Let f(x) = x^2, and compute the Riemann sum of fover the interval [6, 81, choosing the representative points to be the left endpoints of the subintervals and using the following number of subintervals (a) (Round your answers to two decimal places)
Two subintervals of equal lengtj (n = 2)
Answers
the Riemann sum of f(x) = x^2 over the interval [6, 81] with two subintervals of equal length, using the left endpoints as the representative points, is approximately 72318.75.
To compute the Riemann sum of f(x) = x^2 over the interval [6, 81] with two subintervals of equal length, we divide the interval into two subintervals: [6, 43.5] and [43.5, 81].
Since we are using the left endpoints as the representative points, the left endpoint of the first subinterval is 6, and the left endpoint of the second subinterval is 43.5.
Next, we calculate the width of each subinterval. The width is obtained by taking the difference between the endpoints of each subinterval: 43.5 - 6 = 37.5.
To compute the Riemann sum, we evaluate the function f(x) = x^2 at the left endpoint of each subinterval and multiply it by the width of the subinterval.
For the first subinterval: f(6) * 37.5 = 36 * 37.5 = 1350.
For the second subinterval: f(43.5) * 37.5 = 1892.25 * 37.5 = 70968.75.
Finally, we sum up the individual products to obtain the Riemann sum: 1350 + 70968.75 = 72318.75.
Therefore, the Riemann sum of f(x) = x^2 over the interval [6, 81] with two subintervals of equal length, using the left endpoints as the representative points, is approximately 72318.75.
Learn more about Riemann sum here:
https://brainly.com/question/30404402
#SPJ11
Related Questions
Answer the following questions a Find A b 3 whose eigenvalues are 1 and 4, and whose eigenvectors are *> respectively b Find B whose eigenvalues are 1 and 3
Answers
This gives us the equation -2x + y = 0 and 4x - 3y = 0, which has the solution x = y/2. Therefore, the eigenvector for λ = 3 is v2 = [1; 2].
a) To find matrix A with eigenvalues 1 and 4 and corresponding eigenvectors v1 and v2 respectively, we can use the formula A = PDP^-1 where P is the matrix of eigenvectors and D is the diagonal matrix of eigenvalues.
We know that v1 and v2 are eigenvectors with eigenvalues 1 and 4 respectively, so we can set up the following equations:
Av1 = 1v1 and Av2 = 4v2
Multiplying both sides of each equation by P^-1, we get:
PDv1 = v1 and PDv2 = 4v2
Therefore, P = [v1 v2] and D = [1 0; 0 4], which gives us the matrix A = PDP^-1.
b) To find matrix B with eigenvalues 1 and 3, we can use the same formula A = PDP^-1. However, we don't know the eigenvectors yet. To find them, we can use the characteristic polynomial of B, which is (1-λ)(3-λ) = 0. This gives us eigenvalues λ = 1 and λ = 3.
To find the eigenvectors for λ = 1, we need to solve the equation (B-λI)v = 0, which gives us:
(B-1I)v = 0
[0 1; 1 2][x; y] = [0; 0]
This gives us the equation x + y = 0, so the eigenvector for λ = 1 is v1 = [1; -1].
To find the eigenvectors for λ = 3, we need to solve the equation (B-λI)v = 0, which gives us:
(B-3I)v = 0
[-2 1; 4 -3][x; y] = [0; 0]
Using these eigenvectors and the formula A = PDP^-1, we can find the matrix B = PDP^-1 where P = [v1 v2] and D = [1 0; 0 3].
To learn more about : eigenvector
https://brainly.com/question/17079851
#SPJ11
If 5/8 of a number is 40, what is quarter of the number
Answers
Answer: 16
If 5/8 of a number, let's call it x, is 40, we can set up the following equation:
5/8 * x = 40
Dividing both sides by 5/8, we get x = 64
Now that we know that the number is 64, we can find a quarter of it by multiplying by 1/4 as follows:
64 * (1/4) = 16
For the curve given by r(t) = (-8t, -6,1 + 91²), Find the derivative pl (t) = ( ) Find the second derivative p" (t) = 10 0 18 Find the curvature at t=1 ( )
Answers
The derivative p'(t) of the curve r(t) = (-8t, -6, 1 + 91t^2) is given by (-8, 0, 182t). The second derivative p"(t) is (0, 0, 182). To find the curvature at t = 1,
To find the derivative p'(t), we differentiate each component of the curve separately. The x-component of p'(t) is the derivative of -8t, which is -8. The y-component is the derivative of -6, which is 0. The z-component is the derivative of 1 + 91t^2, which is 182t. Therefore, p'(t) = (-8, 0, 182t).
