsFrom the question, we are to determine the number that the teacher gave Ross
From the given information,
Mr. David gave Ross a number and asked him to divide it by 15.
Let the number be x
That is,
x/15
The quotient and remainder obtained by ross are 341 and 12 respectively
That is,
x/15 = 341 + 12/15
Now, we will solve the equation for x
x/15 = 341 + 12/15
Multiply through by 15
x = 15×341 + 12
x = 5115 + 12
x = 5127
Hence, the number the teacher gave Ross is 5127
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explain how to use a graph of the function f(x) to find f(3)
Answers
Answer:
Just find the coordinate at the point where the x-coordinate is 3
Step-by-step explanation:
F(x) is just another term for Y. The variable of X is the value that you input into the f(x), which just stands for a function. Since the value that they asked for was 3, you know that they inputted the value of 3 as x. Just look where the coordinate at the point where the x-coordinate is 3 to find the answer.
Answer:
Sample Response: For f(3), the input is 3 and you are looking for the output. To determine the function's value when x = 3, go to the value of 3 on the x-axis and then locate the graph for that value of x. Determine the value of y from the y-axis at that location on the graph.
Step-by-step explanation:
answer on edge2020