Identify each expression and value that represents the area under the curve y= x^2+4 on the interval [-3, 2].
Answers
The area is given exactly by the definite integral,
[tex]\displaystyle\int_{-3}^2(x^2+4)\,\mathrm dx=\left(\frac{x^3}3+5x\right)\bigg|_{-3}^2=\frac{95}3\approx31.67[/tex]
We can write this as a Riemann sum, i.e. the infinite sum of rectangular areas:
• Split up the integration interval into n equally-spaced subintervals, each with length (2 - (-3))/n = 5/n - - this will be the width of each rectangle. The intervals would then be
[-3, -3 + 5/n], [-3 + 5/n, -3 + 10/n], …, [-3 + 5(n - 1)/n, 2]
• Over each subinterval, take the function value at some point x * to be the height.
Then the area is given by
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\Delta x_k=\lim_{n\to\infty}\sum_{k=1}^nf(x^*)\frac5n[/tex]
Now, if we take x * to be the left endpoint of each subinterval, we have
x * = -3 + 5(k - 1)/n → f (x *) = (-3 + 5(k - 1)/n)² + 4
If we instead take x * to be the right endpoint, then
x * = -3 + 5k/n → f (x *) = (-3 + 5k/n)² + 4
So as a Riemann sum, the area is represented by
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(\left(-3+\frac{5k}n\right)^2+4\right)\frac5n[/tex]
and if you expand the summand, this is the same as
[tex]\displaystyle\lim_{n\to\infty}\sum_{k=1}^n\left(13-\frac{30k}n+\frac{25k^2}{n^2}\right)\frac5n=\lim_{n\to\infty}\sum_{k=1}^n\left(\frac{65}n-\frac{150k}{n^2}+\frac{125k^2}{n^3}\right)[/tex]
So from the given choices, the correct ones are
• row 1, column 1
• row 2, column 2
• row 4, column 2
Answer:
Step-by-step explanation:
Related Questions
The following table shows the values of y for different values of x:
x y
0 0
1 0
2 4
Which statement best explains whether the table represents a linear function or a non-linear function?
It represents a linear function because its points are on a straight line.
It represents a linear function because its points are not on a straight line.
It represents a nonlinear function because its points are on a straight line.
It represents a nonlinear function because its points are not on a straight line.
Answers
Answer:
I believe it is D
Step-by-step explanation:
Not 100% dont trust double check
A yard contains 16 ounces. 9 ounces is what fraction of a pound?
Answers
9514 1404 393
Answer:
9/16
Step-by-step explanation:
We presume an error in the problem statement. A yard is a measure of distance, not weight.
A pound contains 16 ounces. Then 9 ounces is 9/16 of a pound.
__
As a decimal fraction, that is 0.5625 lb.
What is the value of the positive zero of the function defined by x2 + x - 30?
Answers
Answer:
5
Step-by-step explanation:
(x+6)(x-5)
x = 5
x = -6
3.2 x 1.4 =
help help help pls
Answers
Answer:
4.48
Step-by-step explanation:
Answer:
4.48
Step-by-step explanation:
Determine any data values that are missing from the table, assuming that the data represent a linear function.
x y
1 2
2 4
3
a. 7
b. 6
c. 2
d. 8
Answers
it multiplies by two
What is the value of y in the equation 2(4y - 1) = 6?
A: 0
B: 1
C: 6
D: 8
Answers
Answer:
Step-by-step explanation:
Fist we multiply the values:
2*4y-2*1=6
8y-2=6
8y=6+2
8y=8
y=8:8
y=1
2*4(1) - 2*1 = 6
Answer = 1
I need help ASAP 30 points
Answers
Volume = length x width x height
Volume = 1.4 x 1.3 x 3.5 = 6.37 cubic cm
What is the area of the composite figure?
Answers
Answer:
132ft squared
Step-by-step explanation:
Divide the figure into one rectangle and on triangle. Area of rectangle: 8x12=96
Area of triangle: 9x8/2=36
Add: 96+36=132
IT IS TIMED!!!!!
please help!!!!!!!