The second derivative p"(t) is obtained by differentiating each component of p'(t). Since the derivative of -8 is 0, the x-component of p"(t) is 0. The y-component is also 0 since the derivative of 0 is 0. The z-component remains as 182. Thus, p"(t) = (0, 0, 182).
To find the curvature at t = 1, we substitute t = 1 into p'(t) and calculate the magnitude of p'(t), which is |p'(t)|. Then, we calculate the magnitude of p'(t) cubed, which is |p'(t)|^3. Finally, we divide |p'(t)| by |p'(t)|^3 to obtain the curvature at t = 1. Overall, by finding the derivatives and applying the curvature formula, we can determine the curvature at t = 1 for the given curve.
Learn more about curves here: brainly.com/question/29736815
#SPJ11
Researchers investigated whether there is a difference between two headache medications, R and S. Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication. Have the conditions been met for inference with a confidence interval for the difference in population means? A Yes, all conditions have been met. B No, because the data were not collected using a random sample. © No, because cause and effect cannot be inferred since there is a random sample No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal. (E) No, because the sample sizes are not the same.
Answers
The correct answer is option D. No, because the sample sizes are not large enough to assume the distribution of the difference in sample means is approximately normal.Researchers investigated whether there is a difference between two headache medications, R and S.
Researchers measured the mean times required to obtain relief from a headache for patients taking one of the medications. From a random sample of 75 people with chronic headaches, 38 were randomly assigned to medication R and the remaining 37 were assigned to medication S. The time, in minutes, until each person experienced relief from a headache was recorded. The sample mean times were calculated for each medication.To construct a confidence interval, we require that some conditions are satisfied. The assumptions that should be met for inference with a confidence interval for the difference in population means are as follows:The data is independent;The data in each group should be roughly normally distributed;Both groups have the same variance, and each group should have a large enough sample size so that the central limit theorem (CLT) holds. The CLT holds for the difference in the sample means since both samples are taken from a population that is normally distributed. We can also assume that the sample size is large enough to use the t-distribution since each sample has more than 30 observations. As a result, all of the conditions have been met. As a result, we may employ a t-distribution to make inferences about the population difference between the two headache medications.
for more questions on headache
https://brainly.com/question/14974427
#SPJ11
need help w this question thanksss!
Answers
Given:
A figure of a circle.
To find:
The value of x.
Solution:
Central angle theorem: According to this theorem, the central angle on an arc is twice of the subtended angle on that arc.
Using the central angle theorem, we get
\(x=2\times 35^\circ\)
\(x=70^\circ\)
Therefore, the value of x is 70 degrees.
x and y are integers.
x>4
y < 10
Work out the smallest negative value of x - y.
Answers
If x and y are integers and x>4 and y<10 then the smallest negative value of x - y is -4.
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality'. So, a lack of balance results in inequality.
If two things are not equal, the first value can be either greater than (>) or lesser than (<) or greater than equal to (≥) or less than equal to (≤) the second value.
According to the given question:
The given variables x and y are subjected to inequality > and < respectively. This implies the values each variable can have.
As given x > 4 ⇒ x = 5, 6, 7, 8, 9, 10, ....
Similarly y < 10 ⇒ y = 9, 8, 7 , 6, 5, ..., 0, -1, -2, -3, -4, ....
Let's work out the smallest value of x - y using trial and error method
Let x = 5 (smallest values of x) and y = -2 (negative value of y)So, x - y = 5 - (-2) = 7
7 is not a negative value.
Therefore y cannot have negative values as subtraction operation
will lead to positive value.
Let x = 5 and y = 6x - y = 5 - 6 = -1
- 1 is a negative number but not the smallest as y can attain values
more than 6.
Let x = 5 and y = 9 (highest value of y)x - y = 5 - 9 = -4
- 4 is the smallest negative value
Therefore if x and y integers subjected to the given inequality, the smallest negative value x - y can attain is -4.
To learn more about inequality visit
https://brainly.com/question/17675534
#SPJ1
-2/3x = -1. What’s the answer?
Answers
Incase you need it in decimal point it’s X=1.5 and Mixed number form it’s X=1 1/2
Explanation : Solve the rational equation by combining expressions and isolating the variable x
The following table lists the ages (in years) and the prices (in thousands of dollars) by a sample of six houses. Age Price 165 182 205 161 180 161 For the regression of price on age, the estimated values of A and B, rounded to two decimal places, are:
Answers
The estimated values of A and B for the regression of price on age are A= 65.67 and B= 0.41.