Answers
Answer:
b
Step-by-step explanation:
What is the distance between J and K
Answers
Answer:
9 i think
Step-by-step explanation:
i don really know
Target sells 12 bottles of water for 2$ and sells 24 bottles for 3$, what is the better price?
Answers
Answer:
The 24 bottles for 3$
Step-by-step explanation:
12 bottles for 2$ x 2
= 24 bottles for 4$
This means the 24 bottles for 3$ is the better price per bottle.
Suppose a white dwarf star has a radius of approximately 9.0415 x 10 km. Use the formula 4 to find the approximate surface area of the star.
Please show work and not just a rando scam link ._.
Answers
Answer:
I like doods
Step-by-step explanation:
Pp + pp
Find the missing angle measure in each triangle 29, 88, x || Hurry :)
Answers
Answer:
63
Step-by-step explanation
180-29-88=63
The numerator that makes the equation true
Answers
A rectangular auditorium seats 2142 people. The number of seats in each row exceeds the number of rows by 9. Find the number of seats in each row.
Answers
9514 1404 393
Answer:
51
Step-by-step explanation:
Let s represent the number of seats in a row. Then the number of rows is (s-9) and the total number of seats is ...
s(s-9) = 2142
s² -9s +4.5² = 2142 +4.5² . . . . . complete the square
(s -4.5) = √2162.25 . . . . . . . . take the positive square root
s = 4.5 +46.5 = 51 . . . . . . . add 4.5
The number of seats in each row is 51.
evaluate the piecewise function for h=0. PLEASE HURRY!!! I WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!!
Answers
t = 0 belongs to the interval [-3, 3] (since -3 ≤ 0 ≤ 3 is true), so use the middle function to evaluate h (0):
h (0) = 0 × (0 + 4) = 0
Scott paid 10.47 for a 6.08 - kg bag of dog food. A few weeks later, he paid 13.88 for a7.48 -kg bag at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent.
Answers
Answer:
Scott paid $ 1.72 per kilo for the first bag, and $ 1.85 per kilo for the second bag, with which the best buy is the first bag.
Step-by-step explanation:
Since Scott paid 10.47 for a 6.08-kg bag of dog food, while a few weeks later, he paid 13.88 for a7.48-kg bag at a different store, to find the unit price for each bag, and then state which bag is the better buy based on the unit price, the following calculation must be performed:
10.47 / 6.08 = X
1.72 = X
13.88 / 7.48 = X
1.85 = X
Thus, Scott paid $ 1.72 per kilo for the first bag, and $ 1.85 per kilo for the second bag, with which the best buy is the first bag.
Convert 210° to radian measure in terms of pi
Answers
Answer:
[tex]210^\circ = \frac{7}{6}\pi[/tex]
Step-by-step explanation:
Given
[tex]\theta = 210^\circ[/tex]
Required
Convert to radians
To convert to radians, we make use of:
[tex]Radians = \theta * \frac{\pi}{180^\circ}[/tex]
Substitute: [tex]\theta = 210^\circ[/tex]
[tex]Radians = 210^\circ* \frac{\pi}{180^\circ}[/tex]
[tex]Radians = \frac{210^\circ* \pi}{180^\circ}[/tex]
Simplify fraction
[tex]Radians = \frac{7\pi}{6}[/tex]
[tex]Radians = \frac{7}{6}\pi[/tex]
Hence:
[tex]210^\circ = \frac{7}{6}\pi[/tex]
Help extra points and mark brainlist
Answers
Answer:
Median is 7
Step-by-step explanation:
Give me brainllest
Mr. Smith is conducting a class raffle. Every 100% on an assignment is an entry into the raffle. Liam has 10 entries, Noah has 3 entries, Oliver has 11 entries, and there are 44 other total entries. What is the probability that Liam will win the raffle? Round your answer to the thousandths place.
Answers
Answer: 0.147
Step-by-step explanation:
Liam / total
total = 10 + 3 + 11 + 44 = 68
10 / 68 = 5 / 34
0.1470588 = 0.147
Find the missing term in each sequence
Answers
Answer:
The answer would be 58.32.
Step-by-step explanation:
Good luck ^___^ .
b)Given 0º < x < 360° , solve for x in:
2 sin (2x - 30°) = √3.
Answers
Answer:
180°
because x is the mid pf 0° and 360°
What is the measured of bacteria at t=0?
Answers
Answer:
Number of bacteria when t = 0 is 2,000
Step-by-step explanation:
Given:
Number of bacteria in a culture by equation
Q(t) = 2(729^t)
Value of t = 0
where t is number of hours
Find:
Number of bacteria when t = 0
Computation:
Given equation
Q(t) = 2(729^t)
Put t = 0
Q(0) = 2(729⁰)
We know that;
a⁰ = 1
So,
Q(0) = 2(729⁰)
Q(0) = 2(1)
Q(0) = 2
Number of bacteria when t = 0 is 2,000
Select the values that are solutions of the inequality X 3<4.
X=4
X=8
X= 12
X= 16
X= 20
X= 24
Answers
Answer:
x=12 if you divide you'll get 4
Uri’s family has an old shower head. It releases about 5 gallons of water per minute. If Uri takes a 5-minute shower, how much water will she use? Help!
Answers
Answer:
25 gallons
Step-by-step explanation:
5 gallons per minute, 5 minutes, 5, 10, 15, 20, 25. multiple 5 by 5
Answer:
The answer is 25 gallons of water
Step-by-step explanation:
I just took the test and seriously it is correct!
Given sec A = 5/3 and that angle A is in Quadrant I, find the exact value of csc A in simplest radical form using a rational denominator.
Answers
9514 1404 393
Answer:
5/4
Step-by-step explanation:
The relationship between the sec and csc functions is ...
csc(A) = sec(A)/√(sec²(A) -1)
For the given value of sec(A), this is ...
csc(A) = (5/3)/√((5/3)² -1) = (5/3)/√(16/9) = (5/3)/(4/3)
csc(A) = 5/4
__
Some calculators can tell you the answer directly.
PLEASE HELP .........!!!!!!!!!!!!!!!!!!!!!!!!’!!!!
Answers
It goes in the order 3,1,2,4
View the work below from a student last year. What was their mistake? Be detailed in their response.
-3(x + 4) = 2x - 5
-3x + 4 = 2x - 5
4 = 5x - 5
9 = 5x
1.8 = x
Answers
-3(x+4)=2x-5
-3x+12=2x-5
-5x=7
x=-7/5 or x=-1 2/5 or x=-1.4
Jimmy believes that the shuffle feature on his music player is malfunctioning by not playing songs that meet this distribution of music types. To test this, he listens to 100 songs randomly chosen when his player is in shuffle mode and records the number of songs in each category. Which inference procedure should he use to test whether or not the shuffle feature is working correctly
Answers
Answer:
A chi-square goodness-of-fit test
Step-by-step explanation:
GOF test is used to determine if the data meets the expected values.
A chi-square goodness-of-fit test procedure should be used to test whether or not the shuffle feature is working correctly.
What is a distribution?
A distribution includes an algebraic function that calculates the likelihood that long-been-considered outcomes will occur. In the perspective of its population space as well as event probability, it is a schematic representation of random phenomena.
To ascertain regardless of whether the observed sample frequency deviates noticeably from those given in the null hypothesis, should use the chi-square goodness of fit test.
He notes the number of tracks in each classification after listening to 100 songs selected at random while his player is in shuffle mode. One can determine out whether the quality of fit is "good enough" and draw the conclusion that the population matches the distribution by applying the chi-square goodness of fit test.
Learn more about distribution, Here:
https://brainly.com/question/29062095
#SPJ5
Ellen jogs 2.45 miles each day. In the month
of July she jogged 26 days. How far did Ellen
jog in the month of July?
Answers
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer: 63.7 miles
Explanation:
2.45 x 26
I hope this helped!
<!> Brainliest is appreciated! <!>
- Zack Slocum
*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆
Answer:
Ellen jogged for 26 days in month of July is total of 63.7 miles
Step-by-step explanation:
Braniliest please