To find the estimated values of A and B, we need to use the formula for simple linear regression: Y = A + BX, where Y is the dependent variable (price), X is the independent variable (age), A is the intercept, and B is the slope.
We can start by calculating the means of the age and price variables:
mean age = (165 + 182 + 205 + 161 + 180 + 161) / 6 = 174.33
mean price = (182 + 205 + 161 + 180 + 161 + 161) / 6 = 174.83
Next, we need to calculate the sample covariance and variance:
covariance = [(165-174.33)(182-174.83) + (182-174.33)(205-174.83) + (205-174.33)(161-174.83) + (161-174.33)(180-174.83) + (180-174.33)(161-174.83) + (161-174.33)(161-174.83)] / 5
= -301.1
variance of age = [(165-174.33)^2 + (182-174.33)^2 + (205-174.33)^2 + (161-174.33)^2 + (180-174.33)^2 + (161-174.33)^2] / 5
= 771.77
Now we can calculate the slope:
B = covariance / variance of age
= -301.1 / 771.77
= -0.39
And the intercept:
A = mean price - B * mean age
= 174.83 - (-0.39 * 174.33)
= 65.67
Therefore, the estimated values of A and B for the regression of price on age are A= 65.67 and B= 0.41 (rounded to two decimal places).
To know more about regression of price visit:
https://brainly.com/question/8952452
#SPJ11
BRAINLEST to whoever
Solve the given proportion
X= ?
Answers
Answer:
49
Step-by-step explanation:
ayudenme con esto por favor
Answers
Answer:
the answer is on the computer
Step-by-step explanation:
!!!!!! What are the names of four coplanar points?
Answers
These points are all in the vertical plane shown in the diagram. Think of the plane as a flat sheet of paper that doesn't bend.
Only points L and K are outside of this plane. So if we listed {L, D, A, J} then that list of points isn't coplanar.
A, B, D, J points are all in the vertical plane shown. The plane as a flat sheet of paper that doesn't bend.
How to find if the point are coplanar or not?The points are not coplanar if there does not exist any plane that contains those points.
Only points are outside of this plane. So if we listed {L, D, A, J} then that list of points isn't coplanar.
Therefore a plane is formed by a line and one point outside of it.
Then, we need to select the last point in such a way that it lies outside of the plane generated by the first 3 points selected.
Thus, A, B, D, J
These points are all in the vertical plane shown. The plane as a flat sheet of paper that doesn't bend.
LEarn more about the concept here, please visit the link;
https://brainly.com/question/17191790
#SPJ2
find the nth maclaurin polynomial for the function. f(x) = sin(x), n = 3
P3(x) = ___
Answers
The third-degree Maclaurin polynomial for f(x) = sin(x) is P3(x) = x - (x^3) / 6.
To find the nth Maclaurin polynomial for the function f(x) = sin(x) when n = 3, we need to compute the polynomial up to the third-degree term.
The Maclaurin polynomial for a function f(x) centered at x = 0 is given by the formula:
Pn(x) = f(0) + f'(0)x + (f''(0)x^2) / 2! + (f'''(0)x^3) / 3! + ...
Let's calculate the nth Maclaurin polynomial for f(x) = sin(x) when n = 3:
First, we find the values of the function and its derivatives at x = 0:
f(0) = sin(0) = 0
f'(x) = cos(x), so f'(0) = cos(0) = 1
f''(x) = -sin(x), so f''(0) = -sin(0) = 0
f'''(x) = -cos(x), so f'''(0) = -cos(0) = -1
Using these values, we can write the Maclaurin polynomial:
P3(x) = 0 + 1x + (0x^2) / 2! + (-1x^3) / 3!
Simplifying further, we have:
P3(x) = x - (x^3) / 6.
Therefore, the third-degree Maclaurin polynomial for f(x) = sin(x) is:
P3(x) = x - (x^3) / 6.
Learn more about polynomial here
https://brainly.com/question/24662212
#SPJ11
help meee, thank you
Answers
Answer:
not clear send again
Step-by-step explanation:
A commercial jetliner hits an air pocket and drops 264 feet. After climbing 151 feet, it drops another 103 feet. What is its overall vertical change?
Answers
Answer:
If we take the drops as negatives, and the climbs as positives (the answer will be the absolute value of these) we get:
-221 +174 -156.
When you add these together, you get -203. So the overall vertical change is the absolute value of this, or 203 ft.
IM STUCC ON THIS ONE!! CAN YALL HELP!
Answers
Answer:
Step-by-step explanation:
???????????
Which expression has the greatest value? A. 2.7 x 10^4 B. 3.9 x 10^3 C. 1.4 x 10^6 D. 8.1 x 10^4
Answers
This is because it involves the largest exponent.
1.4 x 10^6 = 1,400,000 = 1.4 million
The exponent of 6 means "move the decimal point 6 spots to the right"
Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have? a. $50,000 b. $70,000 c. $90,000 d. $120,000 Please select the best answer from the choices provided A B C D.
Answers
The number of sales Bob needs to make to get $6000 salary this month's is, 70000. The option B is the correct option.
What is percentage ?
Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.
The annual salary of Bob is $30,000. As, there is total 12 months in a year. Thus, the monthly salary of Bob is,
\(S=\dfrac{30000}{12}\\S=2500\)
Thus, the monthly salary of Bob is $2500.
The commission on the sale is 5% on all sales he makes, and the Bob wants to make $6,000 this month. Thus, the number of sales he needs to make is,
\(6000=2500+\dfrac{5}{100}\times n\\0.05n=6000-2500\\n=\dfrac{3500}{0.05}\\n=70000\)
The number of sales Bob needs to make to get $6000 salary this month's is, 70000. The option B is the correct option.
Learn more about the percentage here;
https://brainly.com/question/24304697
Answer:
It's B
Step-by-step explanation:
took thhe test on edge
Find the domain of the graphed function.
Answers
Simplify the expression.
- 2.5f + 0.35 - 16 - 6
Answers
Answer:
−2.5f−21.65
Step-by-step explanation:
Simplify the expression.
-2.5f - 21.65
(Answer) −24.15
MATH HELP PLEASE DUE SOON
Answers
Answer:
a. Alternate exterior angles.
b. <A and <B are congruent. This diagram involves a line intersecting two parallel lines, forming the congruent angles <A and <B on opposite sides of the transversal.
c. They are alternate exterior angles like <A and <B, but because it is not guaranteed that the transversal is intersecting parallel lines in this case, we cannot prove that <C and <D are congruent alternate exterior angles.
Maya is saving money to buy a game. So far she has saved $6, which is two-thirds of the total cost of the game. How much does the game cost?
Answers
Answer:
9 dollars
Step-by-step explanation:
Since 6 is 2/3 of the total price, and half of 6 is 3, add three to 6 and you get 9.
Answer:
9 dollars
Step-by-step explanation:
if 6 dollors==>2/3from the game totall price
1 complete game how much
6÷2/3=9dollars
Plss Help DUE Tomorrow I will give branist Show Your Work to Verified
Answers
Answer:
x = 9
Step-by-step explanation:
Make 2 fractions, one for each triangle:
25 / 4x - 1 = 10 / x + 5
Cross multiply the denominator of one x the numerator of the other
25 (x + 5) = 10 (4x - 1)
Use the distributive property
25x + 125 = 40 x - 10
Subtract 25x from each side
125 = 15x - 10
Add 10 to each side
135 = 15x
Divide each side by 15
x = 9
6 Suppose the circumference of each circular base of a
cylinder is equal to the height of the cylinder. What does
this indicate about the curved section of the cylinder?
Answers
A cylinder's curved section has a constant diameter if the circumference of each of its circular bases equals the height of the cylinder.
We have to given that;
the circumference of each circular base of a cylinder is equal to the height of the cylinder.
Now, We get;
A cylinder's curved section has a constant diameter if the circumference of each of its circular bases equals the height of the cylinder.
Hence, As a result, the cylinder's cross section, or the form you see when you cut it perpendicular to its height, will always be round and its diameter will remain constant over the course of the cylinder's height.
Thus, A cylinder's curved section has a constant diameter if the circumference of each of its circular bases equals the height of the cylinder.
To learn more about the volume visit:
brainly.com/question/24372707
#SPJ1
select the correct answer
Answers
Answer:
-4x^2+5x-28
Step-by-step explanation:
3x^2 +5x - 7(x^2 +4)
Distribute the -7
3x^2+5x-7x^2-28
Combine like terms
-4x^2+5x-28
Oxygen is being added to a canister which originally contained 5 cubic feet of the gas at
the rate of 0.3 cubic feet per second.
Which function represents the volume, V(t), of oxygen in the cylinder after t seconds of
adding the gas?
Answers
Answer:
The change is negative, since the volume in the final state is smaller than the volume in the initial state. 2.25 We express V for the ideal gas as a function of T , p and n: V (T , p, n) = ... each smooth part of the curve and add the integrals, used up yearly by living organisms, which means that even if the oxygen supply was.
Vt = 0.3t + 5 is a function that depicts the volume, V(t), of oxygen in the cylinder after introducing the gas for t seconds.
What is Volume?
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
Given, Oxygen is being added to a canister that originally contained 5 cubic feet of the gas at the rate of 0.3 cubic feet per second.
Let V is the volume of oxygen t be the time in seconds and Vt be the changing volume at time t.
From the formula of volume of a cylinder (V) = π r²h
The initial volume of gas = 5 feet
gas added at the rate = 0.3 feet per second
Thus equation for volume = 5 + 0.3t
Vt = 0.3t + 5
therefore, a function that represents the volume, V(t), of oxygen in the cylinder after t seconds of adding the gas is Vt = 0.3t + 5.
Learn more about volume here:
https://brainly.com/question/1578538
#SPJ2
3. 5-6x = 17 - 8x what’s the answer
Answers
Answer:
x=6
Step-by-step explanation:
5-6x=17-8x 5-6x=17-8x
5-6(6)=17-8(6) or 5+2x=17 added 8x to both sides
5-36=17-48 2x=12 subtracted 5 from both sides
-31=-31 x=6 divided both sides by 2
(please mark brainliest, i need it to get to next lvl <3 )
Given f(x)=3x^2+kx-7 and the remainder when f(x) is divided by x-4 is 81, then what is the value of k
Answers
Using the remainder theorem, the value of k in f(x) = 3x^2 + kx - 7 is 10
How to solve for k?The given parameters are:
f(x) = 3x^2 + kx - 7
Divisor = x - 4
Remainder = 81
To solve for k, we use the remainder theorem
Set the divisor to 0
x -4 = 0
Add 4 to both sides of the above equation
x - 4 + 4 = 0 + 4
This gives
x = 4
Substitute x = 4 in the function f(x) = 3x^2 + kx - 7
f(4) = 3(4)^2 + k * 4 - 7
Evaluate the exponents
f(4) = 3 * 16 + k * 4 - 7
Evaluate the products
f(4) = 48 + 4k - 7
So, we have:
f(4) = 41 + 4k
The remainder is 81.
So, we have
41 + 4k = 81
Subtract 41 from both sides
4k = 40
Divide both sides of the above equation by 4
4k/4 = 40/4
Evaluate the division
k = 10
Hence, the value of k in f(x) = 3x^2 + kx - 7 is 10 using the remainder theorem
Read more about remainder at:
https://brainly.com/question/13328536
#SPJ1
Camila tiene 5 años más que un tercio de la edad de Luis. Si Luis tiene 33 años, ¿cuántos años tiene Camila?
Answers
Answer:
16
Step-by-step explanation:
33/3=11
11+5=16
espero que esto ayude:)
The equation y=2x+3 represents the cost y (in dollars) of mailing a package that weighs x pounds. a. Graph the equation. b. Using the graph, which is the best estimate for the cost to mail the package?
a. Graph the equation.
b. Using the graph, which is the best estimate for the cost to mail the package?
the packedge is 1.126 lb
c. Use the equation to find how much it costs to mail the package.
Answers
Answer:
B. Slightly more than $5
Step-by-step explanation:
y = 2x + 3
Firstly we check variables to make sure we understand.
y = dollars
x = pounds
On the scale, it says 1.126 lb. Which means 1.126 pounds.
And so, x = 1.126
y = 2x + 3
y = 2(1.126) + 3
y = 2.252 + 3
y = 2.252
The graph for part a and park b. It is underneath. I wrote 1.1, because it is rounded down from 1.126 lb, which is part b. The one with one line and no dots is part a.
Complete the statements about simplifying this expression: (xy^3/yz^2)(z^3/y^2x^2)
Answers
Hence, the variable y can be entirely eliminated using by applying the identity property of elimination
the numerator of the rational expression in the simplest form is z
the denominator of the rational expression in the simplest form is x
What is an expression?expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)
How to solve?we have,
\((\frac{xy^3}{yz^2} )(\frac{z^3}{y^2x^2} )\)
on simplifying,
we get. \(\frac{z}{x}\)
Hence, the variable y can be entirely eliminated using by applying the identity property of elimination
the numerator of the rational expression in the simplest form is z
the denominator of the rational expression in the simplest form is x
to learn more about expressions: brainly.com/question/1859113
#SPJ4